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©2015 The Zurich Services Corporation

Water supply testing and analysis

Zurich Services Corporation Risk Engineering 2015 Fourth edition

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Table of Contents Introduction ................................................................................................. 5 Water supply sources ................................................................................ 5 Types of water supplies ............................................................................. 6

Gravity supplies ........................................................................................ 6 Pumping supplies ..................................................................................... 6 Combination supplies ............................................................................... 6

Water flow test devices .............................................................................10 Fire pumps taking suction from a static source ........................................10 Fire pump supplied from a town main ......................................................10 Elevated tanks and reservoirs..................................................................12

Test equipment ..........................................................................................12 Testing ........................................................................................................12 Test flow rate..............................................................................................12 Fire hydrant flow tests ..............................................................................13

Special notes for town main systems .......................................................13 Fire hydrant test points ............................................................................13 Dead-end water mains .............................................................................14 Circulating water mains ...........................................................................15 Fire hydrant types ....................................................................................16 Test nozzles.............................................................................................18 Safety during fire hydrant flow tests .........................................................21 Pitot readings ...........................................................................................25 Pressure hydrant readings .......................................................................27

Graphing series and parallel water supplies ...........................................29 Series water supply .................................................................................29 Parallel water supplies .............................................................................29 Graphing series water supply ..................................................................30 Graphing parallel water supplies ..............................................................30

Graphing parallel water supplies – further discussion ..........................31 Graphing water tests .................................................................................33

Zurich semi-log n1.85 graph paper ..........................................................33 Linear graph paper ..................................................................................34 Graphing terminology ..............................................................................34

Fire pump tests ..........................................................................................38 Test header..............................................................................................38 Safety during fire pump tests – flowing water ..........................................39 Safety during fire pump tests – fire pump hazards ...................................43 Pressure readings ....................................................................................43 Fire pump test objectives .........................................................................46

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Plotting data before disassembling test equipment ..................................46 Speed readings ........................................................................................47 Interpreting abnormal fire pump curves ...................................................48

Hydraulic fundamentals ............................................................................53 Pressure ..................................................................................................53 Flow from an orifice .................................................................................55

Calculating orifice flow .............................................................................57 Friction loss ...............................................................................................59

Friction loss calculations ..........................................................................60 Friction loss due to fittings .......................................................................61 Friction loss calculation procedure ...........................................................66

Hydraulic calculation procedure ..............................................................67 Pressure regulating valves (PRV's)..........................................................67

PRV's and hydraulic calculations .............................................................67 Types of PRV's ........................................................................................69 NFPA 13 and PRV's ................................................................................69 Non-listed PRV's ......................................................................................69 Redundant PRV's ....................................................................................70 Providing small PRV's with larger PRV's .................................................70

Loop tests ..................................................................................................70 Hydraulic gradient .....................................................................................71 Sprinkler calculation - Example..............................................................208 References ...............................................................................................217

List of tables Table 1. Water supply test frequencies ..................................................12 Table 2. Number of hose valves for fire pump testing ..........................39 Table 3. Fire pump test points ................................................................46 Table 4. Coefficient "c" of common orifices ..........................................58 Table 5. Hazen-Williams C values ...........................................................60 Table 6. Hazen-Williams C values unlined cast or ductile iron pipe ....61 Table 7. Equivalent length in meters (feet) of common fittings based

upon schedule 40 (EN 10255 Heavy series) pipe ....................63 Table 8. Equivalent length adjustment factors – ASTM schedule 40 to

other pipe types .........................................................................64 Table 9. Equivalent length in meters (feet) of fittings for CPVC pipe ..65 Table 10. Converting Hazen-Williams C=100 to other C-factors ............67 Table 11. Inside diameter of pipe .............................................................76 Table 12. Discharge from circular orifices (lpm) .....................................77 Table 13. Discharge from circular orifices - US ......................................78 Table 14. Friction loss - bar per lineal meter of pipe ..............................81 Table 15. Friction loss - psi per lineal foot of pipe................................126

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Introduction

Manual firefighting facilities and water-based fire extinguishing systems depend upon the presence of an adequate water supply to be effective. To be considered adequate, a water supply must possess sufficient flow, pressure, and capacity to meet the greatest fire protection demand for the anticipated duration. Water supply testing provides the data needed to evaluate water supply adequacy. This booklet provides guidance on the testing of water supplies and the analysis of water supply adequacy. Hydraulic tables are provided to support the analysis of water supply test data. Water supply sources

Water supplies may be provided by town or private water systems. Town systems may deliver water by gravity using elevated tanks or reservoirs, by pump, or by a combination of both. Private supplies may include:

• Elevated tanks or reservoirs • Fire pumps taking suction from static sources of water such

as cisterns, ground tanks, reservoirs, ponds, or rivers • Fire pumps taking suction from pressurized sources of

water such as town mains, elevated tanks, or elevated reservoirs

• Pressurized tanks

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Types of water supplies

Gravity supplies

Gravity supplies include gravity tanks (tanks elevated on legs) as well as tanks or reservoirs elevated on high ground. These supplies can feed either a town or private system. Pumping supplies

Pumping supplies consist of one or more pumps taking suction from:

• A gravity source (gravity tank, elevated reservoir) • A static source (reservoir, cistern, ground tank) • Another pump

Combination supplies

Combined supplies will consist of gravity and pumping supplies feeding into a common system. The following photos and images provide examples of gravity and pumping supplies.

Gravity tank Elevated tank

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Gravity source - Elevated reservoir

Static source – Cistern feeding a vertical turbine pump

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Static source – open reservoir feeding a vertical turbine pump

Static source – indoor water storage tank feeding a fire pump

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Static source – outdoor ground water tank feeding fire pump

Gravity source – town main feeding booster fire pump

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Water flow test devices

Each water supply should include a means to conduct a flow test. Fire pumps taking suction from a static source

The ideal test device is a flowmeter discharging back to the water source. Where the test device discharges water to the ground, water will be wasted requiring tank refill once testing is complete. Fire pump supplied from a town main

The test device may be either a flowmeter or a test header discharging water to the ground. Where there is a desire to avoid wasting water, a flowmeter may be piped back to fire pump suction; however, tests performed with this arrangement:

• Will not test the fire pump water supply as water will only be recirculated

• Will not produce valid suction and discharge gauge readings • Will produce valid fire pump net pressure readings

(discharge pressure – suction pressure) Where a flowmeter is piped back to fire pump suction to conserve water, at least one test every three years should be conducted using a test header or flowmeter discharging water to the ground. This is necessary to verify the fire pump water supply and obtain an actual fire pump discharge curve. The following photos are of various types of devices used for flow testing.

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Flowmeters

Test header

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Elevated tanks and reservoirs

Fire hydrants or other similar outlets will typically be used for testing elevated tanks or reservoirs. Test equipment

Test equipment should be calibrated and in good condition. Where a flow meter is used, its performance should be periodically verified by calibration or comparison to an actual flow test using a pitot tube and calibrated test gauge. Testing

The following table provides an outline of water supply features and recommended test frequencies.

Table 1. Water supply test frequencies Table 1. Water supply test frequencies

Feature Test Frequency Fire pump Automatic start Weekly Fire pump Capacity test Annual Private fire hydrant Flow test Annual Private elevated supply Flow test Annual Private fire main loop Loop test 2 years Public hydrant Flow test 5 years

Test the automatic start of all fire pumps on a weekly basis. Allow electric motor driven fire pumps to operate for at least 10 minutes to dissipate heat form the motor-start inrush current. Allow diesel engine driven fire pumps to operate for at least 30 minutes to bring the engine up to operating temperature, drive moisture from the crankcase, lubricate internal engine surfaces, and reduce the potential for internal corrosion.

Test flow rate

Water tests should be conducted at a flow rate that equals or exceeds the greatest fire protection demand flow rate. The test should actually verify the physical availability of the needed flow rate.

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Flow tests should not be extrapolated beyond the range of the test conducted. Fire hydrant flow tests

Fire hydrant flow tests are useful when water test data is needed remote from a water source. The fire hydrant flow tests can be used on a town main system or a private fire main system. Special notes for town main systems

Where the test involves the use of fire hydrants or the operation of valves on a town main system, it is essential to have the agency responsible for the town main system to authorize and perform the test. Should our customer fail to gain permission, fines may be leveed for unauthorized use of the town water system. A test of a town system should be pursued for locations depending upon the town mains to provide the water supply for either automatic or manual fire protection systems. The water supply available from a town main system can be significantly reduced or impaired by pipe corrosion, pipe obstructions, or shut valves. Periodic water flow tests verify the availability of the town water supply over time. Fire hydrant test points

Fire hydrant tests will often involve the use of two fire hydrants. One hydrant will be used to flow water, and a second hydrant will be used as a pressure or gauge point. The flow and pressure hydrants should be selected so that the "effective point of test" is at the most beneficial location. Pressure gauges can also be mounted on backflow prevention assembly ports, pressure reducing valve ports, sprinkler riser gauge lines, domestic hose outlets, and other available points as long as there will be no closed valves (including check valves, backflow prevention check valves, and pressure reducing valves) between the

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pressure gauge and the water supply being tested. The pressure gauge must not be isolated. The effective point of test is point where the "flow path" and "pressure path" intersect. Figure 1 provides a legend for the symbols that will be used to illustrate flow testing guidelines. Dead-end water mains

Figure 2 shows a water main extending past the hydrant at point A and ending at the hydrant at point B. The hydrant at point A is the flow hydrant and hydrant at point B is the pressure hydrant. The effective point of test is at point A. As this test arrangement will flow no water through the water main between points A and B, the test should ideally be limited to water supply assessments upstream of point A.

Figure 1

Figure 2

A B

Flow

A B

Flow hydrant Pressure hydrant Flow points Flow direction

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Where the water test results are to be applied downstream of point A, the hydrant at point B should be the flow hydrant as shown in figure 3. While the effective point of test will not change, the test will confirm the ability of the pipe between points A and B to flow water at the tested rate.

Figure 3

Circulating water mains

Figure 4 shows a system of circulating water mains where a smaller water main intersects a larger water main. Determine where the results of the water test will be applied, and then select the flowing hydrant closest to that point. In this case, the water test will be applied to a fire system water connection to the smaller water main to the right side of the water main intersection. The hydrant at point B should be selected as the flow hydrant. Any adjacent hydrant such as the hydrant at point A can be used as the pressure hydrant. The location of the effective point will be somewhere between points A and B. Using the intersection of the two water mains as the effective point is a conservative approach. When the water test is applied, friction loss along the entire section of smaller water main from the intersection to the fire system connection will be deducted from the available water test pressure.

A B

Flow

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Figure 4

Fire hydrant types

Fire hydrants can have a variety of outlet configurations and sizes.

US fire hydrants often extend above ground (pillar hydrants) and may be wet barrel (below left) in non-freezing areas or dry barrel (below center and right) in freezing areas. Outlets will include one or more 2½ inch (64 mm) outlets and perhaps a large diameter outlet for fire service vehicle use.

A

B

Smaller water main

Larger water main

US hydrant examples

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UK fire hydrants are located below ground. The hydrant outlet and valve are accessed by lifting distinctive metal cover plates marked “FH”. Below the cover plates, there is a water outlet and a valve operating nut. A standpipe is attached to the water outlet, and fire hoses will then be attached to the standpipe. A handle will be applied to operate the valve. Yellow signs are posted near each fire hydrant. Two numbers are included on the sign. The upper number is the size of the water main supplying the hydrant in millimeters, and the lower number is the distance in meters to the fire hydrant.

The following are additional example of fire hydrants.

Zurich, Switzerland (above left) and Venice, Italy (above right)

Cover plates Cover plates removed Sign UK hydrant

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Test nozzles

For greatest accuracy, conduct a hydrant flow using test equipment listed by a Zurich recognized testing laboratory such as the UL listed Pitotless Nozzle™ and Hose Monster®.

The 2" Pitotless NozzleTM Photo source: Hydro Flow Products

Hose Monster® that uses the Pitotless NozzleTM insert

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Hose Monster® in use for hydrant test Artwork source: Hydro Flow Products

UL listed equipment such as the Pitotless Nozzle™ and the Hose Monster® do not require the use of a hand-held pitot tube. This eliminates the challenges of centering a hand-held pitot tube or manually controlling pitot tube bounce (which will be discussed later).

A hydrant flow can also be conducted using a nozzle. For Zurich in the US, common nozzles include the Underwriters Playpipe and New England nozzle. The nozzle will attached to one of the 2½ inch (64 mm) pillar hydrant outlet.

Underwriters Playpipe nozzle New England nozzle

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The typical Underwriters Playpipe is a 30" (762 mm) long, tapered, smooth bore nozzle that has a 2½" (64 mm) diameter national standard thread base that can be attached to a fire hydrant outlet. The playpipe has a 11/8" (29 mm) diameter tip, which can be removed exposing a 1¾" (44 mm) diameter tip. New England Manufacturing Company produces a straight smooth bore hydrant flow nozzle that has a 2½" (64 mm) diameter national standard thread base that can be attached to a US fire hydrant outlet. As this nozzle does not have a handle, it is not suited for use with fire hoses. The New England nozzle has a 2¼" (57 mm) diameter tip. Flow tests with nozzles are typically conducted using a hand-held pitot tube. As noted above, a hand-held pitot tube will introduce a degree of test error as the user must carefully center the pitot tube in the water stream and simultaneously control pitot tube bounce. While a hand-held pitot tube will introduce a degree of error to the test results, the overall accuracy of the test will be adequate for property insurance purposes. It is also possible to conduct a hydrant test by flowing an open hydrant outlet without a nozzle attached. This test approach is the least accurate approach. To maintain as much accuracy as possible, flow the smallest hydrant outlet.

Tapered nozzle Straight nozzle Large hydrant outlet

Examples of nozzle discharge stream quality

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Safety during fire hydrant flow tests

When conducting a flow test, it is important to consider safety to both people and property. Consider exposures such as:

• Ruptured hose lines • Failed hose couplings • Nozzle reaction forces • The force of discharging water • Disposal of test water • Water reaching electrical equipment

When hose lines are used, their condition should be evaluated by the party conducting the test. Worn hose and damaged hose couplings could fail during a test causing injury or property damage. Underwriters Playpipe nozzles and New England nozzles will produce significant nozzle reactions in the direction opposite the water flow. Personnel should never attempt to hold a flowing smooth bore nozzle. Such attempts have led to many injuries. New England nozzles should not be used with hose as they do not include handles that allow the nozzle to be secured. When possible, nozzles should be attached directly to a hydrant outlet or a fire pump test header. When nozzles are attached to hoses, they must be secured to stay in place when flowing. For example, contractors may provide nozzle racks secured to their service vehicle. When Underwriters Playpipes are used with hose, place the secured nozzles in operation before approaching the nozzle to take pitot readings. Keep in mind that secured nozzles can come lose or shift. In each case, personal injury or property damage could result. Understand that there are no test standards to guide the design of Underwriters Playpipe nozzle racks.

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Nozzle rack secured by vehicle

Hose Monsters® are an example of a test nozzle that incorporates a T-shaped body designed to eliminate the nozzle reaction. The T-shaped body divides and discharges the flow in two opposing directions. By eliminating the nozzle reaction, Hose Monsters® do not require securement during use.

Hose Monster®

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The Pitotless NozzleTM used with the Hose Monster®

Stack of three Hose Monster® in use for a fire pump test

Artwork source: Hydro Flow Products

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Hose Monster® stack with The Pitotless NozzleTM inserts, tubing for remote flow readings, and connected fire hose

Before flowing water, evaluate where the discharging water will travel. For nozzles, consider the direction and range of the discharging water stream. A strong stream of water can injure people, damage paved surfaces, and dig up landscaping. Consider that water systems can contain rocks or other debris that may discharge with the water. Never allow people or vehicles to travel through a discharging stream of water as debris could cause injury or property damage. For any flow test, recognize that water runoff can overwhelm drains, accumulate to unexpected depths, and potentially enter buildings. This can lead to property damage. If the water can also reach electrical equipment, unexpected electrocution hazards can suddenly develop. Do not begin flowing water if there is any question as to where the water will go.

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Pitot readings

Before beginning a water flow test with a nozzle or hydrant outlet, measure the inside diameter of the outlet to be flowed.

For nozzles and hydrant outlets, flow will be measured using a pitot tube and calibrated gauge. The gauge should have a range suited to the anticipated velocity pressure to be measured. Typically, a gauge with a 100 psi range should be suitable, and for accuracy, it is best to limit pitot reading to a range between 10 psi and 60 psi.

Pitot tube and pressure gauge

Measuring a 2½" outlet

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The pitot tube is used to measure the velocity pressure of the water stream flowing from the outlet.

Pitot tube positioned in front of nozzle orifice

The pitot orifice should be positioned in the center of the water stream. Ideally, the pitot tip should be located one half of the outlet diameter out in front of the nozzle tip. Nozzles with attached pitot tubes achieve this placement by design. With handheld pitot tubes, it may be necessary to rest the pitot against the nozzle tip. In either case, the pitot orifice should be carefully aligned with the direction of flow.

Nozzle with attached pitot tube in ideal position

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Handheld pitot in ideal position

Handheld pitot resting on nozzle tip for control

The pitot gauge will register the velocity pressure of the discharging water stream. The velocity pressure and orifice diameter will be used with Table 12. Discharge from circular orifices (lpm) or Table 13. Discharge from circular orifices (gpm) to determine the discharge flow rate. Where test devices such as the Pitotless Nozzle™ or Hose Monster® are used, the hand-held pitot tube is eliminated in favor of a fixed orifice or a fixed pitot. This also eliminates test error associated with the manually positioned, hand-held pitot. Pressure hydrant readings

Static and residual pressure readings will be measured with a calibrated test gauge mounted on an outlet at the pressure hydrant. Typically, a gauge cap will be mounted on one of the smaller hydrant

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outlets. The gauge cap will be fitted with a threaded "tee". One side of the "tee" outlet will be equipped with a bleed valve, and the remaining outlet will be equipped with the test gauge.

Gauge cap with "tee" and test gauge

The bleed valve is an important feature when using a dry-barrel hydrant. Open the bleed valve when the hydrant is turned on to allow air to vent as the hydrant barrel fills with water. Reopen the bleed valve as the hydrant is turned off to protect the gauge from vacuum as the hydrant barrel drains.

Pressure gauge assembly with bleed valve open

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Graphing series and parallel water supplies

Series water supply

A series water supply involves the movement of water from a source through a pump to increase pressure. The series water supply provides just one single water supply. The pump does not add any water volume; it just adds pressure.

Any fire pump will form a series water supply. A fire pump supplied from a town main will boost the incoming town system water pressure. A fire pump supplied from a tank will boost the incoming pressure created by the static head of water in the tank.

Series water supply examples - Ground water tank and fire pump (left), and town water main and fire pump (right)

Parallel water supplies

Parallel water supplies involves two separate water supplies feeding into a system. Parallel water supplies each feed water into a system at the pressure available from that supply.

Gravity tank feeding a private water system in parallel with a fire

pump and ground water tank

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Graphing series water supply

When graphing the total water supply available from a series water supply, add the contributed pressures at any given flow.

Graphing series water supplies (e.g. a town water supply feeding a fire pump)

Graphing parallel water supplies

When graphing the total water supply available from parallel sources, add the contributed flows at any given pressure.

Graphing parallel supplies (e.g. a gravity tank and a fire pump

supplied from a ground water tank)

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Graphing parallel water supplies – further discussion

When graphing a fire hydrant flow test, it is important to identify how many water supplies are contributing to the test. Where there is only one supply, the graph will be a smooth line or curve. Where there are two or more supplies, the graph will have discontinuities.

The following image depicts a town water system supplied by a gravity tank in addition to a pump and tank. The graph below the image shows the resulting water supply curve.

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The following photo shows a town booster pump station with multiple pumps (there are four pumps in all). Each pump starts at a progressively lower water pressure in response to an increasing demand for water by users. The graph below the photo shows the resulting water supply curve.

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Graphing water tests

Zurich semi-log n1.85 graph paper

Zurich n1.85 semi-log graph paper (see image below) can be used with metric (L/min vs. bar) or US (gpm vs. psi) measure. When using this semi-log graph paper, testing of gravity water sources can be limited to the following three data elements:

• Static test point • Flowing test point • Test date and time

The semi-log n1.85 graph paper allows gravity water supplies to plot as a straight line eliminating the need for multiple flow test points.

Zurich n1.85 semi-log graph paper

In the US, town water supplies are often plotted as gravity supplies; however, it is important to recognize that many town systems are pumping or combined systems and will not plot as straight lines.

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Linear graph paper

Any water test can be graphed on linear graph paper as shown in the image below.

Linear graph paper

With linear graph paper, gravity supplies (as well as pumping supplies) graph as curves. To plot a gravity supply, multiple test points are needed to form the resulting water test curve.

Example of gravity supply plotted in linear graph paper

Graphing terminology

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The static test point is the system pressure with the flow hydrant is turned off. For a town main system, this is also referred to as the "normal system residual pressure". A town system is rarely static. It is always flowing water to meet domestic water demands somewhere in the system.

The flowing test point consists of a measured flow rate from the flow hydrant along with a simultaneous residual pressure reading at the pressure hydrant.

For a system with non-fire demands (e.g. a town system), the date and time of test should be selected during a period of high non-fire demand. During these periods, the normal system flow will be high while the residual pressure may be at one of its lowest values. Fires can occur at any time, including these periods of high non-fire demand.

The static and flowing test points will be plotted on graph paper to display a graphical depiction of the available water supply.

Graph 1 depicts a gravity water supply with a static test point (pressure at zero flow) and a flow test point (residual pressure at flow). The water supply curve exceeds the fire system demand.

Graph 1. Water system with single gravity supply

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Graph 2 depicts the water supply for a water system with two gravity water sources. Under normal conditions, the high pressure reservoir supplies the system demands. When the system pressure falls below 47 psi, the low pressure reservoir check valve opens allowing additional water to flow into the system. A test of the high pressure system alone would produce the following results:

• Static = 120 psi; Flow = 600 gpm; Residual = 30 psi A test of the low pressure system alone would produce the following results:

• Static = 50 psi; Flow = 1,200 gpm; Residual = 30 psi With both systems in normal service, it is important not to take a static reading from the high pressure reservoir as the static test point and a combine flow as the flowing test point. Doing so produces the erroneous water supply curve shown with the dashed line. The erroneous water supply curve would represent an adequate water supply. Instead, by understanding the arrangement of the water system, a water test can be devised to capture the following test points:

• High pressure reservoir static pressure • Flow point above low pressure reservoir static pressure • Flow point below low pressure reservoir static pressure • Second flow point below low pressure reservoir static

pressure While this is a more complex water test, it clearly identifies the inadequate water supply.

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Graph 2. Water system with two gravity water sources

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Fire pump tests

Fire pump tests will involve:

• Device to flow water (flowmeter or test header) • Test gauges mounted on the suction and discharge sides of

the fire pump • Tachometer to take pump speed readings

Fire pump

Test header

NFPA 20 "Standard for the Installation of Stationary Pumps for Fire Protection" established the number of 2½ inch (64 mm) hose valves needed based upon the rated flow of the fire pump. In general, one 2½ inch (64 mm) hose valve is needed for each 250 gpm (950 lpm) of rated pump capacity. Table 2 provides the specific requirements of NFPA 20.

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Table 2. Number of hose valves for fire pump testing Table 2. Number of hose valves for fire pump testing

Pump rating (gpm)

Pump rating (lpm) Number of 2½" hose valves

300 1,136 1 400 to 500 1,514 to 1,892 2 750 2,839 3 1,250 4,732 4 1,500 to 2,000 5,678 to 7,570 6 2,500 9,464 8 3,000 to 3,500 11,356 to 13,249 12 4,000 to 4,500 15,142 to 17,034 16 5,000 18,927 20

Safety during fire pump tests – flowing water

Remember, as stated earlier, when flowing water it is important to consider safety to both people and property. Consider:

• Ruptured hose lines • Failed hose couplings • Nozzle reaction forces • The force of discharging water • Disposal of test water • Water reaching electrical equipment

When hose lines are used, their condition should be evaluated by the party conducting the test. Worn hose and damaged hose couplings could fail during a test causing injury or property damage. Underwriters Playpipe nozzles and New England nozzles will produce significant nozzle reactions in the direction opposite the water flow. Personnel should never attempt to hold a flowing smooth bore nozzle. Such attempts have led to many injuries. New England nozzles should not be used with hose as they do not include handles that allow the nozzle to be secured.

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When possible, nozzles should be attached directly to a fire pump test header. When nozzles are attached to hoses, they must be secured to stay in place when flowing. For example, contractors may provide nozzle racks secured to their service vehicle.

When Underwriters Playpipes are used with hose, place the secured nozzles in operation before approaching the nozzle to take pitot readings. Keep in mind that secured nozzles can come lose or shift. In each case, personal injury or property damage can result. Understand that there are no UL test standards to guide the design of Underwriters Playpipe nozzle racks.

Nozzle rack secured by vehicle

Hose Monsters® are test nozzles that incorporate a T-shaped body designed to eliminate the nozzle reaction. The T-shaped body divides and discharges the flow in two opposing directions. By eliminating the nozzle reaction, Hose Monsters® do not require securement during use.

Hose Monster®

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The Pitotless NozzleTM used with the Hose Monster®

Stack of three Hose Monster® in use for a fire pump test

Artwork source: Hydro Flow Products

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Hose Monster® stack with The Pitotless NozzleTM inserts, tubing for remote flow readings, and connected fire hose

Before flowing water, evaluate where the discharging water will travel. For nozzles, consider the direction and range of the discharging water stream. A strong stream of water can injure people, damage paved surfaces, and dig up landscaping. Consider that water systems can contain rocks or other debris that may discharge with the water. Never allow people or vehicles travel through a discharging stream of water where debris could cause injury or property damage. For any flow test, recognize that water runoff can overwhelm drains, accumulate to unexpected depths, and potentially enter buildings. This can lead to property damage. If the water can also reach electrical equipment, unexpected electrocution hazards can suddenly develop. Do not begin flowing water if there is any question as to where the water will go.

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Safety during fire pump tests – fire pump hazards

As the fire pump and driver will be in operation during flow tests, exercise appropriate safety precautions to avoid hazards associated with this machinery. This includes:

• Never placing any portions of your body over the machinery • Keeping hands away from the drive shaft, impeller shaft, and

coupling and any other moving parts • Avoiding loose fitting clothing, neck ties, jewelry or other

apparel that could get caught in the machinery • Using appropriate personal protective equipment including

hearing protection and eye protection • Managing arc flash hazards. When conducting tests of

electric motor driven fire pumps where the controller door will be open to allow volt and amp readings, NFPA 70E Article 130.3 specifies that an arc flash hazard analysis shall be completed to identify the arc flash protection boundary and the level of personal protective equipment needed within the arc flash hazard boundary. Unqualified personnel and personnel without the appropriate level of personal protective equipment should not be permitted within the arc flash protection boundary

Pressure readings

During a fire pump test, pressure readings will be taken at both the inlet or suction side of the pump and the outlet or discharge side of the pump. The suction gauge displays the available pressure provided by the upstream water supply, the discharge gauge displays the pressure available to the downstream fire system, and the difference between the discharge and suction gauges, the net pressure, is the actual pressure developed by the fire pump. The fire pump discharge pressure is important, as it will be compared to the fire system demands being served by the fire pump. For the fire pump to be considered adequate, it must meet or exceed each sprinkler demands plus the associate hose allowance. Where hose stream can only be supplied from a point before the fire pump, the hose allowance can be deducted from the suction curve and then

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the net performance added to the adjusted suction curve. Where hose streams are supplied from a separate water source, the hose allowance is not included. The fire pump net pressure is important as it will be compared to the original fire pump bench test curve or fire pump nameplate performance data. The fire pump is to be maintained in good condition throughout its service life. This includes replacing internal wear rings when the net performance of the fire pump deteriorates to a point where meeting the fire system demands becomes a concern.

Example of a fire pump bench test curve

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LPCB approved fire pump nameplate (UK) Provides one benchmark test points as follows:

• Rated flow, pressure, and speed

UL listed fire pump nameplate (US) Provides three bench test points as follows: • Pressure at zero flow (S.O.H. or shut off head) • Rated flow, pressure, and speed • Pressure at 150% of rated flow

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Fire pump test objectives

The fire pump test has two objectives:

• Verify the fire pump meets or exceeds all fire system demands

• Verify the fire pump is in good condition (is reasonably close to meeting the nameplate data).

When testing a fire pump, at least three test points are needed to plot the test results on graph paper. The three test points are:

Table 3. Fire pump test points Table 3. Fire pump test points

Test point UK LPCB approved fire pump

US UL listed fire pump

#1 No flow No flow (also known as churn)

#2 Flow at fire pump mid-range Fire pump rated flow

#3 Fire pump rated flow 150% of fire pump rated flow (also known as overload)

Plotting data before disassembling test equipment

All too often, one or more elements of fire pump test data will reflect inadequate results. The issue may be inadequate pump performance, inadequate test accuracy, or a combination of both. Resolving the source of the inadequate test data requires further testing, and the best opportunity to pursue further testing is during the same test. Therefore, always plot all test data before any test equipment is disassembled. Retest any data points that are in question. Leave the test with confidence that the test data is within a suitable range of accuracy.

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Speed readings

The fire pump nameplate performance data is based upon the pump operating at rated speed. If the pump is operating below rated speed, the pump performance will appear deficient. If the pump is operating above rated speed, the pump will appear to be exceeding its rated capability. With any fire pump test, it is desirable to capture the pump rotating speed so that if needed, the pump net test results can be adjusted to rated conditions for comparison with the original bench test curve or nameplate performance data.

Digital tachometer

The digital tachometer shown above is set up for measuring pump shaft speed by contact. The contact adaptor can be removed to allow non-contact speed readings. The following formulas are used to correct fire pump flow and pressure test data to rated speed. Flow correction:

• Qrated = flow at rated speed (gpm) • Nrated = rated speed (rpm) • Ntest = measured test speed (rpm) • Qtest = measured test flow (gpm)

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Pressure correction:

• Prated = pressure at rated speed (psi) • Nrated = rated speed (rpm) • Ntest = measured test speed (rpm) • Ptest = measured test pressure (psi)

Interpreting abnormal fire pump curves

Reading abnormal fire pump net performance test curves often offers insight into the cause of the abnormal performance. The graphs provided on the following pages depict the following fire pump performance issues:

• Wear ring deterioration • Obstructed suction or clogged impeller vane • Fire pump running in reverse • Fire pump air bound

The objective of the annual fire pump capacity flow test is to detect issues that may affect the ability of the pump to meet the connected fire protection system demands. Careful analyses of all fire pump test results, including the net performance curve, is an essential aspect of the test purpose.

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Hydraulic fundamentals

Pressure

Pressure is a ratio of force applied per unit area or:

P = F/A Where:

P = Pressure bar (psi) F = Force kg (lb force) A = Area cm2 (in2)

Real-world application While pressure is used every day in fire protection, the above pressure formula is not. Rather than measure force and area and then compute pressure, pressure is observed directly using gauges. Water pressure in a fire protection system has two components – normal pressure and velocity pressure. Normal pressure is the pressure exerted on the walls of pipes and vessels. Velocity pressure is the pressure created by moving water in the direction of flow.

Normal pressure is displayed on gauges tapped into various locations of a fire system.

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Fire pump gauge Sprinkler riser gauges Velocity pressure is displayed on gauges when taking pitot readings.

Pitot tube measuring water flow from a nozzle

55

Flow from an orifice

The orifice flow formula is applied when conducting a water flow test with discharging nozzles. This formula converts a pitot pressure reading to water flow rate.

Water flow from an orifice is represented by the following formula:

Q = 0.666 d2 (Pv)1/2 metric

Q = 29.8 d2 (Pv)1/2 US measure

Where:

Q = Flow lpm (gpm) d = orifice diameter mm (inches) Pv = velocity pressure bar (psi) measured with a pitot tube

Formula note: The values 0.666 and 29.8 are constants to adjust units.

Real-world application

While computing water flow rates is a frequent activity, the use of the above formulas is not. In the field, flow measurement is performed in two manners:

Flowmeter - Where a flowmeter is used, the measurement of flow is taken directly from the flowmeter.

Orifice pitot - Where a pitot tube is used with a nozzle or other orifice, Pv will be measured with the pitot tube and d will be measured with a scale. The measured values of Pv and d can be used to look up Q in charts or tables prepared using the orifice flow formulas. See Table 12. Discharge from circular orifices (lpm) and Table 13. Discharge from circular orifices (gpm). When flow is measured with a pitot tube, the orifice flow formula will be used if a table or chart is not available for the specific nozzle being flowed.

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Dial flowmeter Tube flowmeter Pitot Elevation Water pressure for fire protection is developed in two primary ways, gravity and pumps. Gravity develops pressure through elevation. The elevation - or height - of a given column of water is converted into pressure with the following formula:

P = 0.0981 x h metric P = 0.433 x h US measure

Where:

P = Pressure bar (psi) h = Height meter (feet) The units for the constants are 0.0981 bar/m (0.433 psi/ft).

Real world application The above formulas are use often. They allow:

• A known height of water to be converted to a pressure • A known pressure from a gauge to be used to check water

height in a tank (is it full?)

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Calculating orifice flow

Flow is the time it takes for a given volume of water to reach a specific point. For fire protection, this is measured in liters per minute (lpm) or gallons per minute (gpm). When studying flow, it is important to remember that whatever flow enters a pipe or system will be the same coming out of the pipe or system. Since water is non-compressible, total flow will be a constant. As stated earlier, water flow from an orifice is represented by the following formula:

Q = 0.666 d2 (Pv)1/2 metric

Q = 29.8 d2 (Pv)1/2 US measure

Where:

Q = Flow lpm (gpm) d = orifice diameter mm (inches) Pv = velocity pressure bar (psi) measured with a pitot tube

Formula note: The values 0.666 and 29.8 are constants to adjust units.

The variables listed above are easily measured in the field. However, there is one additional concept that needs to be incorporated. The above equation assumes the stream of water is perfectly smooth and that the velocity pressure is uniform over the entire cross section of the stream. This is referred to as laminar flow. In reality, water streams are never perfectly smooth. In fact, flow test from hydrants are quite turbulent. Laminar or smooth flow will result in a higher flow for a given orifice as compared to turbulent flow. In the field, we use special nozzles to reduce turbulence and increase accuracy. However, true linear flow cannot be achieved in the field. For this reason, we have to adjust the flow by using an orifice coefficient "c". Therefore, the equation that we use for calculating flow in the field is:

58

Q = 0.666 d2 c (Pv)1/2 metric

Q = 29.84 d2 c (Pv)1/2 US measure Where: Q = flow lpm (gpm) 6.66 (29.84) Constant to correct units d = orifice diameter mm (in.) c = orifice coefficient dimensionless Pv = velocity pressure bar (psi) The orifice coefficient “c” is representative of how smooth the flow will be from a given orifice. The following is a list of the common orifices encountered in the field:

Table 4. Coefficient "c" of common orifices Table 4. Coefficient "c" of common orifices

Type of orifice "c" factor Hydrant outlet with a smooth, well rounded internal transition from the barrel to the outlet

0.90*

Hydrant outlet with a square internal transition from the barrel to the outlet

0.80*

Hydrant outlet that protrudes into the hydrant barrel 0.70*

Underwriter’s Playpipe smooth tapered nozzle 0.97

*See image titled “Hydrant outlet coefficients”. Hydrant outlets

When a hydrant is flowed, always evaluate the outlet shape. Apply the appropriate coefficient from Table 4. The image titled “Hydrant outlet coefficients” provides a visual aid to identify smooth outlets, square outlets, and outlets that protrude into the hydrant barrel. For large hydrant outlets - e.g. 100 mm (4 in) or larger - multiply the Table 4 coefficients by an additional factor of 0.83.

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Hydrant outlet coefficients

Converting pitot readings to flows

After pitot reading are measured and recorded, the orifice flow formula can be used to calculate the flow. As an alternative, Table 12. Discharge from circular orifices (lpm) and Table 13. Discharge from circular orifices (gpm) can be used; however, Table 12 and 13 are intended for specific types of outlets and appropriate coefficients have been included in the flow values displayed in these tables. Be careful to avoid the use of Table 12 and 13 if the orifice and coefficient are not applicable to the actual orifice flowed.

Some flow tests, such as fire pump tests, will involve measuring flow from multiple orifices. It is important to note that the pitot measurements from each orifice are to be converted to a flow before summing the flows to determine the total flow. Do not sum pitot reading and then determine the flow.

Friction loss

When water flows through a pipe, there is friction occurring between the water molecules and the pipe walls. Energy is needed to overcome this friction. Friction loss, or pressure drop, occurs because some of the system's energy is used up in overcoming friction. The energy does not disappear. Energy is neither created nor destroyed, but is converted into heat due to the friction. The magnitude of friction loss in a pipe depends upon:

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• Pipe length • Pipe diameter • Flow rate • Interior roughness of the pipe

Friction loss calculations

The formula commonly used for fire protection applications is the Hazen-Williams formula. This formula was derived by actual measurements of the effect of each variable on friction loss. The formula computes friction loss per linear foot of pipe as follows:

Pf = (6.05x105 Q

1.85) / (C

1.85 d

4.87) metric

Pf = (4.52 Q1.85

) / (C1.85

d4.87

) US measure

Where:

Pf = friction loss per foot bar/m (psi/ft) Q = flow lpm (gpm) C = Hazen-Williams pipe coefficient no units d = internal diameter of pipe mm (in.)

The interior roughness of the pipe is represented by the Hazen-Williams pipe coefficient or C-factor. The larger the C-factor value the smoother the interior of the pipe walls. Based upon NFPA 13 (2013) Table 23.4.4.7, the following is a table of common "C" factors.

Table 5. Hazen-Williams C values Table 5. Hazen-Williams C values

Pipe or tube C value Unlined cast or ductile iron pipe See Table 6 Black steel (dry or pre-action system) 100 Black steel (wet or deluge system) 120 Galvanized pipe 120 Plastic listed sprinkler pipe 150 Cement-lined cast or ductile iron 140 Copper tube or stainless steel 150 Asbestos cement 140 Concrete 140

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Based upon the 2008 NFPA Fire Protection Handbook Table 15.3.6, the following is a table of C-factors for unlined cast iron pipe.

Table 6. Hazen-Williams C values unlined cast or ductile iron pipe

Table 6. Hazen-Williams C values unlined cast or ductile iron pipe

Pipe age Mildly

corrosive water

Moderately corrosive

water

Severely corrosive

water New 120 120 120 10 years old 110 90 75 15 years old 100 75 65 20 years old 90 65 55 30 years old 80 55 45 50 years old 70 50 40

Friction loss due to fittings

In addition to pressure drop due to friction through sections of pipe, there is a need to account for the impact of:

• Flow through fittings that changes pipe size or direction • Flow through restrictive devices such as valves, check

valves, water meters, strainers, back flow prevention devices, and similar devices.

The friction loss due to flow through fittings and devices can be added to friction loss calculations in the following two manners. First, all fittings and some devices can be converted to an equivalent length of pipe of the same nominal diameter as the attached pipe. These equivalent lengths are captured in Table 7 for steel pipe and Table 9 for CPVC pipe. Second, the manufacturers of devices such as alarm check valves, detector check valves, backflow prevention assemblies, meters, and strainers will publish flow vs. pressure loss curves for each nominal pipe size. These published curves are typically available at the manufacturer's web site. Pressure losses will be selected from the

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manufacturer's curve and added as a fixed pressure drop in the friction loss calculations.

Backflow prevention assembly Strainer/meter/check valve assembly

63

Table 7. Equivalent length in meters (feet) of common fittings based upon schedule 40 (EN 10255 Heavy series)

pipe

64

Table 8. Equivalent length adjustment factors – ASTM schedule 40 to other pipe types

65

Table 9. Equivalent length in meters (feet) of fittings for CPVC pipe

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Friction loss calculation procedure

For each size of pipe, the associated fittings and devices are converted to equivalent lengths and added to the length of pipe. The friction loss can then be calculated using the following equation:

F = (L) f Where: F = Friction loss for the selected section of pipe L= Length of pipe including equivalent length of fittings f = Friction loss per lineal length of pipe for the flow rate

and pipe size Table 14. Friction loss per lineal meter of pipe provides friction loss values for various size steel pipe (25, 32, 40, 50, 65, 80, 100, and 150 mm), various C-factors (C=100 and C=120), and various schedules of steel pipe (heavy and medium series). Table 15. Friction loss per lineal foot of pipe provides friction loss values for various size pipe (3/4", 1", 1¼", 1½", 2", 2½", 3", 4", 5", 6", 8" and 10"), various C-factors (C=100 and C=120 for steel pipe and C=150 for CPVC pipe), and various schedules of steel pipe (schedules 10 and 40 for all sizes and schedules 10, 30, and 40 for 8" and 10" pipe). There are many other types of pipe that are specifically listed for use in sprinkler systems that are not covered by Tables 14 and 15. For these pipes, manufacturer's literature will need to be consulted for guidance in calculating friction loss. In some cases, manufacturers will provide friction loss tables; however, when manufacturer's tables are not available, the friction loss per foot of pipe will have to be calculated using the friction loss formula shown below (and discussed earlier in this booklet).

Pf = (6.05x105 Q

1.85) / (C

1.85 d

4.87) metric

Pf = (4.52 Q1.85

) / (C1.85

d4.87

) US measure

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Table 11. Inside diameters of pipe (inches) provides the inside diameters for schedules 10, 30, and 40 pipe as well as a number of other types of pipe specifically listed for use in sprinkler systems. As this is US pipe, only data in US measure is provided. At times, it may be desirable to convert friction loss based upon a C=100 to another C-factor. Based upon the 2008 NFPA Fire Protection Handbook Table 15.3.5, the following conversion factors are provided to change from C=100 to other C" factors.

Table 10. Converting Hazen-Williams C=100 to other C-factors

Table 10. Converting Hazen-Williams C=100 to other C-factors Desired

"C" Conversion

factor Desired

"C" Conversion

factor Desired

"C" Conversion

factor 150 0.472 110 0.838 70 1.93 145 0.503 105 0.914 65 2.22 140 0.537 100 1.00 60 2.57 135 0.574 95 1.10 55 3.02 130 0.615 90 1.22 50 3.61 125 0.662 85 1.35 45 4.38 120 0.714 80 1.51 40 5.48 115 0.772 75 1.70 35 6.97

Hydraulic calculation procedure

See Annex A for an example using friction loss calculations to determine the base of riser demand for a simple tree sprinkler system. Pressure regulating valves (PRV's)

PRV's and hydraulic calculations

When a PRV is introduced into a sprinkler system, the PRV creates a discontinuity in the hydraulic calculation. Unlike other devices, the PRV cannot be converted into an equivalent length of pipe. The design of the PRV allows it to change its "equivalent length" in response to the ever changing inlet pressure. Because of this behavior, PRV's introduce a challenge to sprinkler system hydraulic

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calculations and design. Sprinkler calculations should be carried back to the PRV outlet. The available water supply should then be projected forward to the PRV inlet. PRV data should be applied to the projected water supply to select the appropriate PRV that will meet the sprinkler demand on the outlet side.

Pilot operated PRV

Note unacceptable shutoff valves in pilot lines

Direct acting factory-set PRV's

PRV's for both sprinklers and fire hose Note oversize drain riser for PRV testing

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Types of PRV's

There are two types of PRV's, pilot operated and direct acting. Pilot operated PRV's use a pilot regulator on a pilot line system outside the valve to control the regulating action of the main valve. Direct acting PRV's incorporate a spring or other mechanism inside the valve to directly regulate the valve operation. Pilot operated PRV's are field adjustable. Direct acting PRV's may be either factory set or field adjustable. Factory set PRV's will be shipped with a tag indicating their intended installed location. If a factor set PRV is not meeting the required outlet flow and pressure, replacement is the only option. NFPA 13 and PRV's

NFPA 13 stipulates the following for PRV's:

• Provide a listed PRV • Set outlet pressure at 165 psi at maximum inlet pressure • Provide pressure gauges on inlet and outlet side • Provide a relief valve 12 mm (½ in) or larger on outlet side • Provide a listed control valve on inlet and outlet side

- Except for PRV's serving one sprinkler system - Except for PRV's that are also listed control valves

• Provide a means for full flow testing on outlet side • Acceptance test each PRV to confirm

- Proper operation under flow and no-flow conditions - Record test result on Contractor's Material and Test

certificate - Record static and residual inlet pressures - Record static and residual outlet pressures - Record flow rate

Non-listed PRV's

As noted above, PRV's are to be listed. This is particularly important for pilot operated PRV's which are readily available in non-listed versions for domestic and process use. Non-listed PRV's are periodically installed in sprinkler systems. The non-listed PRV's can

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include shutoff valves (see photo earlier) in the pilot trim lines which if closed can impair the valve. Non-listed PRV valves must be avoided. Redundant PRV's

PRV's may serve a single sprinkler system or multiple sprinkler systems. Where a PRV serves more than one sprinkler system, redundant PRV's should be installed in parallel. Providing small PRV's with larger PRV's

Direct acting PRV's are available in sizes ranging from 38 to 76 mm (1½ to 3 in.). Pilot operated PRV's are available is sizes ranging from 64 to 203 mm (2½ to 8 in). For PRV's over 76 mm (3 in.) in size serving closed-head sprinklers, a smaller PRV should be provided in parallel to support the low flows associated with one or two sprinklers operating. Larger PRV's will not necessarily reliably regulate low flows, and may compromise the continuous delivery of water to operating sprinklers. The manufacturer of the PRV should be consulted for guidance. Loop tests

Where a facility is provided with an underground fire main loop, it is necessary to perform a loop test at least every two years to verify that all sectional valves are open and the loop is in good condition. The sequence of a loop test is important if all test objectives are to be accomplished. The Loop test diagram will be used to highlight the test sequence and benefits. Loop test 1 will involve closing valve 1 to form a short flow path to hydrant H. Pressure readings will be taken at riser R. The results of this test will be plotted on graph paper. Loop test 2 will involve reopening valve 1 and closing valve 2. This will form a long flow path to hydrant H. Pressure readings once again will be taken at riser R. The results of this test will be plotted

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on the same graph paper as loop test 1. By comparison, loop test 2 should be weaker than loop test 1. Loop test 3 will involve reopening valve 2. No valves will be closed for this test. This test will allow the full loop to flow water to hydrant H. Pressure readings once again will be taken at riser R. The results of this test will be plotted on the same graph paper as loop tests 1 and 2. By comparison, loop test 3 should be the strongest test. This outcome will verify that both legs of the loop are open and flowing water, and that all valves have returned to the open position.

Loop test diagram

Hydraulic gradient

A hydraulic gradient test is a method of analyzing the condition of an existing underground main. It compares the anticipated C-factor of an underground main against the actual C-factor.

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Anticipated performance is based upon the documented configuration of the main including:

• Type of pipe • Diameter of pipe • Length of pipe • Number and size of fittings and devices • Elevation change

Actual performance is based upon a flow test along the main with gauges placed at as many locations as possible along the length of the main. This includes hydrants, risers, backflow prevention assemblies, etc. Consider the Hydraulic gradient sketch and tables. This example has been simplified with no fittings or device equivalent lengths. The Documented pipe configuration table provides an estimated pressure profile at each gauge location. All pipes are 8". Using Table 14, the friction loss of 0.007 psi/ft is selected based upon 8" schedule 30 pipe flowing 750 gpm. The first three sections of pipe are unlined ductile iron pipe. Based upon the pipe age, C-factors are selected using Table 6 and "mildly corrosive water". The C-factor corrections are obtained from Table 10. The estimated friction loss for each section of pipe is then calculated using the following formula.

F1 = (f1) (L) (fc) Where: F1 = Friction loss in a given length of pipe (psi) f1 = friction loss per lineal foot of pipe L= Length of pipe including equivalent length of fittings fc = Conversion factor for C values other than C=100 Knowing that the actual test will have an adjusted residual at Gauge 1 of 70 psi, the estimated residual readings for the remaining gauge locations are developed based upon the estimated friction.

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Hydraulic gradient sketch and tables

The Flow and pressure test data begins by capturing the static gauge readings at each location. This allows a profile curve to be graphed. The actual residual gauge readings are then added to the profile curve to plot the adjusted residual pressures. The estimated residual values are then plotted and compared with the adjusted actual readings.

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Hydraulic gradient graph - actual vs. estimated

The graphical results clearly show a significant pressure drop between gauge locations 3 and 4. The pressure drop is 8 psi in 100 feet of 8" pipe. This is a friction loss of 0.08 psi/ft. The effective correction factor compared to C=100 pipe can be calculated as follows:

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fc = f1 Actual / f1 Table 11 = 0.08 / 0.007 =11.4 Comparing the above with the correction factors in Table 10, the section of pipe between gauge locations 3 and 4 which should have a C-factor of 90 is actually behaving worse than pipe with a C-factor of 35. Action is needed to determine the cause of this inadequate performance.

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Table 11. Inside diameter of pipe

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Table 12. Discharge from circular orifices (lpm) Table 12. Discharge from circular orifices (lpm)

Pitot (bar)

Orifice diameter - mm (in) 29 44 64 64 64 108 114

(1⅛) (1¾) (2½) (2½) (2½) (4¼) (4½)

Playpipe Playpipe Hydrant outlet Hydrant outlet

C = 0.9 x 0.83, See NFPA 291 Table 4.8.2 round square protruding

C factors 0.970 0.970 0.900 0.800 0.700 0.747 0.747

0.75 471 1,083 2,126 1,890 1,654 5,025 5,599

1.00 543 1,251 2,455 2,182 1,910 5,803 6,466

1.25 607 1,398 2,745 2,440 2,135 6,488 7,229

1.50 665 1,532 3,007 2,673 2,339 7,107 7,919

1.75 719 1,655 3,248 2,887 2,526 7,676 8,553

2.00 768 1,769 3,472 3,086 2,701 8,206 9,144

2.25 815 1,876 3,683 3,274 2,864 8,704 9,698

2.50 859 1,978 3,882 3,451 3,019 9,175 10,223

2.75 901 2,074 4,071 3,619 3,167 9,623 10,722

3.00 941 2,166 4,252 3,780 3,307 10,051 11,199

3.25 979 2,255 4,426 3,934 3,442 10,461 11,656

3.50 1,016 2,340 4,593 4,083 3,572 10,856 12,096

3.75 1,052 2,422 4,754 4,226 3,698 11,237 12,520

4.00 1,087 2,501 4,910 4,365 3,819 11,606 12,931

4.25 1,120 2,578 5,061 4,499 3,937 11,963 13,329

4.50 1,153 2,653 5,208 4,629 4,051 12,310 13,715

4.75 1,184 2,726 5,351 4,756 4,162 12,647 14,091

5.00 1,215 2,797 5,490 4,880 4,270 12,976 14,457

5.25 1,245 2,866 5,625 5,000 4,375 13,296 14,814

5.50 1,274 2,933 5,758 5,118 4,478 13,609 15,163

5.75 1,303 2,999 5,887 5,233 4,579 13,915 15,504

6.00 1,331 3,064 6,014 5,346 4,677 14,214 15,837

6.25 1,358 3,127 6,138 5,456 4,774 14,507 16,164

6.50 1,385 3,189 6,259 5,564 4,868 14,794 16,484

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Table 13. Discharge from circular orifices - US Table 13. Discharge from circular orifices (gpm)

Pitot (psi)

Orifice diameter (inches) 11/8 1¾ 2¼ 2½ 2½ 2½ 4¼ 4½

Playpipe Playpipe New England

Hydrant outlet

round, square, protruding

Hydrant outlet C = 0.9 x 0.83, See NFPA 291 Table 4.8.2

C factors 0.970 0.970 0.881 0.900 0.800 0.700 0.747 0.747

5 82 198 375 333 292 1083 1214 6 90 217 411 365 319 1187 1330 7 97 234 443 394 345 1282 1437

8 103 250 474 421 369 1370 1536 9 110 266 503 447 391 1453 1629

Avoid pitot readings below 10 psi 10 116 280 421 530 471 412 1532 1717 11 121 294 441 556 494 432 1607 1801 12 127 307 461 581 516 452 1678 1881 13 132 320 480 604 537 470 1747 1958 14 137 332 498 627 558 488 1813 2032 15 142 343 515 649 577 505 1876 2103 16 146 355 532 671 596 522 1938 2172 17 151 365 549 691 614 538 1997 2239 18 155 376 565 711 632 553 2055 2304 19 159 386 580 731 649 568 2112 2367 20 164 396 595 750 666 583 2166 2429 21 168 406 610 768 683 597 2220 2489 22 172 416 624 786 699 612 2272 2547 23 175 425 638 804 715 625 2323 2605 24 179 434 652 821 730 639 2373 2661 25 183 443 665 838 745 652 2422 2716 26 187 452 678 855 760 665 2470 2769 27 190 461 692 871 774 677 2517 2822 28 194 469 704 887 788 690 2563 2874 29 197 477 717 903 802 702 2609 2925 30 200 486 729 918 816 714 2653 2975 31 204 494 741 933 830 726 2697 3024 32 207 501 753 948 843 738 2740 3072 33 210 509 765 963 856 749 2783 3120 34 213 517 776 977 869 760 2825 3167 35 216 524 787 992 881 771 2866 3213 36 220 532 799 1006 894 782 2907 3259 37 223 539 810 1020 906 793 2947 3304 38 226 546 820 1033 918 804 2986 3348 39 228 554 831 1047 931 814 3025 3392 40 231 561 841 1060 942 825 3064 3435 41 234 568 852 1073 954 835 3102 3478

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Table 13. Discharge from circular orifices (gpm)

Pitot (psi)



Hydrant outlet



C factors 0.970 0.970 0.881 0.900 0.800 0.700 0.747 0.747

42 237 574 863 1086 966 845 3140 3520 43 240 581 873 1099 977 855 3177 3561 44 243 588 883 1112 988 865 3213 3603 45 245 595 893 1124 1000 875 3250 3643 46 248 601 903 1137 1011 884 3286 3684 47 251 608 912 1149 1021 894 3321 3723 48 253 614 922 1161 1032 903 3356 3763 49 256 621 932 1173 1043 913 3391 3802 50 259 627 941 1185 1054 922 3425 3840 51 261 633 950 1197 1064 931 3460 3879 52 264 639 960 1209 1074 940 3493 3916 53 266 645 969 1220 1085 949 3527 3954 54 269 651 978 1232 1095 958 3560 3991 55 271 657 987 1243 1105 967 3593 4028 56 274 663 996 1254 1115 976 3625 4064 57 276 669 1266 1125 984 3657 4100 58 279 675 1277 1135 993 3689 4136 59 281 681 1288 1144 1001 3721 4172 60 283 687 1298 1154 1010 3752 4207 61 286 692 1309 1164 1018 3784 4242 62 288 699 1320 1173 1027 3814 4276 63 290 704 1330 1183 1035 3845 4311 64 293 709 1341 1192 1043 3875 4345 65 295 715 1351 1201 1051 3906 4379 66 297 720 1362 1210 1059 3936 4412 67 299 726 1372 1220 1067 3965 4446 68 302 731 1382 1229 1075 3995 4479 69 304 736 1392 1238 1083 4024 4511 70 306 742 1402 1247 1091 4053 4544 71 308 747 1412 1255 1099 4082 4576 72 310 752 1422 1264 1106 4111 4608 73 313 757 1432 1273 1114 4139 4640 74 315 763 1442 1282 1122 4167 4672 75 317 768 1452 1290 1129 4195 4703 76 319 773 1461 1299 1137 4223 4735 77 321 778 1471 1307 1144 4251 4766 78 323 783 1480 1316 1151 4278 4797 79 325 788 1490 1324 1159 4306 4827 80 327 793 1499 1333 1166 4333 4858 81 329 798 1509 1341 1173 4360 4888

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Table 13. Discharge from circular orifices (gpm)

Pitot (psi)



Hydrant outlet



C factors 0.970 0.970 0.881 0.900 0.800 0.700 0.747 0.747

82 331 803 1518 1349 1181 4387 4918 83 333 808 1527 1357 1188 4413 4948 84 335 812 1536 1366 1195 4440 4978 85 337 817 1545 1374 1202 4466 5007 86 339 822 1554 1382 1209 4492 5037 87 341 827 1564 1390 1216 4519 5066 88 343 832 1572 1398 1223 4544 5095 89 345 836 1581 1406 1230 4570 5124 90 347 841 1590 1414 1237 4596 5152 91 349 846 1599 1421 1244 4621 5181 92 351 850 1608 1429 1251 4647 5209 93 353 855 1617 1437 1257 4672 5238 94 355 859 1625 1445 1264 4697 5266 95 357 864 1634 1452 1271 4722 5294 96 358 869 1642 1460 1277 4746 5321 97 360 873 1651 1467 1284 4771 5349 98 362 878 1659 1475 1291 4796 5376 99 364 882 1668 1483 1297 4820 5404

100 366 886 1676 1490 1304 4844 5431 101 368 891 1685 1497 1310 4869 5458 102 369 895 1693 1505 1317 4893 5485 103 371 900 1701 1512 1323 4916 5512 104 373 904 1709 1520 1330 4940 5539 105 375 908 1718 1527 1336 4964 5565 106 377 913 1726 1534 1342 4988 5592 107 378 917 1734 1541 1349 5011 5618 108 380 921 1742 1548 1355 5034 5644 109 382 925 1750 1556 1361 5058 5670 110 384 930 1758 1563 1367 5081 5696

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Table 14. Friction loss - bar per lineal meter of pipe Table 14. Friction loss - bar per lineal meter of pipe

25 mm pipe Pipe type Medium Heavy C Factor 100 120 100 120 ID (mm) 27.35 27.35 25.75 25.75

Flow (lpm) Friction loss (bar / meter) 5 0.0002 0.0002 0.0003 0.0002

10 0.0009 0.0006 0.0012 0.0008 15 0.0018 0.0013 0.0024 0.0017 20 0.0031 0.0022 0.0042 0.0030 25 0.0047 0.0033 0.0063 0.0045 30 0.0066 0.0047 0.0088 0.0063 35 0.0087 0.0062 0.0117 0.0083 40 0.0112 0.0080 0.0150 0.0107 45 0.0139 0.0099 0.0186 0.0133 50 0.0169 0.0120 0.0226 0.0161 55 0.0201 0.0144 0.0270 0.0193 60 0.0236 0.0169 0.0317 0.0226 65 0.0274 0.0196 0.0367 0.0262 70 0.0314 0.0224 0.0421 0.0301 75 0.0357 0.0255 0.0479 0.0342 80 0.0402 0.0287 0.0539 0.0385 85 0.0450 0.0321 0.0604 0.0431 90 0.0500 0.0357 0.0671 0.0479 95 0.0553 0.0395 0.0741 0.0529 100 0.0608 0.0434 0.0815 0.0582 105 0.0665 0.0475 0.0892 0.0637 110 0.0725 0.0517 0.0972 0.0694 115 0.0787 0.0562 0.1056 0.0753 120 0.0852 0.0608 0.1142 0.0815 125 0.0918 0.0655 0.1232 0.0879 130 0.0988 0.0705 0.1325 0.0945 135 0.1059 0.0756 0.1420 0.1014 140 0.1133 0.0808 0.1519 0.1084

82

Table 14. Friction loss - bar per lineal meter of pipe 25 mm pipe

Pipe type Medium Heavy C Factor 100 120 100 120 ID (mm) 27.35 27.35 25.75 25.75

Flow (lpm) Friction loss (bar / meter) 145 0.1209 0.0863 0.1621 0.1157 150 0.1287 0.0918 0.1726 0.1232 155 0.1367 0.0976 0.1834 0.1309 160 0.1450 0.1035 0.1945 0.1388 165 0.1535 0.1096 0.2059 0.1469 170 0.1622 0.1158 0.2176 0.1553 175 0.1712 0.1222 0.2296 0.1638 180 0.1803 0.1287 0.2418 0.1726 185 0.1897 0.1354 0.2544 0.1816 190 0.1993 0.1422 0.2673 0.1908 195 0.2091 0.1492 0.2804 0.2001 200 0.2191 0.1564 0.2939 0.2097 205 0.2294 0.1637 0.3076 0.2195 210 0.2398 0.1712 0.3216 0.2296 215 0.2505 0.1788 0.3360 0.2398 220 0.2614 0.1865 0.3506 0.2502 225 0.2725 0.1945 0.3654 0.2608 230 0.2838 0.2025 0.3806 0.2716 235 0.2953 0.2107 0.3960 0.2827 240 0.3070 0.2191 0.4118 0.2939 245 0.3190 0.2276 0.4278 0.3053 250 0.3311 0.2363 0.4441 0.3169 255 0.3435 0.2451 0.4606 0.3288 260 0.3560 0.2541 0.4775 0.3408 265 0.3688 0.2632 0.4946 0.3530 270 0.3818 0.2725 0.5120 0.3654 275 0.3949 0.2819 0.5297 0.3781 280 0.4083 0.2914 0.5477 0.3909

83




10 0.0002 0.0002 0.0003 0.0002 15 0.0005 0.0003 0.0006 0.0004 20 0.0008 0.0006 0.0010 0.0007 25 0.0012 0.0009 0.0015 0.0011 30 0.0017 0.0012 0.0021 0.0015 35 0.0023 0.0016 0.0028 0.0020 40 0.0029 0.0021 0.0036 0.0026 45 0.0036 0.0026 0.0045 0.0032 50 0.0044 0.0031 0.0055 0.0039 55 0.0052 0.0037 0.0065 0.0047 60 0.0062 0.0044 0.0077 0.0055 65 0.0071 0.0051 0.0089 0.0064 70 0.0082 0.0058 0.0102 0.0073 75 0.0093 0.0066 0.0116 0.0083 80 0.0105 0.0075 0.0131 0.0093 85 0.0117 0.0084 0.0146 0.0104 90 0.0130 0.0093 0.0163 0.0116 95 0.0144 0.0103 0.0180 0.0128 100 0.0158 0.0113 0.0198 0.0141 105 0.0173 0.0124 0.0216 0.0154 110 0.0189 0.0135 0.0236 0.0168 115 0.0205 0.0146 0.0256 0.0183 120 0.0222 0.0158 0.0277 0.0198 125 0.0239 0.0171 0.0298 0.0213 130 0.0257 0.0184 0.0321 0.0229 135 0.0276 0.0197 0.0344 0.0246

84



Flow (lpm) Friction loss (bar / meter) 140 0.0295 0.0211 0.0368 0.0263 145 0.0315 0.0225 0.0393 0.0280 150 0.0335 0.0239 0.0418 0.0298 155 0.0356 0.0254 0.0444 0.0317 160 0.0378 0.0270 0.0471 0.0336 165 0.0400 0.0285 0.0499 0.0356 170 0.0423 0.0302 0.0527 0.0376 175 0.0446 0.0318 0.0556 0.0397 180 0.0470 0.0335 0.0586 0.0418 185 0.0494 0.0353 0.0616 0.0440 190 0.0519 0.0371 0.0648 0.0462 195 0.0545 0.0389 0.0680 0.0485 200 0.0571 0.0407 0.0712 0.0508 205 0.0598 0.0426 0.0745 0.0532 210 0.0625 0.0446 0.0779 0.0556 215 0.0653 0.0466 0.0814 0.0581 220 0.0681 0.0486 0.0849 0.0606 225 0.0710 0.0507 0.0885 0.0632 230 0.0739 0.0528 0.0922 0.0658 235 0.0769 0.0549 0.0960 0.0685 240 0.0800 0.0571 0.0998 0.0712 245 0.0831 0.0593 0.1037 0.0740 250 0.0863 0.0616 0.1076 0.0768 255 0.0895 0.0639 0.1116 0.0797 260 0.0928 0.0662 0.1157 0.0826 265 0.0961 0.0686 0.1199 0.0855 270 0.0995 0.0710 0.1241 0.0885

85




86




87




88




89




90




91




92




93




10 0.0000 0.0000 0.0000 0.0000 15 0.0001 0.0001 0.0001 0.0001 20 0.0001 0.0001 0.0001 0.0001 25 0.0002 0.0001 0.0002 0.0002 30 0.0003 0.0002 0.0003 0.0002 35 0.0003 0.0002 0.0004 0.0003 40 0.0004 0.0003 0.0005 0.0004 45 0.0006 0.0004 0.0007 0.0005 50 0.0007 0.0005 0.0008 0.0006 55 0.0008 0.0006 0.0009 0.0007 60 0.0009 0.0007 0.0011 0.0008 65 0.0011 0.0008 0.0013 0.0009 70 0.0012 0.0009 0.0015 0.0011 75 0.0014 0.0010 0.0017 0.0012 80 0.0016 0.0011 0.0019 0.0013 85 0.0018 0.0013 0.0021 0.0015 90 0.0020 0.0014 0.0023 0.0017 95 0.0022 0.0016 0.0026 0.0019 100 0.0024 0.0017 0.0029 0.0020 105 0.0026 0.0019 0.0031 0.0022 110 0.0029 0.0021 0.0034 0.0024 115 0.0031 0.0022 0.0037 0.0026 120 0.0034 0.0024 0.0040 0.0029 125 0.0036 0.0026 0.0043 0.0031 130 0.0039 0.0028 0.0046 0.0033 135 0.0042 0.0030 0.0050 0.0035

94




95




96




97




98




99




100




101




102




103




104




105




106




107




108



Flow (lpm) Friction loss (bar / meter) 2200 0.2078 0.1483 0.2365 0.1688 2220 0.2113 0.1508 0.2405 0.1716 2240 0.2149 0.1534 0.2445 0.1745 2260 0.2184 0.1559 0.2486 0.1774 2280 0.2220 0.1585 0.2527 0.1803 2300 0.2256 0.1610 0.2568 0.1833 2320 0.2293 0.1636 0.2609 0.1862 2340 0.2330 0.1663 0.2651 0.1892 2360 0.2367 0.1689 0.2693 0.1922 2380 0.2404 0.1716 0.2735 0.1952 2400 0.2441 0.1742 0.2778 0.1983 2420 0.2479 0.1769 0.2821 0.2013 2440 0.2517 0.1796 0.2864 0.2044 2460 0.2555 0.1824 0.2908 0.2075 2480 0.2594 0.1851 0.2952 0.2107 2500 0.2633 0.1879 0.2996 0.2138

109




110




111




112




113




114




115



Flow (lpm) Friction loss (bar / meter) 4100 0.0834 0.0595 0.0907 0.0648 4150 0.0853 0.0609 0.0928 0.0662 4200 0.0872 0.0622 0.0949 0.0677 4250 0.0891 0.0636 0.0970 0.0692 4300 0.0911 0.0650 0.0991 0.0707 4350 0.0931 0.0664 0.1012 0.0722 4400 0.0950 0.0678 0.1034 0.0738 4450 0.0971 0.0693 0.1056 0.0754 4500 0.0991 0.0707 0.1078 0.0769 4550 0.1011 0.0722 0.1100 0.0785 4600 0.1032 0.0737 0.1123 0.0801 4650 0.1053 0.0751 0.1145 0.0817 4700 0.1074 0.0766 0.1168 0.0834 4750 0.1095 0.0782 0.1191 0.0850 4800 0.1116 0.0797 0.1215 0.0867 4850 0.1138 0.0812 0.1238 0.0884 4900 0.1160 0.0828 0.1262 0.0901 4950 0.1182 0.0844 0.1286 0.0918 5000 0.1204 0.0859 0.1310 0.0935

116




117




118




119




120




121




122




123




124




125




126

Table 15. Friction loss - psi per lineal foot of pipe Table 15. Friction loss - psi per lineal foot of pipe

3/4" pipe Pipe Type CPVC Pipe Pipe Type CPVC Pipe C Factor 150 C Factor 150

ID (inches) 0.874 ID (inches) 0.874

Flow (gpm) Friction loss (psi)

Flow (gpm)

Friction loss (psi)

1 0.0008 21 0.2293 2 0.0030 22 0.2499 3 0.0063 23 0.2713 4 0.0107 24 0.2935 5 0.0161 25 0.3165 6 0.0226 26 0.3403 7 0.0300 27 0.3649 8 0.0385 28 0.3903 9 0.0478 29 0.4165 10 0.0581 30 0.4435 11 0.0693 31 0.4712 12 0.0814 32 0.4997 13 0.0944 33 0.5290 14 0.1083 34 0.5590 15 0.1230 35 0.5898 16 0.1386 36 0.6214 17 0.1551 37 0.6537 18 0.1724 38 0.6868 19 0.1905 39 0.7206 20 0.2095 40 0.7551

127

Table 15. Friction loss - psi per lineal foot of pipe 1" pipe

Pipe Type Schedule 40 Schedule 10 CPVC Pipe

C Factor 100 120 100 120 150 ID (inches) 1.049 1.049 1.097 1.097 1.101 Flow (gpm) Friction loss (psi)

1 0.0007 0.0005 0.0006 0.0004 0.0003 2 0.0026 0.0018 0.0021 0.0015 0.0010 3 0.0055 0.0039 0.0044 0.0031 0.0020 4 0.0093 0.0066 0.0075 0.0053 0.0035 5 0.0140 0.0100 0.0113 0.0081 0.0052 6 0.0197 0.0140 0.0158 0.0113 0.0073 7 0.0261 0.0187 0.0210 0.0150 0.0098 8 0.0335 0.0239 0.0269 0.0192 0.0125 9 0.0416 0.0297 0.0335 0.0239 0.0155

10 0.0506 0.0361 0.0407 0.0290 0.0189 11 0.0603 0.0431 0.0485 0.0346 0.0225 12 0.0709 0.0506 0.0570 0.0407 0.0264 13 0.0822 0.0587 0.0661 0.0472 0.0307 14 0.0943 0.0673 0.0758 0.0541 0.0352 15 0.1071 0.0764 0.0861 0.0615 0.0400 16 0.1207 0.0861 0.0970 0.0693 0.0450 17 0.1350 0.0963 0.1086 0.0775 0.0504 18 0.1500 0.1071 0.1207 0.0861 0.0560 19 0.1658 0.1184 0.1334 0.0952 0.0619 20 0.1823 0.1301 0.1466 0.1047 0.0680 21 0.1996 0.1424 0.1605 0.1145 0.0745 22 0.2175 0.1552 0.1749 0.1248 0.0812 23 0.2361 0.1685 0.1899 0.1355 0.0881 24 0.2555 0.1823 0.2055 0.1466 0.0953 25 0.2755 0.1966 0.2216 0.1581 0.1028 26 0.2963 0.2114 0.2382 0.1700 0.1106 27 0.3177 0.2267 0.2555 0.1823 0.1185 28 0.3398 0.2425 0.2733 0.1950 0.1268

128




29 0.3626 0.2588 0.2916 0.2081 0.1353 30 0.3860 0.2755 0.3105 0.2216 0.1441 31 0.4102 0.2927 0.3299 0.2354 0.1531 32 0.4350 0.3105 0.3498 0.2497 0.1623 33 0.4605 0.3286 0.3703 0.2643 0.1718 34 0.4866 0.3473 0.3914 0.2793 0.1816 35 0.5134 0.3664 0.4129 0.2947 0.1916 36 0.5409 0.3860 0.4350 0.3105 0.2018 37 0.5690 0.4061 0.4576 0.3266 0.2123 38 0.5978 0.4267 0.4808 0.3431 0.2231 39 0.6272 0.4477 0.5044 0.3600 0.2341 40 0.6573 0.4691 0.5286 0.3773 0.2453 41 0.6880 0.4911 0.5533 0.3949 0.2568 42 0.7194 0.5134 0.5786 0.4129 0.2685 43 0.7514 0.5363 0.6043 0.4313 0.2804 44 0.7841 0.5596 0.6306 0.4500 0.2926 45 0.8173 0.5833 0.6573 0.4691 0.3050 46 0.8513 0.6075 0.6846 0.4886 0.3177 47 0.8858 0.6322 0.7124 0.5084 0.3306 48 0.9210 0.6573 0.7407 0.5286 0.3437 49 0.9568 0.6829 0.7695 0.5492 0.3570 50 0.9932 0.7089 0.7988 0.5701 0.3706 51 1.0303 0.7353 0.8286 0.5914 0.3845 52 1.0680 0.7622 0.8589 0.6130 0.3985 53 1.1063 0.7896 0.8897 0.6350 0.4128 54 1.1452 0.8173 0.9210 0.6573 0.4274 55 1.1848 0.8456 0.9528 0.6800 0.4421 56 1.2249 0.8742 0.9851 0.7031 0.4571

129




57 1.2657 0.9033 1.0179 0.7265 0.4723 58 1.3071 0.9329 1.0512 0.7502 0.4878 59 1.3491 0.9628 1.0849 0.7743 0.5034 60 1.3917 0.9932 1.1192 0.7988 0.5193 61 1.4349 1.0241 1.1540 0.8236 0.5355 62 1.4787 1.0554 1.1892 0.8487 0.5518 63 1.5231 1.0871 1.2249 0.8742 0.5684 64 1.5682 1.1192 1.2611 0.9001 0.5852 65 1.6138 1.1518 1.2978 0.9263 0.6022 66 1.6600 1.1848 1.3350 0.9528 0.6195 67 1.7069 1.2182 1.3727 0.9797 0.6369 68 1.7543 1.2520 1.4108 1.0069 0.6546 69 1.8023 1.2863 1.4494 1.0345 0.6726 70 1.8509 1.3210 1.4886 1.0624 0.6907

Table 15. Friction loss - psi per lineal foot of pipe

1-1/4" pipe


C Factor 100 120 100 120 150 ID (inches) 1.380 1.380 1.442 1.442 1.394


1 0.0002 0.0001 0.0002 0.0001 0.0001 2 0.0007 0.0005 0.0005 0.0004 0.0003 3 0.0014 0.0010 0.0012 0.0008 0.0006 4 0.0024 0.0017 0.0020 0.0014 0.0011 5 0.0037 0.0026 0.0030 0.0021 0.0017

130

Table 15. Friction loss - psi per lineal foot of pipe 1-1/4" pipe




6 0.0052 0.0037 0.0042 0.0030 0.0023 7 0.0069 0.0049 0.0056 0.0040 0.0031 8 0.0088 0.0063 0.0071 0.0051 0.0040 9 0.0109 0.0078 0.0088 0.0063 0.0049 10 0.0133 0.0095 0.0107 0.0077 0.0060 11 0.0159 0.0113 0.0128 0.0091 0.0071 12 0.0186 0.0133 0.0150 0.0107 0.0084 13 0.0216 0.0154 0.0174 0.0125 0.0097 14 0.0248 0.0177 0.0200 0.0143 0.0111 15 0.0282 0.0201 0.0227 0.0162 0.0127 16 0.0317 0.0226 0.0256 0.0183 0.0143 17 0.0355 0.0253 0.0287 0.0205 0.0160 18 0.0395 0.0282 0.0319 0.0227 0.0177 19 0.0436 0.0311 0.0352 0.0251 0.0196 20 0.0480 0.0342 0.0387 0.0276 0.0216 21 0.0525 0.0375 0.0424 0.0302 0.0236 22 0.0572 0.0408 0.0462 0.0330 0.0257 23 0.0621 0.0443 0.0501 0.0358 0.0279 24 0.0672 0.0480 0.0542 0.0387 0.0302 25 0.0725 0.0517 0.0585 0.0418 0.0326 26 0.0779 0.0556 0.0629 0.0449 0.0350 27 0.0836 0.0596 0.0675 0.0481 0.0376 28 0.0894 0.0638 0.0721 0.0515 0.0402 29 0.0954 0.0681 0.0770 0.0549 0.0429 30 0.1015 0.0725 0.0820 0.0585 0.0457 31 0.1079 0.0770 0.0871 0.0622 0.0485 32 0.1144 0.0817 0.0924 0.0659 0.0514

131





33 0.1211 0.0864 0.0978 0.0698 0.0545 34 0.1280 0.0913 0.1033 0.0737 0.0576 35 0.1350 0.0964 0.1090 0.0778 0.0607 36 0.1423 0.1015 0.1149 0.0820 0.0640 37 0.1497 0.1068 0.1208 0.0862 0.0673 38 0.1572 0.1122 0.1269 0.0906 0.0707 39 0.1650 0.1177 0.1332 0.0951 0.0742 40 0.1729 0.1234 0.1396 0.0996 0.0777 41 0.1810 0.1291 0.1461 0.1043 0.0814 42 0.1892 0.1350 0.1528 0.1090 0.0851 43 0.1976 0.1410 0.1595 0.1139 0.0889 44 0.2062 0.1472 0.1665 0.1188 0.0927 45 0.2150 0.1534 0.1735 0.1239 0.0967 46 0.2239 0.1598 0.1808 0.1290 0.1007 47 0.2330 0.1663 0.1881 0.1342 0.1048 48 0.2422 0.1729 0.1956 0.1396 0.1089 49 0.2516 0.1796 0.2032 0.1450 0.1132 50 0.2612 0.1864 0.2109 0.1505 0.1175 51 0.2710 0.1934 0.2188 0.1561 0.1218 52 0.2809 0.2005 0.2268 0.1618 0.1263 53 0.2910 0.2077 0.2349 0.1676 0.1308 54 0.3012 0.2150 0.2432 0.1735 0.1354 55 0.3116 0.2224 0.2516 0.1795 0.1401 56 0.3222 0.2299 0.2601 0.1856 0.1449 57 0.3329 0.2376 0.2687 0.1918 0.1497 58 0.3438 0.2453 0.2775 0.1981 0.1546 59 0.3548 0.2532 0.2865 0.2044 0.1595

132





60 0.3660 0.2612 0.2955 0.2109 0.1646 61 0.3774 0.2693 0.3047 0.2174 0.1697 62 0.3889 0.2776 0.3140 0.2241 0.1749 63 0.4006 0.2859 0.3234 0.2308 0.1801 64 0.4124 0.2944 0.3330 0.2376 0.1855 65 0.4244 0.3029 0.3427 0.2446 0.1909 66 0.4366 0.3116 0.3525 0.2516 0.1963 67 0.4489 0.3204 0.3624 0.2587 0.2019 68 0.4614 0.3293 0.3725 0.2658 0.2075 69 0.4740 0.3383 0.3827 0.2731 0.2131 70 0.4868 0.3474 0.3930 0.2805 0.2189 71 0.4998 0.3567 0.4035 0.2880 0.2247 72 0.5129 0.3660 0.4140 0.2955 0.2306 73 0.5261 0.3755 0.4247 0.3031 0.2366 74 0.5395 0.3851 0.4356 0.3109 0.2426 75 0.5531 0.3947 0.4465 0.3187 0.2487 76 0.5668 0.4045 0.4576 0.3266 0.2549 77 0.5807 0.4144 0.4688 0.3346 0.2611 78 0.5947 0.4244 0.4801 0.3427 0.2674 79 0.6089 0.4346 0.4916 0.3508 0.2738 80 0.6232 0.4448 0.5031 0.3591 0.2802 81 0.6377 0.4551 0.5148 0.3674 0.2868 82 0.6524 0.4656 0.5267 0.3759 0.2933 83 0.6671 0.4761 0.5386 0.3844 0.3000 84 0.6821 0.4868 0.5507 0.3930 0.3067 85 0.6972 0.4976 0.5629 0.4017 0.3135 86 0.7124 0.5085 0.5752 0.4105 0.3204

133





87 0.7278 0.5195 0.5876 0.4194 0.3273 88 0.7434 0.5306 0.6002 0.4283 0.3343 89 0.7591 0.5418 0.6128 0.4374 0.3413 90 0.7750 0.5531 0.6256 0.4465 0.3485 91 0.7910 0.5645 0.6386 0.4557 0.3557 92 0.8071 0.5760 0.6516 0.4651 0.3629 93 0.8234 0.5877 0.6648 0.4744 0.3703 94 0.8399 0.5994 0.6781 0.4839 0.3777 95 0.8565 0.6113 0.6915 0.4935 0.3851 96 0.8732 0.6232 0.7050 0.5031 0.3927 97 0.8901 0.6353 0.7186 0.5129 0.4003 98 0.9072 0.6475 0.7324 0.5227 0.4079 99 0.9244 0.6597 0.7463 0.5326 0.4157 100 0.9417 0.6721 0.7603 0.5426 0.4235 101 0.9592 0.6846 0.7744 0.5527 0.4313 102 0.9769 0.6972 0.7887 0.5629 0.4393 103 0.9947 0.7099 0.8030 0.5731 0.4473 104 1.0126 0.7227 0.8175 0.5835 0.4553 105 1.0307 0.7356 0.8321 0.5939 0.4635 106 1.0489 0.7486 0.8468 0.6044 0.4717 107 1.0673 0.7617 0.8617 0.6150 0.4799 108 1.0858 0.7750 0.8766 0.6256 0.4883 109 1.1045 0.7883 0.8917 0.6364 0.4966 110 1.1233 0.8017 0.9069 0.6472 0.5051 111 1.1423 0.8152 0.9222 0.6582 0.5136 112 1.1614 0.8289 0.9376 0.6692 0.5222 113 1.1807 0.8426 0.9532 0.6803 0.5309

134





114 1.2001 0.8565 0.9688 0.6915 0.5396 115 1.2196 0.8704 0.9846 0.7027 0.5484 116 1.2393 0.8845 1.0005 0.7141 0.5573 117 1.2591 0.8986 1.0165 0.7255 0.5662 118 1.2791 0.9129 1.0327 0.7370 0.5752 119 1.2992 0.9273 1.0489 0.7486 0.5842 120 1.3195 0.9417 1.0653 0.7603 0.5933 121 1.3399 0.9563 1.0818 0.7720 0.6025 122 1.3605 0.9710 1.0984 0.7839 0.6118 123 1.3812 0.9857 1.1151 0.7958 0.6211 124 1.4020 1.0006 1.1319 0.8078 0.6304 125 1.4230 1.0156 1.1488 0.8199 0.6399 126 1.4442 1.0307 1.1659 0.8321 0.6494 127 1.4654 1.0459 1.1831 0.8444 0.6589 128 1.4868 1.0612 1.2004 0.8567 0.6686 129 1.5084 1.0765 1.2178 0.8691 0.6783 130 1.5301 1.0920 1.2353 0.8816 0.6880 131 1.5520 1.1076 1.2529 0.8942 0.6978 132 1.5739 1.1233 1.2707 0.9069 0.7077 133 1.5961 1.1391 1.2886 0.9196 0.7177 134 1.6183 1.1550 1.3065 0.9325 0.7277 135 1.6408 1.1710 1.3246 0.9454 0.7378 136 1.6633 1.1871 1.3428 0.9584 0.7479 137 1.6860 1.2033 1.3612 0.9715 0.7581 138 1.7088 1.2196 1.3796 0.9846 0.7684 139 1.7318 1.2360 1.3982 0.9979 0.7787 140 1.7549 1.2525 1.4168 1.0112 0.7891

135





141 1.7782 1.2691 1.4356 1.0246 0.7996 142 1.8016 1.2858 1.4545 1.0381 0.8101 143 1.8252 1.3026 1.4735 1.0516 0.8207 144 1.8488 1.3195 1.4926 1.0653 0.8313 145 1.8727 1.3365 1.5118 1.0790 0.8421


1-1/2" pipe




1 0.0001 0.0001 0.0001 0.0001 0.0000 2 0.0003 0.0002 0.0003 0.0002 0.0002 3 0.0007 0.0005 0.0005 0.0004 0.0003 4 0.0012 0.0008 0.0009 0.0007 0.0006 5 0.0017 0.0012 0.0014 0.0010 0.0009 6 0.0024 0.0017 0.0020 0.0014 0.0012 7 0.0032 0.0023 0.0026 0.0019 0.0016 8 0.0042 0.0030 0.0034 0.0024 0.0020 9 0.0052 0.0037 0.0042 0.0030 0.0025 10 0.0063 0.0045 0.0051 0.0036 0.0031 11 0.0075 0.0053 0.0061 0.0043 0.0037 12 0.0088 0.0063 0.0071 0.0051 0.0043 13 0.0102 0.0073 0.0082 0.0059 0.0050 14 0.0117 0.0084 0.0095 0.0067 0.0057

136





15 0.0133 0.0095 0.0107 0.0077 0.0065 16 0.0150 0.0107 0.0121 0.0086 0.0073 17 0.0168 0.0120 0.0135 0.0097 0.0082 18 0.0186 0.0133 0.0151 0.0107 0.0091 19 0.0206 0.0147 0.0166 0.0119 0.0101 20 0.0226 0.0162 0.0183 0.0131 0.0111 21 0.0248 0.0177 0.0200 0.0143 0.0121 22 0.0270 0.0193 0.0218 0.0156 0.0132 23 0.0293 0.0209 0.0237 0.0169 0.0144 24 0.0317 0.0226 0.0256 0.0183 0.0155 25 0.0342 0.0244 0.0276 0.0197 0.0168 26 0.0368 0.0262 0.0297 0.0212 0.0180 27 0.0394 0.0281 0.0319 0.0227 0.0193 28 0.0422 0.0301 0.0341 0.0243 0.0207 29 0.0450 0.0321 0.0364 0.0260 0.0220 30 0.0479 0.0342 0.0387 0.0276 0.0235 31 0.0509 0.0363 0.0412 0.0294 0.0249 32 0.0540 0.0385 0.0436 0.0311 0.0265 33 0.0572 0.0408 0.0462 0.0330 0.0280 34 0.0604 0.0431 0.0488 0.0348 0.0296 35 0.0637 0.0455 0.0515 0.0368 0.0312 36 0.0672 0.0479 0.0543 0.0387 0.0329 37 0.0706 0.0504 0.0571 0.0407 0.0346 38 0.0742 0.0530 0.0600 0.0428 0.0364 39 0.0779 0.0556 0.0629 0.0449 0.0381 40 0.0816 0.0582 0.0659 0.0471 0.0400 41 0.0854 0.0610 0.0690 0.0493 0.0418

137





42 0.0893 0.0637 0.0722 0.0515 0.0437 43 0.0933 0.0666 0.0754 0.0538 0.0457 44 0.0973 0.0695 0.0787 0.0561 0.0477 45 0.1015 0.0724 0.0820 0.0585 0.0497 46 0.1057 0.0754 0.0854 0.0610 0.0518 47 0.1100 0.0785 0.0889 0.0634 0.0539 48 0.1143 0.0816 0.0924 0.0659 0.0560 49 0.1188 0.0848 0.0960 0.0685 0.0582 50 0.1233 0.0880 0.0996 0.0711 0.0604 51 0.1279 0.0913 0.1034 0.0738 0.0627 52 0.1326 0.0946 0.1071 0.0765 0.0649 53 0.1373 0.0980 0.1110 0.0792 0.0673 54 0.1422 0.1015 0.1149 0.0820 0.0696 55 0.1471 0.1050 0.1189 0.0848 0.0720 56 0.1521 0.1085 0.1229 0.0877 0.0745 57 0.1571 0.1121 0.1270 0.0906 0.0770 58 0.1623 0.1158 0.1311 0.0936 0.0795 59 0.1675 0.1195 0.1353 0.0966 0.0820 60 0.1728 0.1233 0.1396 0.0996 0.0846 61 0.1781 0.1271 0.1440 0.1027 0.0873 62 0.1836 0.1310 0.1484 0.1059 0.0899 63 0.1891 0.1350 0.1528 0.1091 0.0926 64 0.1947 0.1389 0.1573 0.1123 0.0954 65 0.2003 0.1430 0.1619 0.1156 0.0981 66 0.2061 0.1471 0.1665 0.1189 0.1010 67 0.2119 0.1512 0.1712 0.1222 0.1038 68 0.2178 0.1554 0.1760 0.1256 0.1067

138





69 0.2238 0.1597 0.1808 0.1290 0.1096 70 0.2298 0.1640 0.1857 0.1325 0.1126 71 0.2359 0.1684 0.1906 0.1361 0.1156 72 0.2421 0.1728 0.1956 0.1396 0.1186 73 0.2483 0.1772 0.2007 0.1432 0.1216 74 0.2547 0.1818 0.2058 0.1469 0.1247 75 0.2611 0.1863 0.2110 0.1506 0.1279 76 0.2675 0.1909 0.2162 0.1543 0.1311 77 0.2741 0.1956 0.2215 0.1581 0.1343 78 0.2807 0.2003 0.2269 0.1619 0.1375 79 0.2874 0.2051 0.2323 0.1658 0.1408 80 0.2942 0.2100 0.2377 0.1697 0.1441 81 0.3010 0.2148 0.2433 0.1736 0.1475 82 0.3079 0.2198 0.2488 0.1776 0.1508 83 0.3149 0.2248 0.2545 0.1816 0.1543 84 0.3220 0.2298 0.2602 0.1857 0.1577 85 0.3291 0.2349 0.2659 0.1898 0.1612 86 0.3363 0.2400 0.2718 0.1940 0.1647 87 0.3436 0.2452 0.2776 0.1981 0.1683 88 0.3509 0.2504 0.2836 0.2024 0.1719 89 0.3583 0.2557 0.2896 0.2067 0.1755 90 0.3658 0.2611 0.2956 0.2110 0.1792 91 0.3734 0.2665 0.3017 0.2153 0.1829 92 0.3810 0.2719 0.3079 0.2197 0.1866 93 0.3887 0.2774 0.3141 0.2242 0.1904 94 0.3964 0.2829 0.3204 0.2286 0.1942 95 0.4043 0.2885 0.3267 0.2332 0.1980

139





96 0.4122 0.2942 0.3331 0.2377 0.2019 97 0.4202 0.2999 0.3395 0.2423 0.2058 98 0.4282 0.3056 0.3460 0.2470 0.2098 99 0.4363 0.3114 0.3526 0.2517 0.2137 100 0.4445 0.3173 0.3592 0.2564 0.2177 101 0.4528 0.3232 0.3659 0.2611 0.2218 102 0.4611 0.3291 0.3726 0.2659 0.2259 103 0.4695 0.3351 0.3794 0.2708 0.2300 104 0.4780 0.3411 0.3863 0.2757 0.2341 105 0.4865 0.3472 0.3932 0.2806 0.2383 106 0.4951 0.3534 0.4001 0.2856 0.2425 107 0.5038 0.3596 0.4071 0.2906 0.2468 108 0.5125 0.3658 0.4142 0.2956 0.2511 109 0.5214 0.3721 0.4213 0.3007 0.2554 110 0.5302 0.3784 0.4285 0.3058 0.2597 111 0.5392 0.3848 0.4357 0.3110 0.2641 112 0.5482 0.3913 0.4430 0.3162 0.2685 113 0.5573 0.3977 0.4504 0.3214 0.2730 114 0.5665 0.4043 0.4578 0.3267 0.2775 115 0.5757 0.4109 0.4652 0.3320 0.2820 116 0.5850 0.4175 0.4727 0.3374 0.2865 117 0.5943 0.4242 0.4803 0.3428 0.2911 118 0.6038 0.4309 0.4879 0.3482 0.2958 119 0.6133 0.4377 0.4956 0.3537 0.3004 120 0.6228 0.4445 0.5033 0.3592 0.3051 121 0.6325 0.4514 0.5111 0.3648 0.3098 122 0.6422 0.4583 0.5190 0.3704 0.3146

140





123 0.6520 0.4653 0.5269 0.3760 0.3194 124 0.6618 0.4723 0.5348 0.3817 0.3242 125 0.6717 0.4794 0.5428 0.3874 0.3290 126 0.6817 0.4865 0.5509 0.3932 0.3339 127 0.6917 0.4937 0.5590 0.3989 0.3388 128 0.7018 0.5009 0.5672 0.4048 0.3438 129 0.7120 0.5082 0.5754 0.4106 0.3488 130 0.7223 0.5155 0.5837 0.4166 0.3538 131 0.7326 0.5228 0.5920 0.4225 0.3588 132 0.7429 0.5302 0.6004 0.4285 0.3639 133 0.7534 0.5377 0.6088 0.4345 0.3690 134 0.7639 0.5452 0.6173 0.4406 0.3742 135 0.7745 0.5527 0.6259 0.4467 0.3794 136 0.7851 0.5603 0.6345 0.4528 0.3846 137 0.7958 0.5680 0.6431 0.4590 0.3898 138 0.8066 0.5757 0.6518 0.4652 0.3951 139 0.8175 0.5834 0.6606 0.4715 0.4004 140 0.8284 0.5912 0.6694 0.4778 0.4058 141 0.8394 0.5991 0.6783 0.4841 0.4112 142 0.8504 0.6069 0.6872 0.4905 0.4166 143 0.8615 0.6149 0.6962 0.4969 0.4220 144 0.8727 0.6228 0.7052 0.5033 0.4275 145 0.8839 0.6309 0.7143 0.5098 0.4330 146 0.8953 0.6389 0.7235 0.5163 0.4385 147 0.9066 0.6471 0.7327 0.5229 0.4441 148 0.9181 0.6552 0.7419 0.5295 0.4497 149 0.9296 0.6634 0.7512 0.5361 0.4553

141





150 0.9412 0.6717 0.7606 0.5428 0.4610 151 0.9528 0.6800 0.7700 0.5495 0.4667 152 0.9645 0.6884 0.7794 0.5563 0.4725 153 0.9763 0.6968 0.7889 0.5631 0.4782 154 0.9881 0.7052 0.7985 0.5699 0.4840 155 1.0000 0.7137 0.8081 0.5768 0.4899 156 1.0120 0.7223 0.8178 0.5837 0.4957 157 1.0240 0.7308 0.8275 0.5906 0.5016 158 1.0361 0.7395 0.8373 0.5976 0.5075 159 1.0483 0.7482 0.8471 0.6046 0.5135 160 1.0605 0.7569 0.8570 0.6116 0.5195 161 1.0728 0.7657 0.8669 0.6187 0.5255 162 1.0852 0.7745 0.8769 0.6259 0.5316 163 1.0976 0.7834 0.8870 0.6330 0.5376 164 1.1101 0.7923 0.8971 0.6402 0.5438 165 1.1226 0.8012 0.9072 0.6475 0.5499 166 1.1353 0.8102 0.9174 0.6548 0.5561 167 1.1479 0.8193 0.9277 0.6621 0.5623 168 1.1607 0.8284 0.9380 0.6694 0.5686 169 1.1735 0.8375 0.9483 0.6768 0.5748 170 1.1864 0.8467 0.9587 0.6842 0.5811 171 1.1993 0.8560 0.9692 0.6917 0.5875 172 1.2123 0.8652 0.9797 0.6992 0.5939 173 1.2254 0.8746 0.9903 0.7068 0.6003 174 1.2385 0.8839 1.0009 0.7143 0.6067 175 1.2517 0.8934 1.0115 0.7219 0.6132 176 1.2650 0.9028 1.0223 0.7296 0.6197

142





177 1.2783 0.9124 1.0330 0.7373 0.6262 178 1.2917 0.9219 1.0439 0.7450 0.6327 179 1.3052 0.9315 1.0547 0.7528 0.6393 180 1.3187 0.9412 1.0657 0.7606 0.6460 181 1.3323 0.9509 1.0766 0.7684 0.6526 182 1.3459 0.9606 1.0877 0.7763 0.6593 183 1.3597 0.9704 1.0988 0.7842 0.6660 184 1.3734 0.9802 1.1099 0.7921 0.6728 185 1.3873 0.9901 1.1211 0.8001 0.6795 186 1.4012 1.0000 1.1323 0.8081 0.6864 187 1.4152 1.0100 1.1436 0.8162 0.6932 188 1.4292 1.0200 1.1549 0.8243 0.7001 189 1.4433 1.0301 1.1663 0.8324 0.7070 190 1.4574 1.0402 1.1778 0.8406 0.7139 191 1.4717 1.0503 1.1893 0.8488 0.7209 192 1.4859 1.0605 1.2008 0.8570 0.7279 193 1.5003 1.0708 1.2124 0.8653 0.7349 194 1.5147 1.0810 1.2240 0.8736 0.7420 195 1.5292 1.0914 1.2357 0.8820 0.7491 196 1.5437 1.1018 1.2475 0.8903 0.7562 197 1.5583 1.1122 1.2593 0.8988 0.7633 198 1.5730 1.1226 1.2711 0.9072 0.7705 199 1.5877 1.1332 1.2831 0.9157 0.7777 200 1.6025 1.1437 1.2950 0.9242 0.7850 201 1.6174 1.1543 1.3070 0.9328 0.7923 202 1.6323 1.1650 1.3191 0.9414 0.7996 203 1.6473 1.1757 1.3312 0.9501 0.8069

143





204 1.6623 1.1864 1.3433 0.9587 0.8143 205 1.6774 1.1972 1.3555 0.9674 0.8217 206 1.6926 1.2080 1.3678 0.9762 0.8291 207 1.7078 1.2189 1.3801 0.9850 0.8366 208 1.7231 1.2298 1.3925 0.9938 0.8440 209 1.7385 1.2407 1.4049 1.0027 0.8516 210 1.7539 1.2517 1.4173 1.0115 0.8591 211 1.7694 1.2628 1.4298 1.0205 0.8667 212 1.7849 1.2739 1.4424 1.0294 0.8743 213 1.8005 1.2850 1.4550 1.0384 0.8820 214 1.8162 1.2962 1.4677 1.0475 0.8896 215 1.8319 1.3074 1.4804 1.0566 0.8973 216 1.8477 1.3187 1.4932 1.0657 0.9051 217 1.8636 1.3300 1.5060 1.0748 0.9129 218 1.8795 1.3414 1.5188 1.0840 0.9207 219 1.8955 1.3528 1.5317 1.0932 0.9285 220 1.9115 1.3642 1.5447 1.1025 0.9363 221 1.9276 1.3757 1.5577 1.1117 0.9442 222 1.9438 1.3873 1.5708 1.1211 0.9521 223 1.9600 1.3989 1.5839 1.1304 0.9601

144





1 0.0000 0.0000 0.0000 0.0000 0.0000 2 0.0001 0.0001 0.0001 0.0001 0.0001 3 0.0002 0.0001 0.0002 0.0001 0.0001 4 0.0003 0.0002 0.0003 0.0002 0.0002 5 0.0005 0.0004 0.0004 0.0003 0.0003 6 0.0007 0.0005 0.0006 0.0004 0.0004 7 0.0010 0.0007 0.0008 0.0006 0.0005 8 0.0012 0.0009 0.0010 0.0007 0.0007 9 0.0015 0.0011 0.0012 0.0009 0.0008 10 0.0019 0.0013 0.0015 0.0011 0.0010 11 0.0022 0.0016 0.0018 0.0013 0.0012 12 0.0026 0.0019 0.0021 0.0015 0.0014 13 0.0030 0.0022 0.0025 0.0018 0.0017 14 0.0035 0.0025 0.0028 0.0020 0.0019 15 0.0039 0.0028 0.0032 0.0023 0.0022 16 0.0044 0.0032 0.0036 0.0026 0.0024 17 0.0050 0.0035 0.0040 0.0029 0.0027 18 0.0055 0.0039 0.0045 0.0032 0.0030 19 0.0061 0.0044 0.0050 0.0035 0.0034 20 0.0067 0.0048 0.0054 0.0039 0.0037 21 0.0073 0.0052 0.0060 0.0043 0.0040 22 0.0080 0.0057 0.0065 0.0046 0.0044 23 0.0087 0.0062 0.0071 0.0050 0.0048 24 0.0094 0.0067 0.0076 0.0054 0.0052 25 0.0101 0.0072 0.0082 0.0059 0.0056 26 0.0109 0.0078 0.0089 0.0063 0.0060 27 0.0117 0.0083 0.0095 0.0068 0.0064

145





28 0.0125 0.0089 0.0102 0.0072 0.0069 29 0.0133 0.0095 0.0108 0.0077 0.0073 30 0.0142 0.0101 0.0115 0.0082 0.0078 31 0.0151 0.0108 0.0123 0.0087 0.0083 32 0.0160 0.0114 0.0130 0.0093 0.0088 33 0.0169 0.0121 0.0138 0.0098 0.0093 34 0.0179 0.0128 0.0145 0.0104 0.0098 35 0.0189 0.0135 0.0153 0.0109 0.0104 36 0.0199 0.0142 0.0162 0.0115 0.0109 37 0.0209 0.0149 0.0170 0.0121 0.0115 38 0.0220 0.0157 0.0179 0.0127 0.0121 39 0.0231 0.0165 0.0187 0.0134 0.0127 40 0.0242 0.0172 0.0196 0.0140 0.0133 41 0.0253 0.0181 0.0206 0.0147 0.0139 42 0.0265 0.0189 0.0215 0.0153 0.0146 43 0.0276 0.0197 0.0224 0.0160 0.0152 44 0.0288 0.0206 0.0234 0.0167 0.0159 45 0.0301 0.0214 0.0244 0.0174 0.0165 46 0.0313 0.0223 0.0254 0.0182 0.0172 47 0.0326 0.0232 0.0265 0.0189 0.0179 48 0.0339 0.0242 0.0275 0.0196 0.0186 49 0.0352 0.0251 0.0286 0.0204 0.0194 50 0.0365 0.0261 0.0297 0.0212 0.0201 51 0.0379 0.0270 0.0308 0.0220 0.0209 52 0.0393 0.0280 0.0319 0.0228 0.0216 53 0.0407 0.0290 0.0331 0.0236 0.0224 54 0.0421 0.0301 0.0342 0.0244 0.0232

146





55 0.0436 0.0311 0.0354 0.0253 0.0240 56 0.0450 0.0321 0.0366 0.0261 0.0248 57 0.0465 0.0332 0.0378 0.0270 0.0256 58 0.0481 0.0343 0.0391 0.0279 0.0265 59 0.0496 0.0354 0.0403 0.0288 0.0273 60 0.0512 0.0365 0.0416 0.0297 0.0282 61 0.0528 0.0377 0.0429 0.0306 0.0290 62 0.0544 0.0388 0.0442 0.0315 0.0299 63 0.0560 0.0400 0.0455 0.0325 0.0308 64 0.0577 0.0412 0.0469 0.0334 0.0317 65 0.0593 0.0423 0.0482 0.0344 0.0327 66 0.0610 0.0436 0.0496 0.0354 0.0336 67 0.0628 0.0448 0.0510 0.0364 0.0345 68 0.0645 0.0460 0.0524 0.0374 0.0355 69 0.0663 0.0473 0.0538 0.0384 0.0365 70 0.0681 0.0486 0.0553 0.0395 0.0375 71 0.0699 0.0499 0.0568 0.0405 0.0385 72 0.0717 0.0512 0.0583 0.0416 0.0395 73 0.0735 0.0525 0.0598 0.0427 0.0405 74 0.0754 0.0538 0.0613 0.0437 0.0415 75 0.0773 0.0552 0.0628 0.0448 0.0426 76 0.0792 0.0566 0.0644 0.0460 0.0436 77 0.0812 0.0579 0.0660 0.0471 0.0447 78 0.0831 0.0593 0.0676 0.0482 0.0458 79 0.0851 0.0608 0.0692 0.0494 0.0469 80 0.0871 0.0622 0.0708 0.0505 0.0480 81 0.0892 0.0636 0.0724 0.0517 0.0491

147





82 0.0912 0.0651 0.0741 0.0529 0.0502 83 0.0933 0.0666 0.0758 0.0541 0.0513 84 0.0954 0.0681 0.0775 0.0553 0.0525 85 0.0975 0.0696 0.0792 0.0565 0.0537 86 0.0996 0.0711 0.0809 0.0578 0.0548 87 0.1018 0.0726 0.0827 0.0590 0.0560 88 0.1039 0.0742 0.0844 0.0603 0.0572 89 0.1061 0.0757 0.0862 0.0615 0.0584 90 0.1083 0.0773 0.0880 0.0628 0.0596 91 0.1106 0.0789 0.0898 0.0641 0.0609 92 0.1128 0.0805 0.0917 0.0654 0.0621 93 0.1151 0.0822 0.0935 0.0668 0.0634 94 0.1174 0.0838 0.0954 0.0681 0.0646 95 0.1197 0.0855 0.0973 0.0694 0.0659 96 0.1221 0.0871 0.0992 0.0708 0.0672 97 0.1244 0.0888 0.1011 0.0722 0.0685 98 0.1268 0.0905 0.1031 0.0735 0.0698 99 0.1292 0.0922 0.1050 0.0749 0.0711 100 0.1317 0.0940 0.1070 0.0763 0.0725 101 0.1341 0.0957 0.1090 0.0778 0.0738 102 0.1366 0.0975 0.1110 0.0792 0.0752 103 0.1391 0.0992 0.1130 0.0806 0.0765 104 0.1416 0.1010 0.1150 0.0821 0.0779 105 0.1441 0.1028 0.1171 0.0836 0.0793 106 0.1466 0.1047 0.1192 0.0850 0.0807 107 0.1492 0.1065 0.1212 0.0865 0.0821 108 0.1518 0.1083 0.1233 0.0880 0.0836

148





109 0.1544 0.1102 0.1255 0.0895 0.0850 110 0.1570 0.1121 0.1276 0.0911 0.0864 111 0.1597 0.1140 0.1298 0.0926 0.0879 112 0.1624 0.1159 0.1319 0.0942 0.0894 113 0.1651 0.1178 0.1341 0.0957 0.0909 114 0.1678 0.1197 0.1363 0.0973 0.0924 115 0.1705 0.1217 0.1385 0.0989 0.0939 116 0.1733 0.1236 0.1408 0.1005 0.0954 117 0.1760 0.1256 0.1430 0.1021 0.0969 118 0.1788 0.1276 0.1453 0.1037 0.0984 119 0.1816 0.1296 0.1476 0.1053 0.1000 120 0.1845 0.1317 0.1499 0.1070 0.1015 121 0.1873 0.1337 0.1522 0.1086 0.1031 122 0.1902 0.1357 0.1545 0.1103 0.1047 123 0.1931 0.1378 0.1569 0.1120 0.1063 124 0.1960 0.1399 0.1593 0.1137 0.1079 125 0.1989 0.1420 0.1616 0.1154 0.1095 126 0.2019 0.1441 0.1640 0.1171 0.1111 127 0.2049 0.1462 0.1665 0.1188 0.1128 128 0.2079 0.1483 0.1689 0.1205 0.1144 129 0.2109 0.1505 0.1713 0.1223 0.1161 130 0.2139 0.1527 0.1738 0.1241 0.1178 131 0.2170 0.1548 0.1763 0.1258 0.1194 132 0.2200 0.1570 0.1788 0.1276 0.1211 133 0.2231 0.1592 0.1813 0.1294 0.1228 134 0.2262 0.1615 0.1838 0.1312 0.1245 135 0.2294 0.1637 0.1864 0.1330 0.1263

149





136 0.2325 0.1660 0.1889 0.1348 0.1280 137 0.2357 0.1682 0.1915 0.1367 0.1298 138 0.2389 0.1705 0.1941 0.1385 0.1315 139 0.2421 0.1728 0.1967 0.1404 0.1333 140 0.2453 0.1751 0.1994 0.1423 0.1351 141 0.2486 0.1774 0.2020 0.1442 0.1368 142 0.2519 0.1798 0.2047 0.1461 0.1386 143 0.2552 0.1821 0.2073 0.1480 0.1405 144 0.2585 0.1845 0.2100 0.1499 0.1423 145 0.2618 0.1868 0.2127 0.1518 0.1441 146 0.2651 0.1892 0.2154 0.1538 0.1460 147 0.2685 0.1916 0.2182 0.1557 0.1478 148 0.2719 0.1941 0.2209 0.1577 0.1497 149 0.2753 0.1965 0.2237 0.1597 0.1516 150 0.2787 0.1989 0.2265 0.1616 0.1534 151 0.2822 0.2014 0.2293 0.1636 0.1553 152 0.2857 0.2039 0.2321 0.1657 0.1573 153 0.2891 0.2064 0.2349 0.1677 0.1592 154 0.2926 0.2089 0.2378 0.1697 0.1611 155 0.2962 0.2114 0.2407 0.1718 0.1630 156 0.2997 0.2139 0.2435 0.1738 0.1650 157 0.3033 0.2165 0.2464 0.1759 0.1670 158 0.3069 0.2190 0.2493 0.1780 0.1689 159 0.3105 0.2216 0.2523 0.1800 0.1709 160 0.3141 0.2242 0.2552 0.1821 0.1729 161 0.3177 0.2268 0.2582 0.1843 0.1749 162 0.3214 0.2294 0.2612 0.1864 0.1769

150





163 0.3251 0.2320 0.2641 0.1885 0.1789 164 0.3288 0.2346 0.2671 0.1907 0.1810 165 0.3325 0.2373 0.2702 0.1928 0.1830 166 0.3362 0.2400 0.2732 0.1950 0.1851 167 0.3400 0.2426 0.2763 0.1972 0.1872 168 0.3438 0.2453 0.2793 0.1994 0.1892 169 0.3476 0.2480 0.2824 0.2016 0.1913 170 0.3514 0.2508 0.2855 0.2038 0.1934 171 0.3552 0.2535 0.2886 0.2060 0.1955 172 0.3591 0.2563 0.2918 0.2082 0.1977 173 0.3629 0.2590 0.2949 0.2105 0.1998 174 0.3668 0.2618 0.2981 0.2127 0.2019 175 0.3707 0.2646 0.3012 0.2150 0.2041 176 0.3747 0.2674 0.3044 0.2173 0.2062 177 0.3786 0.2702 0.3076 0.2196 0.2084 178 0.3826 0.2730 0.3109 0.2219 0.2106 179 0.3866 0.2759 0.3141 0.2242 0.2128 180 0.3906 0.2787 0.3174 0.2265 0.2150 181 0.3946 0.2816 0.3206 0.2288 0.2172 182 0.3986 0.2845 0.3239 0.2312 0.2194 183 0.4027 0.2874 0.3272 0.2335 0.2217 184 0.4068 0.2903 0.3305 0.2359 0.2239 185 0.4109 0.2932 0.3339 0.2383 0.2262 186 0.4150 0.2962 0.3372 0.2407 0.2284 187 0.4191 0.2991 0.3406 0.2431 0.2307 188 0.4233 0.3021 0.3439 0.2455 0.2330 189 0.4274 0.3051 0.3473 0.2479 0.2353

151





190 0.4316 0.3081 0.3507 0.2503 0.2376 191 0.4359 0.3111 0.3542 0.2528 0.2399 192 0.4401 0.3141 0.3576 0.2552 0.2423 193 0.4443 0.3171 0.3611 0.2577 0.2446 194 0.4486 0.3202 0.3645 0.2602 0.2470 195 0.4529 0.3232 0.3680 0.2626 0.2493 196 0.4572 0.3263 0.3715 0.2651 0.2517 197 0.4615 0.3294 0.3750 0.2676 0.2541 198 0.4659 0.3325 0.3785 0.2702 0.2565 199 0.4702 0.3356 0.3821 0.2727 0.2589 200 0.4746 0.3387 0.3857 0.2752 0.2613 205 0.4968 0.3546 0.4037 0.2881 0.2735 210 0.5194 0.3707 0.4221 0.3012 0.2859 215 0.5426 0.3872 0.4409 0.3146 0.2987 220 0.5661 0.4040 0.4600 0.3283 0.3116 225 0.5902 0.4212 0.4795 0.3422 0.3249 230 0.6146 0.4387 0.4994 0.3565 0.3384 235 0.6396 0.4565 0.5197 0.3709 0.3521 240 0.6650 0.4746 0.5404 0.3857 0.3661 245 0.6909 0.4931 0.5614 0.4006 0.3803 250 0.7172 0.5118 0.5827 0.4159 0.3948 255 0.7439 0.5309 0.6045 0.4314 0.4095 260 0.7711 0.5504 0.6266 0.4472 0.4245 265 0.7988 0.5701 0.6491 0.4632 0.4397 270 0.8269 0.5902 0.6719 0.4795 0.4552 275 0.8555 0.6105 0.6951 0.4961 0.4709 280 0.8844 0.6312 0.7187 0.5129 0.4869

152





285 0.9139 0.6522 0.7426 0.5300 0.5031 290 0.9438 0.6736 0.7669 0.5473 0.5195 295 0.9741 0.6952 0.7915 0.5649 0.5362 300 1.0049 0.7172 0.8165 0.5827 0.5532 305 1.0361 0.7394 0.8419 0.6008 0.5703 310 1.0677 0.7620 0.8676 0.6192 0.5878 315 1.0998 0.7849 0.8936 0.6378 0.6054 320 1.1323 0.8081 0.9201 0.6566 0.6233 325 1.1652 0.8316 0.9468 0.6758 0.6415 330 1.1986 0.8555 0.9740 0.6951 0.6598 335 1.2324 0.8796 1.0014 0.7147 0.6784 340 1.2667 0.9040 1.0293 0.7346 0.6973 345 1.3014 0.9288 1.0574 0.7547 0.7164 350 1.3365 0.9538 1.0860 0.7750 0.7357 355 1.3720 0.9792 1.1148 0.7957 0.7553 360 1.4080 1.0049 1.1441 0.8165 0.7751 365 1.4443 1.0308 1.1736 0.8376 0.7951 370 1.4812 1.0571 1.2035 0.8590 0.8154 375 1.5184 1.0837 1.2338 0.8806 0.8359 380 1.5561 1.1106 1.2644 0.9024 0.8566 385 1.5942 1.1378 1.2954 0.9245 0.8776 390 1.6327 1.1652 1.3267 0.9468 0.8988 395 1.6716 1.1930 1.3583 0.9694 0.9202 400 1.7110 1.2211 1.3903 0.9922 0.9419 405 1.7507 1.2495 1.4226 1.0153 0.9638

153





5 0.0002 0.0002 0.0002 0.0001 0.0001 10 0.0008 0.0006 0.0006 0.0004 0.0004 15 0.0017 0.0012 0.0012 0.0009 0.0009 20 0.0028 0.0020 0.0021 0.0015 0.0015 25 0.0043 0.0030 0.0031 0.0022 0.0022 30 0.0060 0.0043 0.0044 0.0031 0.0031 35 0.0079 0.0057 0.0058 0.0041 0.0041 40 0.0102 0.0073 0.0074 0.0053 0.0053 45 0.0126 0.0090 0.0092 0.0066 0.0065 50 0.0154 0.0110 0.0112 0.0080 0.0080 55 0.0183 0.0131 0.0134 0.0095 0.0095 60 0.0215 0.0154 0.0157 0.0112 0.0111 65 0.0250 0.0178 0.0182 0.0130 0.0129 70 0.0286 0.0204 0.0209 0.0149 0.0148 75 0.0325 0.0232 0.0237 0.0169 0.0168 80 0.0367 0.0262 0.0267 0.0191 0.0190 85 0.0410 0.0293 0.0299 0.0213 0.0212 90 0.0456 0.0325 0.0332 0.0237 0.0236 95 0.0504 0.0360 0.0367 0.0262 0.0261 100 0.0554 0.0395 0.0404 0.0288 0.0287 105 0.0606 0.0433 0.0442 0.0315 0.0314 110 0.0661 0.0472 0.0481 0.0344 0.0342 115 0.0718 0.0512 0.0523 0.0373 0.0371 120 0.0776 0.0554 0.0565 0.0404 0.0402 125 0.0837 0.0598 0.0610 0.0435 0.0433 130 0.0900 0.0642 0.0656 0.0468 0.0466 135 0.0965 0.0689 0.0703 0.0502 0.0500

154





140 0.1033 0.0737 0.0752 0.0537 0.0534 145 0.1102 0.0786 0.0803 0.0573 0.0570 150 0.1173 0.0837 0.0854 0.0610 0.0607 155 0.1246 0.0890 0.0908 0.0648 0.0645 160 0.1322 0.0943 0.0963 0.0687 0.0684 165 0.1399 0.0999 0.1019 0.0727 0.0724 170 0.1479 0.1055 0.1077 0.0769 0.0765 175 0.1560 0.1114 0.1136 0.0811 0.0808 180 0.1644 0.1173 0.1197 0.0854 0.0851 185 0.1729 0.1234 0.1260 0.0899 0.0895 190 0.1817 0.1296 0.1323 0.0944 0.0940 195 0.1906 0.1360 0.1388 0.0991 0.0987 200 0.1997 0.1426 0.1455 0.1038 0.1034 205 0.2091 0.1492 0.1523 0.1087 0.1082 210 0.2186 0.1560 0.1592 0.1136 0.1132 215 0.2283 0.1630 0.1663 0.1187 0.1182 220 0.2383 0.1700 0.1735 0.1239 0.1233 225 0.2484 0.1773 0.1809 0.1291 0.1286 230 0.2587 0.1846 0.1884 0.1345 0.1339 235 0.2692 0.1921 0.1961 0.1399 0.1393 240 0.2799 0.1997 0.2039 0.1455 0.1449 245 0.2907 0.2075 0.2118 0.1512 0.1505 250 0.3018 0.2154 0.2198 0.1569 0.1562 255 0.3131 0.2234 0.2281 0.1628 0.1621 260 0.3245 0.2316 0.2364 0.1687 0.1680 265 0.3362 0.2399 0.2449 0.1748 0.1740 270 0.3480 0.2484 0.2535 0.1809 0.1801

155





275 0.3600 0.2569 0.2622 0.1872 0.1864 280 0.3722 0.2657 0.2711 0.1935 0.1927 285 0.3846 0.2745 0.2802 0.1999 0.1991 290 0.3972 0.2835 0.2893 0.2065 0.2056 295 0.4100 0.2926 0.2986 0.2131 0.2122 300 0.4229 0.3018 0.3080 0.2198 0.2189 305 0.4360 0.3112 0.3176 0.2267 0.2257 310 0.4493 0.3207 0.3273 0.2336 0.2326 315 0.4628 0.3303 0.3371 0.2406 0.2396 320 0.4765 0.3401 0.3471 0.2477 0.2467 325 0.4904 0.3500 0.3572 0.2549 0.2538 330 0.5044 0.3600 0.3674 0.2622 0.2611 335 0.5187 0.3702 0.3778 0.2696 0.2685 340 0.5331 0.3805 0.3883 0.2771 0.2759 345 0.5477 0.3909 0.3989 0.2847 0.2835 350 0.5625 0.4014 0.4097 0.2924 0.2911 355 0.5774 0.4121 0.4206 0.3002 0.2989 360 0.5925 0.4229 0.4316 0.3080 0.3067 365 0.6079 0.4338 0.4428 0.3160 0.3146 370 0.6234 0.4449 0.4541 0.3241 0.3227 375 0.6390 0.4561 0.4655 0.3322 0.3308 380 0.6549 0.4674 0.4770 0.3404 0.3390 385 0.6709 0.4788 0.4887 0.3488 0.3473 390 0.6871 0.4904 0.5005 0.3572 0.3557 395 0.7035 0.5021 0.5124 0.3657 0.3641 400 0.7201 0.5139 0.5245 0.3743 0.3727 405 0.7368 0.5259 0.5367 0.3830 0.3814

156





410 0.7537 0.5379 0.5490 0.3918 0.3901 415 0.7708 0.5501 0.5615 0.4007 0.3990 420 0.7881 0.5625 0.5740 0.4097 0.4079 425 0.8055 0.5749 0.5868 0.4188 0.4170 430 0.8231 0.5875 0.5996 0.4279 0.4261 435 0.8409 0.6002 0.6126 0.4372 0.4353 440 0.8589 0.6130 0.6256 0.4465 0.4446 445 0.8771 0.6260 0.6389 0.4560 0.4540 450 0.8954 0.6390 0.6522 0.4655 0.4635 455 0.9139 0.6522 0.6657 0.4751 0.4730 460 0.9325 0.6655 0.6793 0.4848 0.4827 465 0.9514 0.6790 0.6930 0.4946 0.4924 470 0.9704 0.6926 0.7068 0.5045 0.5023 475 0.9896 0.7063 0.7208 0.5144 0.5122 480 1.0089 0.7201 0.7349 0.5245 0.5222 485 1.0284 0.7340 0.7491 0.5347 0.5323 490 1.0482 0.7481 0.7635 0.5449 0.5425 495 1.0680 0.7622 0.7780 0.5552 0.5528 500 1.0881 0.7766 0.7926 0.5656 0.5632 505 1.1083 0.7910 0.8073 0.5762 0.5737 510 1.1287 0.8055 0.8221 0.5868 0.5842 515 1.1492 0.8202 0.8371 0.5974 0.5949 520 1.1699 0.8350 0.8522 0.6082 0.6056 525 1.1908 0.8499 0.8674 0.6191 0.6164 530 1.2119 0.8649 0.8828 0.6300 0.6273 535 1.2331 0.8801 0.8982 0.6411 0.6383 540 1.2546 0.8954 0.9138 0.6522 0.6494

157





545 1.2761 0.9108 0.9295 0.6634 0.6605 550 1.2979 0.9263 0.9454 0.6747 0.6718 555 1.3198 0.9419 0.9613 0.6861 0.6831 560 1.3419 0.9577 0.9774 0.6976 0.6946 565 1.3641 0.9736 0.9936 0.7092 0.7061 570 1.3865 0.9896 1.0100 0.7208 0.7177 575 1.4091 1.0057 1.0264 0.7325 0.7294 580 1.4319 1.0219 1.0430 0.7444 0.7412 585 1.4548 1.0383 1.0597 0.7563 0.7530 590 1.4779 1.0548 1.0765 0.7683 0.7650 595 1.5011 1.0714 1.0934 0.7804 0.7770 600 1.5245 1.0881 1.1105 0.7926 0.7891 605 1.5481 1.1049 1.1277 0.8048 0.8013 610 1.5719 1.1219 1.1450 0.8172 0.8136 615 1.5958 1.1389 1.1624 0.8296 0.8260 620 1.6199 1.1561 1.1799 0.8421 0.8385 625 1.6441 1.1734 1.1976 0.8547 0.8510 630 1.6686 1.1908 1.2154 0.8674 0.8637 635 1.6931 1.2084 1.2333 0.8802 0.8764 640 1.7179 1.2261 1.2513 0.8931 0.8892 645 1.7428 1.2438 1.2695 0.9060 0.9021 650 1.7679 1.2617 1.2877 0.9191 0.9151

158





10 0.0003 0.0002 0.0002 0.0001 0.0002 20 0.0010 0.0007 0.0007 0.0005 0.0006 30 0.0021 0.0015 0.0015 0.0011 0.0012 40 0.0035 0.0025 0.0026 0.0019 0.0020 50 0.0053 0.0038 0.0040 0.0028 0.0031 60 0.0075 0.0053 0.0056 0.0040 0.0043 70 0.0099 0.0071 0.0074 0.0053 0.0057 80 0.0127 0.0091 0.0095 0.0068 0.0073 90 0.0158 0.0113 0.0118 0.0084 0.0091 100 0.0192 0.0137 0.0143 0.0102 0.0110 110 0.0229 0.0164 0.0171 0.0122 0.0131 120 0.0270 0.0192 0.0201 0.0143 0.0154 130 0.0313 0.0223 0.0233 0.0166 0.0179 140 0.0359 0.0256 0.0267 0.0190 0.0205 150 0.0407 0.0291 0.0303 0.0216 0.0233 160 0.0459 0.0328 0.0341 0.0244 0.0262 170 0.0513 0.0366 0.0382 0.0273 0.0294 180 0.0571 0.0407 0.0425 0.0303 0.0326 190 0.0631 0.0450 0.0469 0.0335 0.0361 200 0.0694 0.0495 0.0516 0.0368 0.0396 210 0.0759 0.0542 0.0565 0.0403 0.0434 220 0.0827 0.0590 0.0616 0.0439 0.0473 230 0.0898 0.0641 0.0668 0.0477 0.0513 240 0.0972 0.0694 0.0723 0.0516 0.0556 250 0.1048 0.0748 0.0780 0.0557 0.0599 260 0.1127 0.0804 0.0838 0.0598 0.0644 270 0.1208 0.0862 0.0899 0.0642 0.0691

159





280 0.1292 0.0922 0.0962 0.0686 0.0739 290 0.1379 0.0984 0.1026 0.0732 0.0788 300 0.1468 0.1048 0.1093 0.0780 0.0839 310 0.1560 0.1113 0.1161 0.0829 0.0892 320 0.1655 0.1181 0.1231 0.0879 0.0946 330 0.1751 0.1250 0.1303 0.0930 0.1001 340 0.1851 0.1321 0.1377 0.0983 0.1058 350 0.1953 0.1394 0.1453 0.1037 0.1117 360 0.2057 0.1468 0.1531 0.1093 0.1176 370 0.2164 0.1545 0.1610 0.1149 0.1237 380 0.2274 0.1623 0.1692 0.1207 0.1300 390 0.2386 0.1703 0.1775 0.1267 0.1364 400 0.2500 0.1784 0.1860 0.1328 0.1429 410 0.2617 0.1868 0.1947 0.1390 0.1496 420 0.2736 0.1953 0.2036 0.1453 0.1564 430 0.2858 0.2040 0.2127 0.1518 0.1634 440 0.2982 0.2128 0.2219 0.1584 0.1705 450 0.3109 0.2219 0.2313 0.1651 0.1777 460 0.3238 0.2311 0.2409 0.1719 0.1851 470 0.3369 0.2405 0.2507 0.1789 0.1926 480 0.3503 0.2500 0.2607 0.1860 0.2003 490 0.3639 0.2597 0.2708 0.1933 0.2081 500 0.3778 0.2696 0.2811 0.2006 0.2160 510 0.3919 0.2797 0.2916 0.2081 0.2240 520 0.4062 0.2899 0.3023 0.2157 0.2322 530 0.4208 0.3003 0.3131 0.2235 0.2406 540 0.4356 0.3109 0.3241 0.2313 0.2490

160





550 0.4506 0.3216 0.3353 0.2393 0.2576 560 0.4659 0.3325 0.3467 0.2474 0.2664 570 0.4814 0.3436 0.3582 0.2557 0.2752 580 0.4972 0.3548 0.3699 0.2640 0.2842 590 0.5131 0.3662 0.3818 0.2725 0.2934 600 0.5293 0.3778 0.3939 0.2811 0.3026 610 0.5458 0.3895 0.4061 0.2898 0.3120 620 0.5624 0.4014 0.4185 0.2987 0.3216 630 0.5793 0.4135 0.4311 0.3077 0.3312 640 0.5965 0.4257 0.4438 0.3167 0.3410 650 0.6138 0.4381 0.4567 0.3260 0.3509 660 0.6314 0.4506 0.4698 0.3353 0.3610 670 0.6492 0.4633 0.4831 0.3448 0.3712 680 0.6673 0.4762 0.4965 0.3543 0.3815 690 0.6855 0.4893 0.5101 0.3640 0.3919 700 0.7040 0.5025 0.5238 0.3739 0.4025 710 0.7227 0.5158 0.5378 0.3838 0.4132 720 0.7417 0.5293 0.5519 0.3939 0.4240 730 0.7609 0.5430 0.5661 0.4040 0.4350 740 0.7802 0.5569 0.5806 0.4143 0.4461 750 0.7999 0.5709 0.5952 0.4248 0.4573 760 0.8197 0.5850 0.6099 0.4353 0.4686 770 0.8398 0.5993 0.6249 0.4460 0.4801 780 0.8601 0.6138 0.6399 0.4567 0.4917 790 0.8806 0.6285 0.6552 0.4676 0.5034 800 0.9013 0.6433 0.6706 0.4786 0.5153 810 0.9223 0.6582 0.6862 0.4898 0.5273

161





820 0.9434 0.6733 0.7020 0.5010 0.5394 830 0.9648 0.6886 0.7179 0.5124 0.5516 840 0.9864 0.7040 0.7340 0.5238 0.5640 850 1.0083 0.7196 0.7502 0.5354 0.5764 860 1.0303 0.7353 0.7666 0.5471 0.5891 870 1.0526 0.7512 0.7832 0.5590 0.6018 880 1.0751 0.7673 0.7999 0.5709 0.6147 890 1.0978 0.7835 0.8168 0.5830 0.6276 900 1.1207 0.7999 0.8339 0.5952 0.6407 910 1.1439 0.8164 0.8511 0.6074 0.6540 920 1.1672 0.8331 0.8685 0.6199 0.6673 930 1.1908 0.8499 0.8861 0.6324 0.6808 940 1.2146 0.8669 0.9038 0.6450 0.6944 950 1.2386 0.8840 0.9216 0.6578 0.7081 960 1.2629 0.9013 0.9397 0.6706 0.7220 970 1.2873 0.9187 0.9578 0.6836 0.7360 980 1.3120 0.9363 0.9762 0.6967 0.7501 990 1.3368 0.9541 0.9947 0.7099 0.7643 1000 1.3619 0.9720 1.0134 0.7232 0.7786 1010 1.3872 0.9901 1.0322 0.7367 0.7931 1020 1.4127 1.0083 1.0512 0.7502 0.8077 1030 1.4385 1.0266 1.0703 0.7639 0.8224 1040 1.4644 1.0452 1.0896 0.7777 0.8372 1050 1.4906 1.0638 1.1091 0.7916 0.8522 1060 1.5169 1.0826 1.1287 0.8056 0.8673 1070 1.5435 1.1016 1.1485 0.8197 0.8825 1080 1.5703 1.1207 1.1684 0.8339 0.8978

162





1090 1.5973 1.1400 1.1885 0.8482 0.9132 1100 1.6245 1.1594 1.2088 0.8627 0.9288 1110 1.6520 1.1790 1.2292 0.8773 0.9445 1120 1.6796 1.1987 1.2497 0.8919 0.9603 1130 1.7074 1.2186 1.2705 0.9067 0.9762 1140 1.7355 1.2386 1.2913 0.9216 0.9922 1150 1.7638 1.2588 1.3124 0.9366 1.0084


Pipe Type Schedule 40 Schedule 10 C Factor 100 120 100 120

ID (inches) 4.026 4.026 4.260 4.260 Flow (gpm) Friction loss (psi)

10 0.0001 0.0001 0.0001 0.0000 20 0.0003 0.0002 0.0002 0.0001 30 0.0006 0.0004 0.0004 0.0003 40 0.0009 0.0007 0.0007 0.0005 50 0.0014 0.0010 0.0011 0.0008 60 0.0020 0.0014 0.0015 0.0011 70 0.0026 0.0019 0.0020 0.0014 80 0.0034 0.0024 0.0026 0.0018 90 0.0042 0.0030 0.0032 0.0023 100 0.0051 0.0037 0.0039 0.0028 110 0.0061 0.0044 0.0046 0.0033 120 0.0072 0.0051 0.0055 0.0039

163




130 0.0083 0.0059 0.0063 0.0045 140 0.0095 0.0068 0.0072 0.0052 150 0.0108 0.0077 0.0082 0.0059 160 0.0122 0.0087 0.0093 0.0066 170 0.0137 0.0098 0.0104 0.0074 180 0.0152 0.0108 0.0115 0.0082 190 0.0168 0.0120 0.0128 0.0091 200 0.0185 0.0132 0.0140 0.0100 210 0.0202 0.0144 0.0153 0.0110 220 0.0220 0.0157 0.0167 0.0119 230 0.0239 0.0171 0.0182 0.0130 240 0.0259 0.0185 0.0196 0.0140 250 0.0279 0.0199 0.0212 0.0151 260 0.0300 0.0214 0.0228 0.0163 270 0.0322 0.0230 0.0244 0.0174 280 0.0344 0.0246 0.0261 0.0186 290 0.0367 0.0262 0.0279 0.0199 300 0.0391 0.0279 0.0297 0.0212 310 0.0415 0.0296 0.0315 0.0225 320 0.0440 0.0314 0.0335 0.0239 330 0.0466 0.0333 0.0354 0.0253 340 0.0493 0.0352 0.0374 0.0267 350 0.0520 0.0371 0.0395 0.0282 360 0.0548 0.0391 0.0416 0.0297 370 0.0576 0.0411 0.0438 0.0312 380 0.0605 0.0432 0.0460 0.0328 390 0.0635 0.0453 0.0482 0.0344 400 0.0666 0.0475 0.0506 0.0361 410 0.0697 0.0497 0.0529 0.0378

164




420 0.0728 0.0520 0.0553 0.0395 430 0.0761 0.0543 0.0578 0.0412 440 0.0794 0.0567 0.0603 0.0430 450 0.0828 0.0591 0.0629 0.0449 460 0.0862 0.0615 0.0655 0.0467 470 0.0897 0.0640 0.0681 0.0486 480 0.0933 0.0666 0.0708 0.0506 490 0.0969 0.0691 0.0736 0.0525 500 0.1006 0.0718 0.0764 0.0545 510 0.1043 0.0745 0.0792 0.0566 520 0.1081 0.0772 0.0821 0.0586 530 0.1120 0.0800 0.0851 0.0607 540 0.1160 0.0828 0.0881 0.0629 550 0.1200 0.0856 0.0911 0.0650 560 0.1240 0.0885 0.0942 0.0672 570 0.1282 0.0915 0.0973 0.0695 580 0.1324 0.0945 0.1005 0.0717 590 0.1366 0.0975 0.1038 0.0740 600 0.1409 0.1006 0.1070 0.0764 610 0.1453 0.1037 0.1104 0.0788 620 0.1497 0.1069 0.1137 0.0812 630 0.1542 0.1101 0.1171 0.0836 640 0.1588 0.1133 0.1206 0.0861 650 0.1634 0.1166 0.1241 0.0886 660 0.1681 0.1200 0.1277 0.0911 670 0.1728 0.1234 0.1313 0.0937 680 0.1776 0.1268 0.1349 0.0963 690 0.1825 0.1303 0.1386 0.0989 700 0.1874 0.1338 0.1423 0.1016

165




710 0.1924 0.1373 0.1461 0.1043 720 0.1975 0.1409 0.1500 0.1070 730 0.2026 0.1446 0.1538 0.1098 740 0.2077 0.1483 0.1578 0.1126 750 0.2129 0.1520 0.1617 0.1154 760 0.2182 0.1557 0.1657 0.1183 770 0.2236 0.1596 0.1698 0.1212 780 0.2290 0.1634 0.1739 0.1241 790 0.2344 0.1673 0.1780 0.1271 800 0.2399 0.1713 0.1822 0.1301 810 0.2455 0.1752 0.1865 0.1331 820 0.2512 0.1793 0.1908 0.1361 830 0.2569 0.1833 0.1951 0.1392 840 0.2626 0.1874 0.1994 0.1423 850 0.2684 0.1916 0.2039 0.1455 860 0.2743 0.1958 0.2083 0.1487 870 0.2802 0.2000 0.2128 0.1519 880 0.2862 0.2043 0.2174 0.1551 890 0.2923 0.2086 0.2220 0.1584 900 0.2984 0.2129 0.2266 0.1617 910 0.3045 0.2173 0.2313 0.1651 920 0.3107 0.2218 0.2360 0.1684 930 0.3170 0.2263 0.2408 0.1718 940 0.3234 0.2308 0.2456 0.1753 950 0.3298 0.2353 0.2504 0.1787 960 0.3362 0.2399 0.2553 0.1822 970 0.3427 0.2446 0.2603 0.1858 980 0.3493 0.2493 0.2653 0.1893 990 0.3559 0.2540 0.2703 0.1929

166




1000 0.3626 0.2588 0.2754 0.1965 1010 0.3693 0.2636 0.2805 0.2002 1020 0.3761 0.2684 0.2856 0.2039 1030 0.3830 0.2733 0.2908 0.2076 1040 0.3899 0.2782 0.2961 0.2113 1050 0.3968 0.2832 0.3014 0.2151 1060 0.4038 0.2882 0.3067 0.2189 1070 0.4109 0.2933 0.3121 0.2227 1080 0.4181 0.2984 0.3175 0.2266 1090 0.4252 0.3035 0.3230 0.2305 1100 0.4325 0.3087 0.3285 0.2344 1110 0.4398 0.3139 0.3340 0.2384 1120 0.4472 0.3191 0.3396 0.2424 1130 0.4546 0.3244 0.3452 0.2464 1140 0.4620 0.3298 0.3509 0.2504 1150 0.4696 0.3351 0.3566 0.2545 1160 0.4771 0.3405 0.3624 0.2586 1170 0.4848 0.3460 0.3682 0.2628 1180 0.4925 0.3515 0.3740 0.2669 1190 0.5002 0.3570 0.3799 0.2711 1200 0.5080 0.3626 0.3858 0.2754 1210 0.5159 0.3682 0.3918 0.2796 1220 0.5238 0.3738 0.3978 0.2839 1230 0.5318 0.3795 0.4039 0.2882 1240 0.5398 0.3853 0.4100 0.2926 1250 0.5479 0.3910 0.4161 0.2970 1260 0.5560 0.3968 0.4223 0.3014 1270 0.5642 0.4027 0.4285 0.3058 1280 0.5725 0.4086 0.4348 0.3103

167




1290 0.5808 0.4145 0.4411 0.3148 1300 0.5891 0.4204 0.4474 0.3193


5" pipe Pipe Type Schedule 40 Schedule 10 C Factor 100 120 100 120


10 0.0000 0.0000 0.0000 0.0000 20 0.0001 0.0001 0.0001 0.0000 30 0.0002 0.0001 0.0001 0.0001 40 0.0003 0.0002 0.0002 0.0002 50 0.0005 0.0003 0.0004 0.0003 60 0.0007 0.0005 0.0005 0.0004 70 0.0009 0.0006 0.0007 0.0005 80 0.0011 0.0008 0.0009 0.0006 90 0.0014 0.0010 0.0011 0.0008 100 0.0017 0.0012 0.0013 0.0010 110 0.0020 0.0015 0.0016 0.0011 120 0.0024 0.0017 0.0019 0.0013 130 0.0028 0.0020 0.0022 0.0016 140 0.0032 0.0023 0.0025 0.0018 150 0.0036 0.0026 0.0029 0.0020 160 0.0041 0.0029 0.0032 0.0023 170 0.0045 0.0032 0.0036 0.0026 180 0.0051 0.0036 0.0040 0.0029 190 0.0056 0.0040 0.0044 0.0032 200 0.0061 0.0044 0.0049 0.0035

168




210 0.0067 0.0048 0.0053 0.0038 220 0.0073 0.0052 0.0058 0.0041 230 0.0080 0.0057 0.0063 0.0045 240 0.0086 0.0061 0.0068 0.0049 250 0.0093 0.0066 0.0073 0.0052 260 0.0100 0.0071 0.0079 0.0056 270 0.0107 0.0076 0.0085 0.0060 280 0.0114 0.0082 0.0091 0.0065 290 0.0122 0.0087 0.0097 0.0069 300 0.0130 0.0093 0.0103 0.0073 310 0.0138 0.0099 0.0109 0.0078 320 0.0147 0.0105 0.0116 0.0083 330 0.0155 0.0111 0.0123 0.0088 340 0.0164 0.0117 0.0130 0.0093 350 0.0173 0.0123 0.0137 0.0098 360 0.0182 0.0130 0.0144 0.0103 370 0.0192 0.0137 0.0152 0.0108 380 0.0201 0.0144 0.0159 0.0114 390 0.0211 0.0151 0.0167 0.0119 400 0.0221 0.0158 0.0175 0.0125 410 0.0232 0.0165 0.0183 0.0131 420 0.0242 0.0173 0.0192 0.0137 430 0.0253 0.0181 0.0200 0.0143 440 0.0264 0.0188 0.0209 0.0149 450 0.0275 0.0196 0.0218 0.0156 460 0.0287 0.0205 0.0227 0.0162 470 0.0298 0.0213 0.0236 0.0169 480 0.0310 0.0221 0.0246 0.0175 490 0.0322 0.0230 0.0255 0.0182

169




500 0.0335 0.0239 0.0265 0.0189 510 0.0347 0.0248 0.0275 0.0196 520 0.0360 0.0257 0.0285 0.0203 530 0.0373 0.0266 0.0295 0.0211 540 0.0386 0.0275 0.0305 0.0218 550 0.0399 0.0285 0.0316 0.0225 560 0.0413 0.0294 0.0327 0.0233 570 0.0426 0.0304 0.0338 0.0241 580 0.0440 0.0314 0.0349 0.0249 590 0.0454 0.0324 0.0360 0.0257 600 0.0469 0.0335 0.0371 0.0265 610 0.0483 0.0345 0.0383 0.0273 620 0.0498 0.0355 0.0394 0.0281 630 0.0513 0.0366 0.0406 0.0290 640 0.0528 0.0377 0.0418 0.0298 650 0.0544 0.0388 0.0430 0.0307 660 0.0559 0.0399 0.0443 0.0316 670 0.0575 0.0410 0.0455 0.0325 680 0.0591 0.0422 0.0468 0.0334 690 0.0607 0.0433 0.0481 0.0343 700 0.0623 0.0445 0.0494 0.0352 710 0.0640 0.0457 0.0507 0.0362 720 0.0657 0.0469 0.0520 0.0371 730 0.0674 0.0481 0.0533 0.0381 740 0.0691 0.0493 0.0547 0.0390 750 0.0708 0.0506 0.0561 0.0400 760 0.0726 0.0518 0.0575 0.0410 770 0.0744 0.0531 0.0589 0.0420 780 0.0762 0.0544 0.0603 0.0430

170




790 0.0780 0.0557 0.0617 0.0441 800 0.0798 0.0570 0.0632 0.0451 810 0.0817 0.0583 0.0647 0.0461 820 0.0835 0.0596 0.0661 0.0472 830 0.0854 0.0610 0.0676 0.0483 840 0.0874 0.0623 0.0692 0.0494 850 0.0893 0.0637 0.0707 0.0504 860 0.0912 0.0651 0.0722 0.0516 870 0.0932 0.0665 0.0738 0.0527 880 0.0952 0.0679 0.0754 0.0538 890 0.0972 0.0694 0.0770 0.0549 900 0.0992 0.0708 0.0786 0.0561 910 0.1013 0.0723 0.0802 0.0572 920 0.1034 0.0738 0.0818 0.0584 930 0.1055 0.0753 0.0835 0.0596 940 0.1076 0.0768 0.0852 0.0608 950 0.1097 0.0783 0.0868 0.0620 960 0.1118 0.0798 0.0885 0.0632 970 0.1140 0.0814 0.0902 0.0644 980 0.1162 0.0829 0.0920 0.0656 990 0.1184 0.0845 0.0937 0.0669 1000 0.1206 0.0861 0.0955 0.0681 1010 0.1228 0.0877 0.0973 0.0694 1020 0.1251 0.0893 0.0990 0.0707 1030 0.1274 0.0909 0.1008 0.0720 1040 0.1297 0.0926 0.1027 0.0733 1050 0.1320 0.0942 0.1045 0.0746 1060 0.1343 0.0959 0.1063 0.0759 1070 0.1367 0.0976 0.1082 0.0772

171




1080 0.1391 0.0992 0.1101 0.0786 1090 0.1415 0.1010 0.1120 0.0799 1100 0.1439 0.1027 0.1139 0.0813 1110 0.1463 0.1044 0.1158 0.0827 1120 0.1487 0.1062 0.1178 0.0840 1130 0.1512 0.1079 0.1197 0.0854 1140 0.1537 0.1097 0.1217 0.0868 1150 0.1562 0.1115 0.1237 0.0883 1160 0.1587 0.1133 0.1256 0.0897 1170 0.1613 0.1151 0.1277 0.0911 1180 0.1638 0.1169 0.1297 0.0926 1190 0.1664 0.1188 0.1317 0.0940 1200 0.1690 0.1206 0.1338 0.0955 1210 0.1716 0.1225 0.1359 0.0970 1220 0.1742 0.1244 0.1379 0.0984 1230 0.1769 0.1262 0.1400 0.0999 1240 0.1796 0.1281 0.1421 0.1015 1250 0.1822 0.1301 0.1443 0.1030 1260 0.1849 0.1320 0.1464 0.1045 1270 0.1877 0.1339 0.1486 0.1060 1280 0.1904 0.1359 0.1507 0.1076 1290 0.1932 0.1379 0.1529 0.1091 1300 0.1960 0.1399 0.1551 0.1107 1310 0.1988 0.1419 0.1573 0.1123 1320 0.2016 0.1439 0.1596 0.1139 1330 0.2044 0.1459 0.1618 0.1155 1340 0.2073 0.1479 0.1641 0.1171 1350 0.2101 0.1500 0.1664 0.1187 1360 0.2130 0.1520 0.1686 0.1204

172




1370 0.2159 0.1541 0.1709 0.1220 1380 0.2188 0.1562 0.1733 0.1237 1390 0.2218 0.1583 0.1756 0.1253 1400 0.2248 0.1604 0.1779 0.1270 1410 0.2277 0.1625 0.1803 0.1287 1420 0.2307 0.1647 0.1827 0.1304 1430 0.2337 0.1668 0.1850 0.1321 1440 0.2368 0.1690 0.1874 0.1338 1450 0.2398 0.1712 0.1899 0.1355 1460 0.2429 0.1734 0.1923 0.1372 1470 0.2460 0.1756 0.1947 0.1390 1480 0.2491 0.1778 0.1972 0.1407 1490 0.2522 0.1800 0.1997 0.1425 1500 0.2553 0.1822 0.2022 0.1443 1510 0.2585 0.1845 0.2047 0.1461 1520 0.2617 0.1868 0.2072 0.1479 1530 0.2649 0.1890 0.2097 0.1497 1540 0.2681 0.1913 0.2122 0.1515 1550 0.2713 0.1936 0.2148 0.1533 1560 0.2746 0.1960 0.2174 0.1551 1570 0.2778 0.1983 0.2200 0.1570 1580 0.2811 0.2006 0.2225 0.1588 1590 0.2844 0.2030 0.2252 0.1607 1600 0.2877 0.2054 0.2278 0.1626 1610 0.2911 0.2077 0.2304 0.1645 1620 0.2944 0.2101 0.2331 0.1664 1630 0.2978 0.2125 0.2358 0.1683 1640 0.3012 0.2150 0.2384 0.1702 1650 0.3046 0.2174 0.2411 0.1721

173




1660 0.3080 0.2198 0.2438 0.1740 1670 0.3115 0.2223 0.2466 0.1760 1680 0.3149 0.2248 0.2493 0.1779 1690 0.3184 0.2272 0.2521 0.1799 1700 0.3219 0.2297 0.2548 0.1819 1710 0.3254 0.2322 0.2576 0.1839 1720 0.3289 0.2348 0.2604 0.1858 1730 0.3325 0.2373 0.2632 0.1878 1740 0.3360 0.2398 0.2660 0.1899 1750 0.3396 0.2424 0.2689 0.1919 1760 0.3432 0.2450 0.2717 0.1939 1770 0.3468 0.2475 0.2746 0.1960 1780 0.3505 0.2501 0.2775 0.1980 1790 0.3541 0.2527 0.2803 0.2001 1800 0.3578 0.2553 0.2832 0.2022 1810 0.3615 0.2580 0.2862 0.2042 1820 0.3652 0.2606 0.2891 0.2063 1830 0.3689 0.2633 0.2920 0.2084 1840 0.3726 0.2659 0.2950 0.2105 1850 0.3764 0.2686 0.2980 0.2127 1860 0.3802 0.2713 0.3010 0.2148 1870 0.3839 0.2740 0.3040 0.2169 1880 0.3878 0.2767 0.3070 0.2191 1890 0.3916 0.2795 0.3100 0.2212 1900 0.3954 0.2822 0.3130 0.2234 1910 0.3993 0.2850 0.3161 0.2256 1920 0.4032 0.2877 0.3192 0.2278 1930 0.4070 0.2905 0.3222 0.2300 1940 0.4110 0.2933 0.3253 0.2322

174




1950 0.4149 0.2961 0.3285 0.2344 1960 0.4188 0.2989 0.3316 0.2366 1970 0.4228 0.3017 0.3347 0.2389 1980 0.4268 0.3046 0.3379 0.2411 1990 0.4308 0.3074 0.3410 0.2434 2000 0.4348 0.3103 0.3442 0.2457


6" pipe Pipe Type Schedule 40 Schedule 10 C Factor 100 120 100 120


10 0.0000 0.0000 0.0000 0.0000 20 0.0000 0.0000 0.0000 0.0000 30 0.0001 0.0001 0.0001 0.0000 40 0.0001 0.0001 0.0001 0.0001 50 0.0002 0.0001 0.0002 0.0001 60 0.0003 0.0002 0.0002 0.0002 70 0.0004 0.0003 0.0003 0.0002 80 0.0005 0.0003 0.0004 0.0003 90 0.0006 0.0004 0.0005 0.0003 100 0.0007 0.0005 0.0006 0.0004 110 0.0008 0.0006 0.0007 0.0005 120 0.0010 0.0007 0.0008 0.0006 130 0.0011 0.0008 0.0009 0.0006 140 0.0013 0.0009 0.0010 0.0007 150 0.0015 0.0011 0.0012 0.0008 160 0.0017 0.0012 0.0013 0.0009

175




170 0.0019 0.0013 0.0015 0.0011 180 0.0021 0.0015 0.0016 0.0012 190 0.0023 0.0016 0.0018 0.0013 200 0.0025 0.0018 0.0020 0.0014 210 0.0027 0.0020 0.0022 0.0016 220 0.0030 0.0021 0.0024 0.0017 230 0.0033 0.0023 0.0026 0.0018 240 0.0035 0.0025 0.0028 0.0020 250 0.0038 0.0027 0.0030 0.0022 260 0.0041 0.0029 0.0032 0.0023 270 0.0044 0.0031 0.0035 0.0025 280 0.0047 0.0033 0.0037 0.0027 290 0.0050 0.0036 0.0040 0.0028 300 0.0053 0.0038 0.0042 0.0030 310 0.0056 0.0040 0.0045 0.0032 320 0.0060 0.0043 0.0048 0.0034 330 0.0063 0.0045 0.0050 0.0036 340 0.0067 0.0048 0.0053 0.0038 350 0.0071 0.0050 0.0056 0.0040 360 0.0074 0.0053 0.0059 0.0042 370 0.0078 0.0056 0.0062 0.0044 380 0.0082 0.0059 0.0065 0.0047 390 0.0086 0.0062 0.0069 0.0049 400 0.0090 0.0065 0.0072 0.0051 410 0.0095 0.0068 0.0075 0.0054 420 0.0099 0.0071 0.0079 0.0056 430 0.0103 0.0074 0.0082 0.0059 440 0.0108 0.0077 0.0086 0.0061 450 0.0113 0.0080 0.0089 0.0064

176




460 0.0117 0.0084 0.0093 0.0067 470 0.0122 0.0087 0.0097 0.0069 480 0.0127 0.0090 0.0101 0.0072 490 0.0132 0.0094 0.0105 0.0075 500 0.0137 0.0098 0.0109 0.0078 510 0.0142 0.0101 0.0113 0.0081 520 0.0147 0.0105 0.0117 0.0083 530 0.0152 0.0109 0.0121 0.0086 540 0.0158 0.0113 0.0125 0.0089 550 0.0163 0.0116 0.0130 0.0093 560 0.0169 0.0120 0.0134 0.0096 570 0.0174 0.0124 0.0139 0.0099 580 0.0180 0.0128 0.0143 0.0102 590 0.0186 0.0133 0.0148 0.0105 600 0.0192 0.0137 0.0152 0.0109 610 0.0198 0.0141 0.0157 0.0112 620 0.0204 0.0145 0.0162 0.0116 630 0.0210 0.0150 0.0167 0.0119 640 0.0216 0.0154 0.0172 0.0123 650 0.0222 0.0159 0.0177 0.0126 660 0.0229 0.0163 0.0182 0.0130 670 0.0235 0.0168 0.0187 0.0133 680 0.0241 0.0172 0.0192 0.0137 690 0.0248 0.0177 0.0197 0.0141 700 0.0255 0.0182 0.0203 0.0145 710 0.0262 0.0187 0.0208 0.0148 720 0.0268 0.0192 0.0213 0.0152 730 0.0275 0.0197 0.0219 0.0156 740 0.0282 0.0202 0.0225 0.0160

177




750 0.0289 0.0207 0.0230 0.0164 760 0.0297 0.0212 0.0236 0.0168 770 0.0304 0.0217 0.0242 0.0173 780 0.0311 0.0222 0.0248 0.0177 790 0.0319 0.0227 0.0253 0.0181 800 0.0326 0.0233 0.0259 0.0185 810 0.0334 0.0238 0.0265 0.0189 820 0.0341 0.0244 0.0272 0.0194 830 0.0349 0.0249 0.0278 0.0198 840 0.0357 0.0255 0.0284 0.0203 850 0.0365 0.0260 0.0290 0.0207 860 0.0373 0.0266 0.0297 0.0212 870 0.0381 0.0272 0.0303 0.0216 880 0.0389 0.0278 0.0309 0.0221 890 0.0397 0.0284 0.0316 0.0226 900 0.0406 0.0289 0.0323 0.0230 910 0.0414 0.0295 0.0329 0.0235 920 0.0422 0.0301 0.0336 0.0240 930 0.0431 0.0308 0.0343 0.0245 940 0.0440 0.0314 0.0350 0.0250 950 0.0448 0.0320 0.0357 0.0254 960 0.0457 0.0326 0.0363 0.0259 970 0.0466 0.0333 0.0371 0.0264 980 0.0475 0.0339 0.0378 0.0270 990 0.0484 0.0345 0.0385 0.0275 1000 0.0493 0.0352 0.0392 0.0280 1010 0.0502 0.0358 0.0399 0.0285 1020 0.0511 0.0365 0.0407 0.0290 1030 0.0521 0.0372 0.0414 0.0296

178




1040 0.0530 0.0378 0.0422 0.0301 1050 0.0539 0.0385 0.0429 0.0306 1060 0.0549 0.0392 0.0437 0.0312 1070 0.0559 0.0399 0.0444 0.0317 1080 0.0568 0.0406 0.0452 0.0323 1090 0.0578 0.0413 0.0460 0.0328 1100 0.0588 0.0420 0.0468 0.0334 1110 0.0598 0.0427 0.0475 0.0339 1120 0.0608 0.0434 0.0483 0.0345 1130 0.0618 0.0441 0.0491 0.0351 1140 0.0628 0.0448 0.0500 0.0357 1150 0.0638 0.0456 0.0508 0.0362 1160 0.0649 0.0463 0.0516 0.0368 1170 0.0659 0.0470 0.0524 0.0374 1180 0.0669 0.0478 0.0532 0.0380 1190 0.0680 0.0485 0.0541 0.0386 1200 0.0691 0.0493 0.0549 0.0392 1210 0.0701 0.0501 0.0558 0.0398 1220 0.0712 0.0508 0.0566 0.0404 1230 0.0723 0.0516 0.0575 0.0410 1240 0.0734 0.0524 0.0584 0.0417 1250 0.0745 0.0532 0.0592 0.0423 1260 0.0756 0.0539 0.0601 0.0429 1270 0.0767 0.0547 0.0610 0.0435 1280 0.0778 0.0555 0.0619 0.0442 1290 0.0789 0.0563 0.0628 0.0448 1300 0.0801 0.0572 0.0637 0.0455 1310 0.0812 0.0580 0.0646 0.0461 1320 0.0824 0.0588 0.0655 0.0468

179




1330 0.0835 0.0596 0.0664 0.0474 1340 0.0847 0.0605 0.0674 0.0481 1350 0.0859 0.0613 0.0683 0.0487 1360 0.0871 0.0621 0.0692 0.0494 1370 0.0882 0.0630 0.0702 0.0501 1380 0.0894 0.0638 0.0711 0.0508 1390 0.0906 0.0647 0.0721 0.0515 1400 0.0919 0.0656 0.0731 0.0521 1410 0.0931 0.0664 0.0740 0.0528 1420 0.0943 0.0673 0.0750 0.0535 1430 0.0955 0.0682 0.0760 0.0542 1440 0.0968 0.0691 0.0770 0.0549 1450 0.0980 0.0700 0.0780 0.0556 1460 0.0993 0.0708 0.0790 0.0563 1470 0.1005 0.0717 0.0800 0.0571 1480 0.1018 0.0727 0.0810 0.0578 1490 0.1031 0.0736 0.0820 0.0585 1500 0.1044 0.0745 0.0830 0.0592 1510 0.1056 0.0754 0.0840 0.0600 1520 0.1069 0.0763 0.0851 0.0607 1530 0.1083 0.0773 0.0861 0.0614 1540 0.1096 0.0782 0.0871 0.0622 1550 0.1109 0.0791 0.0882 0.0629 1560 0.1122 0.0801 0.0892 0.0637 1570 0.1135 0.0810 0.0903 0.0645 1580 0.1149 0.0820 0.0914 0.0652 1590 0.1162 0.0830 0.0924 0.0660 1600 0.1176 0.0839 0.0935 0.0667 1610 0.1190 0.0849 0.0946 0.0675

180




1620 0.1203 0.0859 0.0957 0.0683 1630 0.1217 0.0869 0.0968 0.0691 1640 0.1231 0.0878 0.0979 0.0699 1650 0.1245 0.0888 0.0990 0.0707 1660 0.1259 0.0898 0.1001 0.0715 1670 0.1273 0.0908 0.1012 0.0723 1680 0.1287 0.0919 0.1024 0.0731 1690 0.1301 0.0929 0.1035 0.0739 1700 0.1315 0.0939 0.1046 0.0747 1710 0.1330 0.0949 0.1058 0.0755 1720 0.1344 0.0959 0.1069 0.0763 1730 0.1359 0.0970 0.1081 0.0771 1740 0.1373 0.0980 0.1092 0.0780 1750 0.1388 0.0991 0.1104 0.0788 1760 0.1403 0.1001 0.1116 0.0796 1770 0.1417 0.1012 0.1127 0.0805 1780 0.1432 0.1022 0.1139 0.0813 1790 0.1447 0.1033 0.1151 0.0821 1800 0.1462 0.1044 0.1163 0.0830 1810 0.1477 0.1054 0.1175 0.0839 1820 0.1492 0.1065 0.1187 0.0847 1830 0.1508 0.1076 0.1199 0.0856 1840 0.1523 0.1087 0.1211 0.0864 1850 0.1538 0.1098 0.1223 0.0873 1860 0.1554 0.1109 0.1236 0.0882 1870 0.1569 0.1120 0.1248 0.0891 1880 0.1585 0.1131 0.1260 0.0900 1890 0.1600 0.1142 0.1273 0.0908 1900 0.1616 0.1153 0.1285 0.0917

181




1910 0.1632 0.1165 0.1298 0.0926 1920 0.1648 0.1176 0.1310 0.0935 1930 0.1664 0.1187 0.1323 0.0944 1940 0.1680 0.1199 0.1336 0.0953 1950 0.1696 0.1210 0.1349 0.0962 1960 0.1712 0.1222 0.1361 0.0972 1970 0.1728 0.1233 0.1374 0.0981 1980 0.1744 0.1245 0.1387 0.0990 1990 0.1760 0.1256 0.1400 0.0999 2000 0.1777 0.1268 0.1413 0.1009 2010 0.1793 0.1280 0.1426 0.1018 2020 0.1810 0.1292 0.1439 0.1027 2030 0.1827 0.1304 0.1453 0.1037 2040 0.1843 0.1315 0.1466 0.1046 2050 0.1860 0.1327 0.1479 0.1056 2060 0.1877 0.1339 0.1493 0.1065 2070 0.1894 0.1351 0.1506 0.1075 2080 0.1911 0.1364 0.1520 0.1085 2090 0.1928 0.1376 0.1533 0.1094 2100 0.1945 0.1388 0.1547 0.1104 2110 0.1962 0.1400 0.1560 0.1114 2120 0.1979 0.1412 0.1574 0.1123 2130 0.1996 0.1425 0.1588 0.1133 2140 0.2014 0.1437 0.1602 0.1143 2150 0.2031 0.1450 0.1616 0.1153 2160 0.2049 0.1462 0.1629 0.1163 2170 0.2066 0.1475 0.1643 0.1173 2180 0.2084 0.1487 0.1657 0.1183 2190 0.2102 0.1500 0.1672 0.1193

182




2200 0.2120 0.1513 0.1686 0.1203 2210 0.2137 0.1525 0.1700 0.1213 2220 0.2155 0.1538 0.1714 0.1223 2230 0.2173 0.1551 0.1728 0.1234 2240 0.2191 0.1564 0.1743 0.1244 2250 0.2209 0.1577 0.1757 0.1254 2260 0.2228 0.1590 0.1772 0.1264 2270 0.2246 0.1603 0.1786 0.1275 2280 0.2264 0.1616 0.1801 0.1285 2290 0.2283 0.1629 0.1815 0.1296 2300 0.2301 0.1642 0.1830 0.1306 2310 0.2320 0.1656 0.1845 0.1317 2320 0.2338 0.1669 0.1860 0.1327 2330 0.2357 0.1682 0.1875 0.1338 2340 0.2376 0.1696 0.1890 0.1349 2350 0.2395 0.1709 0.1904 0.1359 2360 0.2413 0.1722 0.1919 0.1370 2370 0.2432 0.1736 0.1935 0.1381 2380 0.2451 0.1750 0.1950 0.1391 2390 0.2471 0.1763 0.1965 0.1402 2400 0.2490 0.1777 0.1980 0.1413 2410 0.2509 0.1791 0.1995 0.1424 2420 0.2528 0.1804 0.2011 0.1435 2430 0.2548 0.1818 0.2026 0.1446 2440 0.2567 0.1832 0.2042 0.1457 2450 0.2586 0.1846 0.2057 0.1468 2460 0.2606 0.1860 0.2073 0.1479 2470 0.2626 0.1874 0.2088 0.1490 2480 0.2645 0.1888 0.2104 0.1502

183




2490 0.2665 0.1902 0.2120 0.1513 2500 0.2685 0.1916 0.2135 0.1524 2510 0.2705 0.1930 0.2151 0.1535 2520 0.2725 0.1945 0.2167 0.1547 2530 0.2745 0.1959 0.2183 0.1558 2540 0.2765 0.1973 0.2199 0.1569 2550 0.2785 0.1988 0.2215 0.1581 2560 0.2805 0.2002 0.2231 0.1592 2570 0.2826 0.2017 0.2247 0.1604 2580 0.2846 0.2031 0.2264 0.1616 2590 0.2867 0.2046 0.2280 0.1627 2600 0.2887 0.2060 0.2296 0.1639 2610 0.2908 0.2075 0.2313 0.1650 2620 0.2928 0.2090 0.2329 0.1662 2630 0.2949 0.2105 0.2345 0.1674 2640 0.2970 0.2120 0.2362 0.1686 2650 0.2991 0.2134 0.2379 0.1698 2660 0.3012 0.2149 0.2395 0.1709 2670 0.3032 0.2164 0.2412 0.1721 2680 0.3054 0.2179 0.2429 0.1733 2690 0.3075 0.2194 0.2445 0.1745 2700 0.3096 0.2209 0.2462 0.1757 2710 0.3117 0.2225 0.2479 0.1769 2720 0.3138 0.2240 0.2496 0.1781 2730 0.3160 0.2255 0.2513 0.1794 2740 0.3181 0.2270 0.2530 0.1806 2750 0.3203 0.2286 0.2547 0.1818 2760 0.3224 0.2301 0.2564 0.1830 2770 0.3246 0.2317 0.2582 0.1842

184




2780 0.3268 0.2332 0.2599 0.1855 2790 0.3289 0.2348 0.2616 0.1867 2800 0.3311 0.2363 0.2634 0.1880 2810 0.3333 0.2379 0.2651 0.1892 2820 0.3355 0.2395 0.2668 0.1904 2830 0.3377 0.2410 0.2686 0.1917 2840 0.3399 0.2426 0.2704 0.1930 2850 0.3421 0.2442 0.2721 0.1942 2860 0.3444 0.2458 0.2739 0.1955 2870 0.3466 0.2474 0.2757 0.1967 2880 0.3488 0.2490 0.2774 0.1980 2890 0.3511 0.2506 0.2792 0.1993 2900 0.3533 0.2522 0.2810 0.2006 2910 0.3556 0.2538 0.2828 0.2018 2920 0.3579 0.2554 0.2846 0.2031 2930 0.3601 0.2570 0.2864 0.2044 2940 0.3624 0.2586 0.2882 0.2057 2950 0.3647 0.2603 0.2900 0.2070 2960 0.3670 0.2619 0.2919 0.2083 2970 0.3693 0.2636 0.2937 0.2096 2980 0.3716 0.2652 0.2955 0.2109 2990 0.3739 0.2668 0.2974 0.2122 3000 0.3762 0.2685 0.2992 0.2135 3010 0.3785 0.2702 0.3011 0.2149 3020 0.3809 0.2718 0.3029 0.2162 3030 0.3832 0.2735 0.3048 0.2175 3040 0.3855 0.2752 0.3066 0.2188 3050 0.3879 0.2768 0.3085 0.2202 3060 0.3902 0.2785 0.3104 0.2215

185




3070 0.3926 0.2802 0.3123 0.2229 3080 0.3950 0.2819 0.3141 0.2242 3090 0.3974 0.2836 0.3160 0.2255 3100 0.3997 0.2853 0.3179 0.2269 3110 0.4021 0.2870 0.3198 0.2283 3120 0.4045 0.2887 0.3217 0.2296 3130 0.4069 0.2904 0.3236 0.2310 3140 0.4093 0.2921 0.3256 0.2323 3150 0.4117 0.2939 0.3275 0.2337 3160 0.4142 0.2956 0.3294 0.2351 3170 0.4166 0.2973 0.3313 0.2365 3180 0.4190 0.2991 0.3333 0.2379 3190 0.4215 0.3008 0.3352 0.2392 3200 0.4239 0.3025 0.3372 0.2406 3210 0.4264 0.3043 0.3391 0.2420 3220 0.4288 0.3061 0.3411 0.2434 3230 0.4313 0.3078 0.3430 0.2448 3240 0.4338 0.3096 0.3450 0.2462 3250 0.4363 0.3114 0.3470 0.2476 3260 0.4387 0.3131 0.3489 0.2490 3270 0.4412 0.3149 0.3509 0.2505 3280 0.4437 0.3167 0.3529 0.2519 3290 0.4462 0.3185 0.3549 0.2533 3300 0.4487 0.3203 0.3569 0.2547 3310 0.4513 0.3221 0.3589 0.2562 3320 0.4538 0.3239 0.3609 0.2576 3330 0.4563 0.3257 0.3629 0.2590 3340 0.4589 0.3275 0.3649 0.2605 3350 0.4614 0.3293 0.3670 0.2619

186




3360 0.4640 0.3311 0.3690 0.2634 3370 0.4665 0.3330 0.3710 0.2648 3380 0.4691 0.3348 0.3731 0.2663 3390 0.4717 0.3366 0.3751 0.2677 3400 0.4742 0.3385 0.3772 0.2692 3410 0.4768 0.3403 0.3792 0.2707 3420 0.4794 0.3421 0.3813 0.2721 3430 0.4820 0.3440 0.3833 0.2736 3440 0.4846 0.3459 0.3854 0.2751 3450 0.4872 0.3477 0.3875 0.2766 3460 0.4898 0.3496 0.3896 0.2780 3470 0.4924 0.3515 0.3917 0.2795 3480 0.4951 0.3533 0.3938 0.2810 3490 0.4977 0.3552 0.3958 0.2825 3500 0.5004 0.3571 0.3979 0.2840


Pipe Type Schedule 40 Schedule 30 Schedule 10 C Factor 100 120 100 120 100 120

ID (inches) 7.981 7.981 8.071 8.071 8.329 8.329 Flow (gpm) Friction loss (psi)

10 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 20 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 30 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 40 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 50 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 60 0.0001 0.0001 0.0001 0.0000 0.0001 0.0000

187




70 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 80 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 90 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001 100 0.0002 0.0001 0.0002 0.0001 0.0001 0.0001 110 0.0002 0.0002 0.0002 0.0001 0.0002 0.0001 120 0.0003 0.0002 0.0002 0.0002 0.0002 0.0001 130 0.0003 0.0002 0.0003 0.0002 0.0002 0.0002 140 0.0003 0.0002 0.0003 0.0002 0.0003 0.0002 150 0.0004 0.0003 0.0004 0.0003 0.0003 0.0002 160 0.0004 0.0003 0.0004 0.0003 0.0004 0.0003 170 0.0005 0.0003 0.0005 0.0003 0.0004 0.0003 180 0.0005 0.0004 0.0005 0.0004 0.0004 0.0003 190 0.0006 0.0004 0.0006 0.0004 0.0005 0.0003 200 0.0007 0.0005 0.0006 0.0004 0.0005 0.0004 210 0.0007 0.0005 0.0007 0.0005 0.0006 0.0004 220 0.0008 0.0006 0.0007 0.0005 0.0006 0.0005 230 0.0009 0.0006 0.0008 0.0006 0.0007 0.0005 240 0.0009 0.0007 0.0009 0.0006 0.0008 0.0005 250 0.0010 0.0007 0.0009 0.0007 0.0008 0.0006 260 0.0011 0.0008 0.0010 0.0007 0.0009 0.0006 270 0.0011 0.0008 0.0011 0.0008 0.0009 0.0007 280 0.0012 0.0009 0.0012 0.0008 0.0010 0.0007 290 0.0013 0.0009 0.0012 0.0009 0.0011 0.0008 300 0.0014 0.0010 0.0013 0.0009 0.0011 0.0008 310 0.0015 0.0011 0.0014 0.0010 0.0012 0.0009 320 0.0016 0.0011 0.0015 0.0011 0.0013 0.0009 330 0.0017 0.0012 0.0016 0.0011 0.0014 0.0010 340 0.0018 0.0013 0.0017 0.0012 0.0014 0.0010

188




350 0.0019 0.0013 0.0018 0.0013 0.0015 0.0011 360 0.0020 0.0014 0.0019 0.0013 0.0016 0.0011 370 0.0021 0.0015 0.0019 0.0014 0.0017 0.0012 380 0.0022 0.0015 0.0020 0.0015 0.0018 0.0013 390 0.0023 0.0016 0.0021 0.0015 0.0018 0.0013 400 0.0024 0.0017 0.0023 0.0016 0.0019 0.0014 410 0.0025 0.0018 0.0024 0.0017 0.0020 0.0014 420 0.0026 0.0019 0.0025 0.0018 0.0021 0.0015 430 0.0027 0.0019 0.0026 0.0018 0.0022 0.0016 440 0.0028 0.0020 0.0027 0.0019 0.0023 0.0016 450 0.0030 0.0021 0.0028 0.0020 0.0024 0.0017 460 0.0031 0.0022 0.0029 0.0021 0.0025 0.0018 470 0.0032 0.0023 0.0030 0.0022 0.0026 0.0019 480 0.0033 0.0024 0.0032 0.0023 0.0027 0.0019 490 0.0035 0.0025 0.0033 0.0023 0.0028 0.0020 500 0.0036 0.0026 0.0034 0.0024 0.0029 0.0021 510 0.0037 0.0027 0.0035 0.0025 0.0030 0.0022 520 0.0039 0.0028 0.0037 0.0026 0.0031 0.0022 530 0.0040 0.0029 0.0038 0.0027 0.0032 0.0023 540 0.0041 0.0030 0.0039 0.0028 0.0034 0.0024 550 0.0043 0.0031 0.0041 0.0029 0.0035 0.0025 560 0.0044 0.0032 0.0042 0.0030 0.0036 0.0026 570 0.0046 0.0033 0.0043 0.0031 0.0037 0.0027 580 0.0047 0.0034 0.0045 0.0032 0.0038 0.0027 590 0.0049 0.0035 0.0046 0.0033 0.0040 0.0028 600 0.0050 0.0036 0.0048 0.0034 0.0041 0.0029 610 0.0052 0.0037 0.0049 0.0035 0.0042 0.0030 620 0.0053 0.0038 0.0051 0.0036 0.0043 0.0031

189




630 0.0055 0.0039 0.0052 0.0037 0.0045 0.0032 640 0.0057 0.0040 0.0054 0.0038 0.0046 0.0033 650 0.0058 0.0042 0.0055 0.0039 0.0047 0.0034 660 0.0060 0.0043 0.0057 0.0041 0.0049 0.0035 670 0.0062 0.0044 0.0058 0.0042 0.0050 0.0036 680 0.0063 0.0045 0.0060 0.0043 0.0052 0.0037 690 0.0065 0.0047 0.0062 0.0044 0.0053 0.0038 700 0.0067 0.0048 0.0063 0.0045 0.0054 0.0039 710 0.0069 0.0049 0.0065 0.0046 0.0056 0.0040 720 0.0070 0.0050 0.0067 0.0048 0.0057 0.0041 730 0.0072 0.0052 0.0068 0.0049 0.0059 0.0042 740 0.0074 0.0053 0.0070 0.0050 0.0060 0.0043 750 0.0076 0.0054 0.0072 0.0051 0.0062 0.0044 760 0.0078 0.0056 0.0074 0.0053 0.0063 0.0045 770 0.0080 0.0057 0.0076 0.0054 0.0065 0.0046 780 0.0082 0.0058 0.0077 0.0055 0.0066 0.0047 790 0.0084 0.0060 0.0079 0.0057 0.0068 0.0049 800 0.0086 0.0061 0.0081 0.0058 0.0070 0.0050 810 0.0088 0.0063 0.0083 0.0059 0.0071 0.0051 820 0.0090 0.0064 0.0085 0.0061 0.0073 0.0052 830 0.0092 0.0065 0.0087 0.0062 0.0074 0.0053 840 0.0094 0.0067 0.0089 0.0063 0.0076 0.0054 850 0.0096 0.0068 0.0091 0.0065 0.0078 0.0056 860 0.0098 0.0070 0.0093 0.0066 0.0080 0.0057 870 0.0100 0.0071 0.0095 0.0068 0.0081 0.0058 880 0.0102 0.0073 0.0097 0.0069 0.0083 0.0059 890 0.0104 0.0074 0.0099 0.0071 0.0085 0.0060 900 0.0107 0.0076 0.0101 0.0072 0.0087 0.0062

190




910 0.0109 0.0078 0.0103 0.0073 0.0088 0.0063 920 0.0111 0.0079 0.0105 0.0075 0.0090 0.0064 930 0.0113 0.0081 0.0107 0.0076 0.0092 0.0066 940 0.0115 0.0082 0.0109 0.0078 0.0094 0.0067 950 0.0118 0.0084 0.0111 0.0080 0.0096 0.0068 960 0.0120 0.0086 0.0114 0.0081 0.0098 0.0070 970 0.0122 0.0087 0.0116 0.0083 0.0099 0.0071 980 0.0125 0.0089 0.0118 0.0084 0.0101 0.0072 990 0.0127 0.0091 0.0120 0.0086 0.0103 0.0074 1000 0.0129 0.0092 0.0123 0.0087 0.0105 0.0075 1010 0.0132 0.0094 0.0125 0.0089 0.0107 0.0076 1020 0.0134 0.0096 0.0127 0.0091 0.0109 0.0078 1030 0.0137 0.0098 0.0129 0.0092 0.0111 0.0079 1040 0.0139 0.0099 0.0132 0.0094 0.0113 0.0081 1050 0.0142 0.0101 0.0134 0.0096 0.0115 0.0082 1060 0.0144 0.0103 0.0137 0.0097 0.0117 0.0084 1070 0.0147 0.0105 0.0139 0.0099 0.0119 0.0085 1080 0.0149 0.0107 0.0141 0.0101 0.0121 0.0087 1090 0.0152 0.0108 0.0144 0.0103 0.0123 0.0088 1100 0.0154 0.0110 0.0146 0.0104 0.0125 0.0090 1110 0.0157 0.0112 0.0149 0.0106 0.0128 0.0091 1120 0.0160 0.0114 0.0151 0.0108 0.0130 0.0093 1130 0.0162 0.0116 0.0154 0.0110 0.0132 0.0094 1140 0.0165 0.0118 0.0156 0.0111 0.0134 0.0096 1150 0.0168 0.0120 0.0159 0.0113 0.0136 0.0097 1160 0.0170 0.0122 0.0161 0.0115 0.0138 0.0099 1170 0.0173 0.0124 0.0164 0.0117 0.0141 0.0100 1180 0.0176 0.0125 0.0166 0.0119 0.0143 0.0102

191




1190 0.0179 0.0127 0.0169 0.0121 0.0145 0.0104 1200 0.0181 0.0129 0.0172 0.0123 0.0147 0.0105 1210 0.0184 0.0131 0.0174 0.0124 0.0150 0.0107 1220 0.0187 0.0133 0.0177 0.0126 0.0152 0.0108 1230 0.0190 0.0136 0.0180 0.0128 0.0154 0.0110 1240 0.0193 0.0138 0.0182 0.0130 0.0157 0.0112 1250 0.0196 0.0140 0.0185 0.0132 0.0159 0.0113 1260 0.0199 0.0142 0.0188 0.0134 0.0161 0.0115 1270 0.0201 0.0144 0.0191 0.0136 0.0164 0.0117 1280 0.0204 0.0146 0.0194 0.0138 0.0166 0.0118 1290 0.0207 0.0148 0.0196 0.0140 0.0168 0.0120 1300 0.0210 0.0150 0.0199 0.0142 0.0171 0.0122 1310 0.0213 0.0152 0.0202 0.0144 0.0173 0.0124 1320 0.0216 0.0154 0.0205 0.0146 0.0176 0.0125 1330 0.0219 0.0157 0.0208 0.0148 0.0178 0.0127 1340 0.0222 0.0159 0.0211 0.0150 0.0181 0.0129 1350 0.0226 0.0161 0.0214 0.0152 0.0183 0.0131 1360 0.0229 0.0163 0.0216 0.0155 0.0186 0.0133 1370 0.0232 0.0165 0.0219 0.0157 0.0188 0.0134 1380 0.0235 0.0168 0.0222 0.0159 0.0191 0.0136 1390 0.0238 0.0170 0.0225 0.0161 0.0193 0.0138 1400 0.0241 0.0172 0.0228 0.0163 0.0196 0.0140 1410 0.0244 0.0174 0.0231 0.0165 0.0199 0.0142 1420 0.0248 0.0177 0.0234 0.0167 0.0201 0.0144 1430 0.0251 0.0179 0.0238 0.0170 0.0204 0.0145 1440 0.0254 0.0181 0.0241 0.0172 0.0206 0.0147 1450 0.0257 0.0184 0.0244 0.0174 0.0209 0.0149 1460 0.0261 0.0186 0.0247 0.0176 0.0212 0.0151

192




1470 0.0264 0.0188 0.0250 0.0178 0.0214 0.0153 1480 0.0267 0.0191 0.0253 0.0181 0.0217 0.0155 1490 0.0271 0.0193 0.0256 0.0183 0.0220 0.0157 1500 0.0274 0.0196 0.0260 0.0185 0.0223 0.0159 1510 0.0277 0.0198 0.0263 0.0188 0.0225 0.0161 1520 0.0281 0.0200 0.0266 0.0190 0.0228 0.0163 1530 0.0284 0.0203 0.0269 0.0192 0.0231 0.0165 1540 0.0288 0.0205 0.0272 0.0194 0.0234 0.0167 1550 0.0291 0.0208 0.0276 0.0197 0.0237 0.0169 1560 0.0295 0.0210 0.0279 0.0199 0.0239 0.0171 1570 0.0298 0.0213 0.0282 0.0202 0.0242 0.0173 1580 0.0302 0.0215 0.0286 0.0204 0.0245 0.0175 1590 0.0305 0.0218 0.0289 0.0206 0.0248 0.0177 1600 0.0309 0.0220 0.0292 0.0209 0.0251 0.0179 1610 0.0312 0.0223 0.0296 0.0211 0.0254 0.0181 1620 0.0316 0.0226 0.0299 0.0214 0.0257 0.0183 1630 0.0320 0.0228 0.0303 0.0216 0.0260 0.0185 1640 0.0323 0.0231 0.0306 0.0218 0.0263 0.0187 1650 0.0327 0.0233 0.0310 0.0221 0.0266 0.0190 1660 0.0331 0.0236 0.0313 0.0223 0.0269 0.0192 1670 0.0334 0.0239 0.0317 0.0226 0.0272 0.0194 1680 0.0338 0.0241 0.0320 0.0228 0.0275 0.0196 1690 0.0342 0.0244 0.0324 0.0231 0.0278 0.0198 1700 0.0346 0.0247 0.0327 0.0233 0.0281 0.0200 1710 0.0349 0.0249 0.0331 0.0236 0.0284 0.0202 1720 0.0353 0.0252 0.0334 0.0239 0.0287 0.0205 1730 0.0357 0.0255 0.0338 0.0241 0.0290 0.0207 1740 0.0361 0.0257 0.0342 0.0244 0.0293 0.0209

193




1750 0.0365 0.0260 0.0345 0.0246 0.0296 0.0211 1760 0.0368 0.0263 0.0349 0.0249 0.0299 0.0214 1770 0.0372 0.0266 0.0352 0.0252 0.0302 0.0216 1780 0.0376 0.0268 0.0356 0.0254 0.0306 0.0218 1790 0.0380 0.0271 0.0360 0.0257 0.0309 0.0220 1800 0.0384 0.0274 0.0364 0.0260 0.0312 0.0223 1810 0.0388 0.0277 0.0367 0.0262 0.0315 0.0225 1820 0.0392 0.0280 0.0371 0.0265 0.0318 0.0227 1830 0.0396 0.0283 0.0375 0.0268 0.0322 0.0230 1840 0.0400 0.0285 0.0379 0.0270 0.0325 0.0232 1850 0.0404 0.0288 0.0383 0.0273 0.0328 0.0234 1860 0.0408 0.0291 0.0386 0.0276 0.0331 0.0237 1870 0.0412 0.0294 0.0390 0.0278 0.0335 0.0239 1880 0.0416 0.0297 0.0394 0.0281 0.0338 0.0241 1890 0.0420 0.0300 0.0398 0.0284 0.0341 0.0244 1900 0.0424 0.0303 0.0402 0.0287 0.0345 0.0246 1910 0.0429 0.0306 0.0406 0.0290 0.0348 0.0248 1920 0.0433 0.0309 0.0410 0.0292 0.0352 0.0251 1930 0.0437 0.0312 0.0414 0.0295 0.0355 0.0253 1940 0.0441 0.0315 0.0418 0.0298 0.0358 0.0256 1950 0.0445 0.0318 0.0422 0.0301 0.0362 0.0258 1960 0.0450 0.0321 0.0426 0.0304 0.0365 0.0261 1970 0.0454 0.0324 0.0430 0.0307 0.0369 0.0263 1980 0.0458 0.0327 0.0434 0.0310 0.0372 0.0266 1990 0.0462 0.0330 0.0438 0.0312 0.0376 0.0268 2000 0.0467 0.0333 0.0442 0.0315 0.0379 0.0271 2010 0.0471 0.0336 0.0446 0.0318 0.0383 0.0273 2020 0.0475 0.0339 0.0450 0.0321 0.0386 0.0276

194




2030 0.0480 0.0342 0.0454 0.0324 0.0390 0.0278 2040 0.0484 0.0346 0.0458 0.0327 0.0393 0.0281 2050 0.0488 0.0349 0.0463 0.0330 0.0397 0.0283 2060 0.0493 0.0352 0.0467 0.0333 0.0400 0.0286 2070 0.0497 0.0355 0.0471 0.0336 0.0404 0.0288 2080 0.0502 0.0358 0.0475 0.0339 0.0408 0.0291 2090 0.0506 0.0361 0.0479 0.0342 0.0411 0.0294 2100 0.0511 0.0365 0.0484 0.0345 0.0415 0.0296 2110 0.0515 0.0368 0.0488 0.0348 0.0419 0.0299 2120 0.0520 0.0371 0.0492 0.0351 0.0422 0.0301 2130 0.0524 0.0374 0.0496 0.0354 0.0426 0.0304 2140 0.0529 0.0377 0.0501 0.0357 0.0430 0.0307 2150 0.0533 0.0381 0.0505 0.0361 0.0433 0.0309 2160 0.0538 0.0384 0.0509 0.0364 0.0437 0.0312 2170 0.0543 0.0387 0.0514 0.0367 0.0441 0.0315 2180 0.0547 0.0391 0.0518 0.0370 0.0445 0.0317 2190 0.0552 0.0394 0.0523 0.0373 0.0448 0.0320 2200 0.0557 0.0397 0.0527 0.0376 0.0452 0.0323 2210 0.0561 0.0401 0.0532 0.0379 0.0456 0.0325 2220 0.0566 0.0404 0.0536 0.0383 0.0460 0.0328 2230 0.0571 0.0407 0.0540 0.0386 0.0464 0.0331 2240 0.0576 0.0411 0.0545 0.0389 0.0468 0.0334 2250 0.0580 0.0414 0.0549 0.0392 0.0471 0.0336 2260 0.0585 0.0418 0.0554 0.0395 0.0475 0.0339 2270 0.0590 0.0421 0.0559 0.0399 0.0479 0.0342 2280 0.0595 0.0424 0.0563 0.0402 0.0483 0.0345 2290 0.0600 0.0428 0.0568 0.0405 0.0487 0.0348 2300 0.0604 0.0431 0.0572 0.0408 0.0491 0.0350

195




2310 0.0609 0.0435 0.0577 0.0412 0.0495 0.0353 2320 0.0614 0.0438 0.0582 0.0415 0.0499 0.0356 2330 0.0619 0.0442 0.0586 0.0418 0.0503 0.0359 2340 0.0624 0.0445 0.0591 0.0422 0.0507 0.0362 2350 0.0629 0.0449 0.0595 0.0425 0.0511 0.0365 2360 0.0634 0.0452 0.0600 0.0428 0.0515 0.0367 2370 0.0639 0.0456 0.0605 0.0432 0.0519 0.0370 2380 0.0644 0.0460 0.0610 0.0435 0.0523 0.0373 2390 0.0649 0.0463 0.0614 0.0438 0.0527 0.0376 2400 0.0654 0.0467 0.0619 0.0442 0.0531 0.0379 2410 0.0659 0.0470 0.0624 0.0445 0.0535 0.0382 2420 0.0664 0.0474 0.0629 0.0449 0.0539 0.0385 2430 0.0669 0.0478 0.0634 0.0452 0.0544 0.0388 2440 0.0674 0.0481 0.0638 0.0456 0.0548 0.0391 2450 0.0679 0.0485 0.0643 0.0459 0.0552 0.0394 2460 0.0684 0.0488 0.0648 0.0463 0.0556 0.0397 2470 0.0690 0.0492 0.0653 0.0466 0.0560 0.0400 2480 0.0695 0.0496 0.0658 0.0470 0.0564 0.0403 2490 0.0700 0.0500 0.0663 0.0473 0.0569 0.0406 2500 0.0705 0.0503 0.0668 0.0477 0.0573 0.0409 2510 0.0710 0.0507 0.0673 0.0480 0.0577 0.0412 2520 0.0716 0.0511 0.0678 0.0484 0.0581 0.0415 2530 0.0721 0.0515 0.0683 0.0487 0.0586 0.0418 2540 0.0726 0.0518 0.0688 0.0491 0.0590 0.0421 2550 0.0732 0.0522 0.0693 0.0494 0.0594 0.0424 2560 0.0737 0.0526 0.0698 0.0498 0.0599 0.0427 2570 0.0742 0.0530 0.0703 0.0502 0.0603 0.0430 2580 0.0748 0.0533 0.0708 0.0505 0.0607 0.0433

196




2590 0.0753 0.0537 0.0713 0.0509 0.0612 0.0436 2600 0.0758 0.0541 0.0718 0.0512 0.0616 0.0440 2610 0.0764 0.0545 0.0723 0.0516 0.0620 0.0443 2620 0.0769 0.0549 0.0728 0.0520 0.0625 0.0446 2630 0.0775 0.0553 0.0733 0.0523 0.0629 0.0449 2640 0.0780 0.0557 0.0739 0.0527 0.0634 0.0452 2650 0.0785 0.0561 0.0744 0.0531 0.0638 0.0455 2660 0.0791 0.0565 0.0749 0.0535 0.0643 0.0459 2670 0.0796 0.0568 0.0754 0.0538 0.0647 0.0462 2680 0.0802 0.0572 0.0759 0.0542 0.0651 0.0465 2690 0.0808 0.0576 0.0765 0.0546 0.0656 0.0468 2700 0.0813 0.0580 0.0770 0.0549 0.0661 0.0471 2710 0.0819 0.0584 0.0775 0.0553 0.0665 0.0475 2720 0.0824 0.0588 0.0780 0.0557 0.0670 0.0478 2730 0.0830 0.0592 0.0786 0.0561 0.0674 0.0481 2740 0.0836 0.0596 0.0791 0.0565 0.0679 0.0484 2750 0.0841 0.0600 0.0796 0.0568 0.0683 0.0488 2760 0.0847 0.0604 0.0802 0.0572 0.0688 0.0491 2770 0.0853 0.0608 0.0807 0.0576 0.0693 0.0494 2780 0.0858 0.0613 0.0813 0.0580 0.0697 0.0498 2790 0.0864 0.0617 0.0818 0.0584 0.0702 0.0501 2800 0.0870 0.0621 0.0823 0.0588 0.0706 0.0504 2810 0.0875 0.0625 0.0829 0.0592 0.0711 0.0508 2820 0.0881 0.0629 0.0834 0.0595 0.0716 0.0511 2830 0.0887 0.0633 0.0840 0.0599 0.0721 0.0514 2840 0.0893 0.0637 0.0845 0.0603 0.0725 0.0518 2850 0.0899 0.0641 0.0851 0.0607 0.0730 0.0521 2860 0.0904 0.0646 0.0856 0.0611 0.0735 0.0524

197




2870 0.0910 0.0650 0.0862 0.0615 0.0739 0.0528 2880 0.0916 0.0654 0.0868 0.0619 0.0744 0.0531 2890 0.0922 0.0658 0.0873 0.0623 0.0749 0.0535 2900 0.0928 0.0662 0.0879 0.0627 0.0754 0.0538 2910 0.0934 0.0667 0.0884 0.0631 0.0759 0.0541 2920 0.0940 0.0671 0.0890 0.0635 0.0764 0.0545 2930 0.0946 0.0675 0.0896 0.0639 0.0768 0.0548 2940 0.0952 0.0679 0.0901 0.0643 0.0773 0.0552 2950 0.0958 0.0684 0.0907 0.0647 0.0778 0.0555 2960 0.0964 0.0688 0.0913 0.0651 0.0783 0.0559 2970 0.0970 0.0692 0.0918 0.0655 0.0788 0.0562 2980 0.0976 0.0697 0.0924 0.0660 0.0793 0.0566 2990 0.0982 0.0701 0.0930 0.0664 0.0798 0.0569 3000 0.0988 0.0705 0.0936 0.0668 0.0803 0.0573 3010 0.0994 0.0710 0.0941 0.0672 0.0808 0.0576 3020 0.1000 0.0714 0.0947 0.0676 0.0813 0.0580 3030 0.1006 0.0718 0.0953 0.0680 0.0818 0.0583 3040 0.1013 0.0723 0.0959 0.0684 0.0823 0.0587 3050 0.1019 0.0727 0.0965 0.0688 0.0828 0.0591 3060 0.1025 0.0732 0.0970 0.0693 0.0833 0.0594 3070 0.1031 0.0736 0.0976 0.0697 0.0838 0.0598 3080 0.1037 0.0740 0.0982 0.0701 0.0843 0.0601 3090 0.1044 0.0745 0.0988 0.0705 0.0848 0.0605 3100 0.1050 0.0749 0.0994 0.0709 0.0853 0.0609 3110 0.1056 0.0754 0.1000 0.0714 0.0858 0.0612 3120 0.1062 0.0758 0.1006 0.0718 0.0863 0.0616 3130 0.1069 0.0763 0.1012 0.0722 0.0868 0.0620 3140 0.1075 0.0767 0.1018 0.0727 0.0873 0.0623

198




3150 0.1081 0.0772 0.1024 0.0731 0.0878 0.0627 3160 0.1088 0.0776 0.1030 0.0735 0.0884 0.0631 3170 0.1094 0.0781 0.1036 0.0739 0.0889 0.0634 3180 0.1101 0.0785 0.1042 0.0744 0.0894 0.0638 3190 0.1107 0.0790 0.1048 0.0748 0.0899 0.0642 3200 0.1113 0.0795 0.1054 0.0752 0.0904 0.0645 3210 0.1120 0.0799 0.1060 0.0757 0.0910 0.0649 3220 0.1126 0.0804 0.1066 0.0761 0.0915 0.0653 3230 0.1133 0.0808 0.1073 0.0765 0.0920 0.0657 3240 0.1139 0.0813 0.1079 0.0770 0.0925 0.0661 3250 0.1146 0.0818 0.1085 0.0774 0.0931 0.0664 3260 0.1152 0.0822 0.1091 0.0779 0.0936 0.0668 3270 0.1159 0.0827 0.1097 0.0783 0.0941 0.0672 3280 0.1165 0.0832 0.1103 0.0788 0.0947 0.0676 3290 0.1172 0.0836 0.1110 0.0792 0.0952 0.0679 3300 0.1179 0.0841 0.1116 0.0796 0.0957 0.0683 3310 0.1185 0.0846 0.1122 0.0801 0.0963 0.0687 3320 0.1192 0.0851 0.1129 0.0805 0.0968 0.0691 3330 0.1199 0.0855 0.1135 0.0810 0.0974 0.0695 3340 0.1205 0.0860 0.1141 0.0814 0.0979 0.0699 3350 0.1212 0.0865 0.1147 0.0819 0.0984 0.0703 3360 0.1219 0.0870 0.1154 0.0823 0.0990 0.0706 3370 0.1225 0.0874 0.1160 0.0828 0.0995 0.0710 3380 0.1232 0.0879 0.1167 0.0833 0.1001 0.0714 3390 0.1239 0.0884 0.1173 0.0837 0.1006 0.0718 3400 0.1246 0.0889 0.1179 0.0842 0.1012 0.0722 3410 0.1252 0.0894 0.1186 0.0846 0.1017 0.0726 3420 0.1259 0.0899 0.1192 0.0851 0.1023 0.0730

199




3430 0.1266 0.0903 0.1199 0.0855 0.1028 0.0734 3440 0.1273 0.0908 0.1205 0.0860 0.1034 0.0738 3450 0.1280 0.0913 0.1212 0.0865 0.1039 0.0742 3460 0.1287 0.0918 0.1218 0.0869 0.1045 0.0746 3470 0.1293 0.0923 0.1225 0.0874 0.1051 0.0750 3480 0.1300 0.0928 0.1231 0.0879 0.1056 0.0754 3490 0.1307 0.0933 0.1238 0.0883 0.1062 0.0758 3500 0.1314 0.0938 0.1244 0.0888 0.1068 0.0762 3510 0.1321 0.0943 0.1251 0.0893 0.1073 0.0766 3520 0.1328 0.0948 0.1257 0.0897 0.1079 0.0770 3530 0.1335 0.0953 0.1264 0.0902 0.1085 0.0774 3540 0.1342 0.0958 0.1271 0.0907 0.1090 0.0778 3550 0.1349 0.0963 0.1277 0.0912 0.1096 0.0782 3560 0.1356 0.0968 0.1284 0.0916 0.1102 0.0786 3570 0.1363 0.0973 0.1291 0.0921 0.1107 0.0790 3580 0.1370 0.0978 0.1297 0.0926 0.1113 0.0794 3590 0.1377 0.0983 0.1304 0.0931 0.1119 0.0799 3600 0.1384 0.0988 0.1311 0.0936 0.1125 0.0803 3610 0.1392 0.0993 0.1318 0.0940 0.1130 0.0807 3620 0.1399 0.0998 0.1324 0.0945 0.1136 0.0811 3630 0.1406 0.1003 0.1331 0.0950 0.1142 0.0815 3640 0.1413 0.1008 0.1338 0.0955 0.1148 0.0819 3650 0.1420 0.1014 0.1345 0.0960 0.1154 0.0823 3660 0.1427 0.1019 0.1352 0.0965 0.1160 0.0828 3670 0.1435 0.1024 0.1358 0.0970 0.1165 0.0832 3680 0.1442 0.1029 0.1365 0.0974 0.1171 0.0836 3690 0.1449 0.1034 0.1372 0.0979 0.1177 0.0840 3700 0.1456 0.1039 0.1379 0.0984 0.1183 0.0844

200




3710 0.1464 0.1045 0.1386 0.0989 0.1189 0.0849 3720 0.1471 0.1050 0.1393 0.0994 0.1195 0.0853 3730 0.1478 0.1055 0.1400 0.0999 0.1201 0.0857 3740 0.1486 0.1060 0.1407 0.1004 0.1207 0.0861 3750 0.1493 0.1066 0.1414 0.1009 0.1213 0.0866 3760 0.1500 0.1071 0.1421 0.1014 0.1219 0.0870 3770 0.1508 0.1076 0.1428 0.1019 0.1225 0.0874 3780 0.1515 0.1081 0.1435 0.1024 0.1231 0.0878 3790 0.1523 0.1087 0.1442 0.1029 0.1237 0.0883 3800 0.1530 0.1092 0.1449 0.1034 0.1243 0.0887 3810 0.1538 0.1097 0.1456 0.1039 0.1249 0.0891 3820 0.1545 0.1103 0.1463 0.1044 0.1255 0.0896 3830 0.1553 0.1108 0.1470 0.1049 0.1261 0.0900 3840 0.1560 0.1113 0.1477 0.1054 0.1267 0.0904 3850 0.1568 0.1119 0.1484 0.1059 0.1273 0.0909 3860 0.1575 0.1124 0.1491 0.1064 0.1279 0.0913 3870 0.1583 0.1130 0.1499 0.1070 0.1286 0.0918 3880 0.1590 0.1135 0.1506 0.1075 0.1292 0.0922 3890 0.1598 0.1140 0.1513 0.1080 0.1298 0.0926 3900 0.1605 0.1146 0.1520 0.1085 0.1304 0.0931 3910 0.1613 0.1151 0.1527 0.1090 0.1310 0.0935 3920 0.1621 0.1157 0.1535 0.1095 0.1317 0.0940 3930 0.1628 0.1162 0.1542 0.1100 0.1323 0.0944 3940 0.1636 0.1168 0.1549 0.1106 0.1329 0.0948 3950 0.1644 0.1173 0.1556 0.1111 0.1335 0.0953 3960 0.1651 0.1179 0.1564 0.1116 0.1341 0.0957 3970 0.1659 0.1184 0.1571 0.1121 0.1348 0.0962 3980 0.1667 0.1190 0.1578 0.1126 0.1354 0.0966

201




3990 0.1675 0.1195 0.1586 0.1132 0.1360 0.0971 4000 0.1682 0.1201 0.1593 0.1137 0.1367 0.0975 4010 0.1690 0.1206 0.1600 0.1142 0.1373 0.0980 4020 0.1698 0.1212 0.1608 0.1147 0.1379 0.0984 4030 0.1706 0.1217 0.1615 0.1153 0.1386 0.0989 4040 0.1714 0.1223 0.1623 0.1158 0.1392 0.0994 4050 0.1722 0.1229 0.1630 0.1163 0.1398 0.0998 4060 0.1729 0.1234 0.1637 0.1169 0.1405 0.1003 4070 0.1737 0.1240 0.1645 0.1174 0.1411 0.1007 4080 0.1745 0.1246 0.1652 0.1179 0.1418 0.1012 4090 0.1753 0.1251 0.1660 0.1185 0.1424 0.1016 4100 0.1761 0.1257 0.1667 0.1190 0.1431 0.1021 4110 0.1769 0.1263 0.1675 0.1195 0.1437 0.1026 4120 0.1777 0.1268 0.1683 0.1201 0.1443 0.1030 4130 0.1785 0.1274 0.1690 0.1206 0.1450 0.1035 4140 0.1793 0.1280 0.1698 0.1212 0.1456 0.1039 4150 0.1801 0.1285 0.1705 0.1217 0.1463 0.1044 4160 0.1809 0.1291 0.1713 0.1222 0.1470 0.1049 4170 0.1817 0.1297 0.1720 0.1228 0.1476 0.1053 4180 0.1825 0.1303 0.1728 0.1233 0.1483 0.1058 4190 0.1833 0.1308 0.1736 0.1239 0.1489 0.1063 4200 0.1841 0.1314 0.1743 0.1244 0.1496 0.1068 4210 0.1849 0.1320 0.1751 0.1250 0.1502 0.1072 4220 0.1858 0.1326 0.1759 0.1255 0.1509 0.1077 4230 0.1866 0.1332 0.1767 0.1261 0.1516 0.1082 4240 0.1874 0.1337 0.1774 0.1266 0.1522 0.1086 4250 0.1882 0.1343 0.1782 0.1272 0.1529 0.1091 4260 0.1890 0.1349 0.1790 0.1277 0.1536 0.1096

202




4270 0.1899 0.1355 0.1798 0.1283 0.1542 0.1101 4280 0.1907 0.1361 0.1805 0.1289 0.1549 0.1105 4290 0.1915 0.1367 0.1813 0.1294 0.1556 0.1110 4300 0.1923 0.1373 0.1821 0.1300 0.1562 0.1115 4310 0.1932 0.1379 0.1829 0.1305 0.1569 0.1120 4320 0.1940 0.1384 0.1837 0.1311 0.1576 0.1125 4330 0.1948 0.1390 0.1845 0.1316 0.1583 0.1129 4340 0.1956 0.1396 0.1853 0.1322 0.1589 0.1134 4350 0.1965 0.1402 0.1860 0.1328 0.1596 0.1139 4360 0.1973 0.1408 0.1868 0.1333 0.1603 0.1144 4370 0.1982 0.1414 0.1876 0.1339 0.1610 0.1149 4380 0.1990 0.1420 0.1884 0.1345 0.1617 0.1154 4390 0.1998 0.1426 0.1892 0.1350 0.1623 0.1159 4400 0.2007 0.1432 0.1900 0.1356 0.1630 0.1163 4410 0.2015 0.1438 0.1908 0.1362 0.1637 0.1168 4420 0.2024 0.1444 0.1916 0.1368 0.1644 0.1173 4430 0.2032 0.1450 0.1924 0.1373 0.1651 0.1178 4440 0.2041 0.1456 0.1932 0.1379 0.1658 0.1183 4450 0.2049 0.1463 0.1940 0.1385 0.1665 0.1188 4460 0.2058 0.1469 0.1948 0.1391 0.1672 0.1193 4470 0.2066 0.1475 0.1956 0.1396 0.1678 0.1198 4480 0.2075 0.1481 0.1965 0.1402 0.1685 0.1203 4490 0.2083 0.1487 0.1973 0.1408 0.1692 0.1208 4500 0.2092 0.1493 0.1981 0.1414 0.1699 0.1213 4510 0.2101 0.1499 0.1989 0.1420 0.1706 0.1218 4520 0.2109 0.1505 0.1997 0.1425 0.1713 0.1223 4530 0.2118 0.1512 0.2005 0.1431 0.1720 0.1228 4540 0.2127 0.1518 0.2014 0.1437 0.1727 0.1233

203




4550 0.2135 0.1524 0.2022 0.1443 0.1734 0.1238 4560 0.2144 0.1530 0.2030 0.1449 0.1742 0.1243 4570 0.2153 0.1536 0.2038 0.1455 0.1749 0.1248 4580 0.2161 0.1543 0.2046 0.1461 0.1756 0.1253 4590 0.2170 0.1549 0.2055 0.1466 0.1763 0.1258 4600 0.2179 0.1555 0.2063 0.1472 0.1770 0.1263 4610 0.2188 0.1561 0.2071 0.1478 0.1777 0.1268 4620 0.2196 0.1568 0.2080 0.1484 0.1784 0.1273 4630 0.2205 0.1574 0.2088 0.1490 0.1791 0.1278 4640 0.2214 0.1580 0.2096 0.1496 0.1798 0.1284 4650 0.2223 0.1586 0.2105 0.1502 0.1806 0.1289 4660 0.2232 0.1593 0.2113 0.1508 0.1813 0.1294 4670 0.2241 0.1599 0.2121 0.1514 0.1820 0.1299 4680 0.2249 0.1605 0.2130 0.1520 0.1827 0.1304 4690 0.2258 0.1612 0.2138 0.1526 0.1835 0.1309 4700 0.2267 0.1618 0.2147 0.1532 0.1842 0.1314 4710 0.2276 0.1625 0.2155 0.1538 0.1849 0.1320 4720 0.2285 0.1631 0.2164 0.1544 0.1856 0.1325 4730 0.2294 0.1637 0.2172 0.1550 0.1864 0.1330 4740 0.2303 0.1644 0.2181 0.1556 0.1871 0.1335 4750 0.2312 0.1650 0.2189 0.1562 0.1878 0.1340 4760 0.2321 0.1657 0.2198 0.1569 0.1885 0.1346 4770 0.2330 0.1663 0.2206 0.1575 0.1893 0.1351 4780 0.2339 0.1669 0.2215 0.1581 0.1900 0.1356 4790 0.2348 0.1676 0.2223 0.1587 0.1908 0.1361 4800 0.2357 0.1682 0.2232 0.1593 0.1915 0.1367 4810 0.2366 0.1689 0.2241 0.1599 0.1922 0.1372 4820 0.2376 0.1695 0.2249 0.1605 0.1930 0.1377

204




4830 0.2385 0.1702 0.2258 0.1611 0.1937 0.1383 4840 0.2394 0.1708 0.2267 0.1618 0.1945 0.1388 4850 0.2403 0.1715 0.2275 0.1624 0.1952 0.1393 4860 0.2412 0.1722 0.2284 0.1630 0.1959 0.1398 4870 0.2421 0.1728 0.2293 0.1636 0.1967 0.1404 4880 0.2431 0.1735 0.2301 0.1642 0.1974 0.1409 4890 0.2440 0.1741 0.2310 0.1649 0.1982 0.1414 4900 0.2449 0.1748 0.2319 0.1655 0.1989 0.1420 4910 0.2458 0.1754 0.2328 0.1661 0.1997 0.1425 4920 0.2467 0.1761 0.2336 0.1667 0.2004 0.1431 4930 0.2477 0.1768 0.2345 0.1674 0.2012 0.1436 4940 0.2486 0.1774 0.2354 0.1680 0.2020 0.1441 4950 0.2495 0.1781 0.2363 0.1686 0.2027 0.1447 4960 0.2505 0.1788 0.2372 0.1693 0.2035 0.1452 4970 0.2514 0.1794 0.2380 0.1699 0.2042 0.1458 4980 0.2523 0.1801 0.2389 0.1705 0.2050 0.1463 4990 0.2533 0.1808 0.2398 0.1712 0.2057 0.1468 5000 0.2542 0.1814 0.2407 0.1718 0.2065 0.1474

205


Pipe Type

Schedule 40 Schedule 30 Schedule 10

C Factor 100 120 100 120 100 120 ID

(inches) 10.020 10.020 10.136 10.136 10.420 10.420


500 0.0012 0.0008 0.0011 0.0008 0.0010 0.0007 600 0.0017 0.0012 0.0016 0.0011 0.0014 0.0010 700 0.0022 0.0016 0.0021 0.0015 0.0018 0.0013 800 0.0028 0.0020 0.0027 0.0019 0.0023 0.0017 900 0.0035 0.0025 0.0033 0.0024 0.0029 0.0021 1000 0.0043 0.0031 0.0040 0.0029 0.0035 0.0025 1100 0.0051 0.0036 0.0048 0.0034 0.0042 0.0030 1200 0.0060 0.0043 0.0057 0.0040 0.0050 0.0035 1300 0.0069 0.0050 0.0066 0.0047 0.0057 0.0041 1400 0.0080 0.0057 0.0075 0.0054 0.0066 0.0047 1500 0.0091 0.0065 0.0086 0.0061 0.0075 0.0053 1600 0.0102 0.0073 0.0096 0.0069 0.0084 0.0060 1700 0.0114 0.0081 0.0108 0.0077 0.0094 0.0067 1800 0.0127 0.0091 0.0120 0.0086 0.0105 0.0075 1900 0.0140 0.0100 0.0133 0.0095 0.0116 0.0083 2000 0.0154 0.0110 0.0146 0.0104 0.0127 0.0091 2100 0.0169 0.0120 0.0159 0.0114 0.0139 0.0099 2200 0.0184 0.0131 0.0174 0.0124 0.0152 0.0108 2300 0.0200 0.0142 0.0189 0.0135 0.0165 0.0118 2400 0.0216 0.0154 0.0204 0.0146 0.0178 0.0127 2500 0.0233 0.0166 0.0220 0.0157 0.0192 0.0137 2600 0.0250 0.0179 0.0237 0.0169 0.0207 0.0148 2700 0.0268 0.0192 0.0254 0.0181 0.0222 0.0158 2800 0.0287 0.0205 0.0272 0.0194 0.0237 0.0169 2900 0.0306 0.0219 0.0290 0.0207 0.0253 0.0181 3000 0.0326 0.0233 0.0308 0.0220 0.0270 0.0192

206


Pipe Type


C Factor 100 120 100 120 100 120 ID

(inches) 10.020 10.020 10.136 10.136 10.420 10.420


3100 0.0347 0.0247 0.0328 0.0234 0.0287 0.0204 3200 0.0368 0.0262 0.0348 0.0248 0.0304 0.0217 3300 0.0389 0.0278 0.0368 0.0263 0.0322 0.0230 3400 0.0411 0.0294 0.0389 0.0278 0.0340 0.0243 3500 0.0434 0.0310 0.0410 0.0293 0.0359 0.0256 3600 0.0457 0.0326 0.0432 0.0308 0.0378 0.0270 3700 0.0481 0.0343 0.0455 0.0325 0.0397 0.0284 3800 0.0505 0.0361 0.0478 0.0341 0.0418 0.0298 3900 0.0530 0.0378 0.0501 0.0358 0.0438 0.0313 4000 0.0556 0.0396 0.0525 0.0375 0.0459 0.0328 4100 0.0582 0.0415 0.0550 0.0392 0.0481 0.0343 4200 0.0608 0.0434 0.0575 0.0410 0.0502 0.0359 4300 0.0635 0.0453 0.0600 0.0429 0.0525 0.0375 4400 0.0663 0.0473 0.0627 0.0447 0.0548 0.0391 4500 0.0691 0.0493 0.0653 0.0466 0.0571 0.0407 4600 0.0719 0.0513 0.0680 0.0485 0.0595 0.0424 4700 0.0749 0.0534 0.0708 0.0505 0.0619 0.0442 4800 0.0778 0.0556 0.0736 0.0525 0.0643 0.0459 4900 0.0809 0.0577 0.0765 0.0546 0.0668 0.0477 5000 0.0839 0.0599 0.0794 0.0566 0.0694 0.0495 5100 0.0871 0.0621 0.0823 0.0588 0.0720 0.0514 5200 0.0903 0.0644 0.0853 0.0609 0.0746 0.0532 5300 0.0935 0.0667 0.0884 0.0631 0.0773 0.0552 5400 0.0968 0.0691 0.0915 0.0653 0.0800 0.0571 5500 0.1001 0.0715 0.0947 0.0676 0.0828 0.0591 5600 0.1035 0.0739 0.0979 0.0699 0.0856 0.0611

207


Pipe Type


C Factor 100 120 100 120 100 120 ID

(inches) 10.020 10.020 10.136 10.136 10.420 10.420


5700 0.1070 0.0763 0.1011 0.0722 0.0884 0.0631 5800 0.1105 0.0788 0.1045 0.0745 0.0913 0.0652 5900 0.1140 0.0814 0.1078 0.0769 0.0942 0.0673 6000 0.1176 0.0839 0.1112 0.0794 0.0972 0.0694 6100 0.1213 0.0866 0.1147 0.0818 0.1002 0.0715 6200 0.1250 0.0892 0.1182 0.0843 0.1033 0.0737 6300 0.1287 0.0919 0.1217 0.0869 0.1064 0.0759 6400 0.1325 0.0946 0.1253 0.0894 0.1095 0.0782 6500 0.1364 0.0973 0.1290 0.0920 0.1127 0.0805 6600 0.1403 0.1001 0.1327 0.0947 0.1160 0.0828 6700 0.1443 0.1030 0.1364 0.0973 0.1192 0.0851 6800 0.1483 0.1058 0.1402 0.1001 0.1225 0.0875 6900 0.1523 0.1087 0.1440 0.1028 0.1259 0.0898 7000 0.1564 0.1116 0.1479 0.1056 0.1293 0.0923 7100 0.1606 0.1146 0.1518 0.1084 0.1327 0.0947 7200 0.1648 0.1176 0.1558 0.1112 0.1362 0.0972 7300 0.1691 0.1207 0.1599 0.1141 0.1397 0.0997 7400 0.1734 0.1237 0.1639 0.1170 0.1433 0.1023 7500 0.1777 0.1269 0.1680 0.1199 0.1469 0.1048 7600 0.1821 0.1300 0.1722 0.1229 0.1505 0.1074 7700 0.1866 0.1332 0.1764 0.1259 0.1542 0.1101 7800 0.1911 0.1364 0.1807 0.1290 0.1579 0.1127 7900 0.1957 0.1396 0.1850 0.1320 0.1617 0.1154 8000 0.2003 0.1429 0.1894 0.1351 0.1655 0.1181 8100 0.2049 0.1463 0.1938 0.1383 0.1694 0.1209 8200 0.2096 0.1496 0.1982 0.1415 0.1733 0.1236

208

Sprinkler calculation - Example

The following is an outline of the steps to complete the hydraulic calculation of the sprinkler system shown in the following sketch.

This sprinkler system will be calculated for a density of 4.5 mm/min (0.12 gpm/ft2) over the entire 55.74 m2 (600 ft2) system coverage area. It is a wet pipe system comprised of steel, heavy (schedule 40) pipe (C=120). Step 1. Determine the flow and pressure required at the most remote sprinkler using the following formulas: Q1 = (D)(A)

p1 = (Q/k)2 Where: Q1 = Flow from the sprinkler - lpm (gpm) D = Design density - mm/min (gpm/ft2)

209

A = Area protected by the sprinkler – m2 (ft) P1 = Required pressure at the sprinkler – bar (psi) k = Sprinkler k-factor Computing Q1 and P1:

Metric US measure Q1 = (4.5)(9.3) = 41.9 lpm Q1 = (0.12)(100) = 12 gpm p1 = (41.9/80)2 = 0.27 bar p1 = (12/5.6)2 = 4.6 psi As the minimum required sprinkler pressure is 0.5 bar (7 psi), adjust p1 to 0.5 bar (7 psi) and recalculate the flow using the formula: Q1 = k(p1)1/2 or

Metric US measure Q1 = 80 (0.5)1/2 = 56.6 lpm Q1 = 5.6 (7)1/2 = 14.8 gpm Step 2. Using Table 11, compute the friction loss from sprinkler 1 to sprinkler 2. F1-2 = (L) f1-2 Where: F1-2 = Friction loss for the selected section of pipe – bar (psi) L= Length of pipe including equivalent length of fittings – m (ft.) f1-2 = Friction loss per lineal length (m or ft.) for the flow rate

and pipe size or

Metric US measure F1-2 = (3) 0.0226 = 0.07 bar F1-2 = (10) 0.0764 = 0.8 psi

210

Step 3. Compute the flow from the sprinkler 2 using the following formula: Q2 = k(p2)1/2 Where:

Metric US measure p2 = p1 + F1-2 = 0.5 + 0.07 = 0.57 bar

p2 = p1 + F1-2 = 7 + 0.8 = 7.8 psi

and:

Metric US measure Q2 = 80 (0.57)1/2 = 60.4 lpm Q2 = 5.6 (7.8)1/2 = 15.6 gpm

Step 4. Compute the total flow at sprinkler 2.

Metric US measure Q2T = Q1 + Q2 = 56.6 + 60.4 = 117 lpm

Q2T = Q1 + Q2 = 14.8 + 15.6 = 30.4 gpm

Step 5. Using Table 11, compute the friction loss from sprinkler 2 to the top of riser nipple A. Include 5 equivalent feet of pipe for the 25 mm (1") tee outlet at the top of riser nipple A.

Metric US measure F2-A = (L) Fl2-A = (3) 0.0815 = 0.24 bar

F2-A = (L) Fl2-A = (10) 0.2755 = 2.8 psi

211

Step 6. Determine the total flow and pressure from the top left side of riser nipple A:

Metric US measure QATL = 117 lpm QATL = 30.4 gpm pATL = p1-2 + F2-A = 0.57 + 0.24 = 0.81 bar

pATL = p1-2 + F2-A = 7.8 + 2.8 = 10.6 psi

Step 7. Compute the flow and pressure at sprinkler 3. Ultimately, it is the same as the flow and pressure at sprinkler 1.

Metric US measure Q3 = 56.6 lpm Q3 = 14.8 gpm p3 = 0.5 bar p3 = 7 psi

Step 8. Using Table 11, compute the friction loss from sprinkler 3 to the top of riser nipple A. Include 5 equivalent feet of pipe for the 25 mm (1") tee outlet at the top of riser nipple A.

Metric US measure F3-A = (L) f3-A = (3) 0.0226 = 0.07 bar

F3-A = (L) f3-A = (10) 0.0764 = 0.8 psi

Step 9. Determine the total flow and pressure from the top right side of riser nipple A:

Metric US measure QATR = 56.6 lpm QATR = 14.8 gpm pATR = p3 + F2-A = 0.5 + 0.07 = 0.57 bar

pATR = p3 + F2-A = 7.0 + 0.8 = 7.8 psi

212

Step 10. As the pressures at the top right and top left sides of riser nipple A must be equal, the pressure on the top right must be increased to equal pATL. To make this adjustment, the k-factor for kATR must first be determined using the following formula:

Metric US measure kATR = QATR/(pATR)1/2 = 56.6/(0.57)1/2 = 75

kATR = QATR/(pATR)1/2 = 14.8/(7.8)1/2 = 5.30

With the k-factor determined, the adjusted flow at QATR can be determined as follows:

Metric US measure QATR-ADJ = 75 (0.81)1/2 = 67.5 lpm

QATR-ADJ = 5.30 (10.6)1/2 = 17.3 gpm

Step 11. Calculate the total flow and pressure at the top of riser nipple A.

Metric US measure QAT = 117 + 67.5 = 184.5 lpm

QAT = 30.4 + 17.3 = 47.7 gpm

PAT = 0.81 bar PAT = 10.6 psi Step 12. Calculate the friction loss down riser nipple A. Include 1.8 (6) equivalent meters (feet) of pipe for the 32 mm (1¼") tee outlet at the bottom of riser nipple A.

Metric US Measure FAT-A = (L) fAT-A = (2.5) 0.0440 = 0.11bar

FAT-A = (L) fAT-A = (8) 0.1729 = 1.4 psi

213

Step 13. Calculate the elevation loss down riser nipple A using the following formula:

Metric US measure FEL = L (0.0981 bar/m) FEL = L (0.433 psi/ft)

Note that L is positive for a drop and negative for a rise.

Metric US measure FEL@A = +0.7 (0.0981) = +0.07 bar

FEL@A = +2 (0.433) = +0.9 psi

Step 14. Compute the total flow and pressure at the bottom of riser nipple A.

Metric US measure QA = 184.5 lpm QA = 47.7 gpm pA = pAT + FAT-A + FEL@A = 0.81 + 0.11 + (+0.07) = 0.99 bar

pA = pAT + FAT-A + FEL@A = 10.6 + 1.4 + (+0.9) = 12.9 psi

Step 15. Calculate the k-factor at the bottom of riser nipple A. This k-factor will be used again to determine the flow in riser nipple B.

Metric US measure kA = QA/(pA)1/2 = 184.5/(0.99)1/2 = 185.4

kA = QA/(pA)1/2 = 47.7/(12.9)1/2 = 13.28

214

Step 16. Calculate the friction loss between riser nipple A and B.

Metric US measure FA-B = (L) fA-B = (3) 0.0440 = 0.13 bar

FA-B = (L) fA-B = (10) 0.1729 = 1.7 psi

Step 17. Compute the total flow between riser nipple A and B.

Metric US measure QA-B = 184.5 lpm QA-B = 47.7 gpm PB = pA + FA-B = 0.99 + 0.13 = 1.12 bar

PB = pA + FA-B = 12.9 + 1.7 = 14.6 psi

Step 18. As the branch line configuration at riser nipple B is exactly the same as at riser nipple B, the k-factor at riser nipple A can be used to compute the flow in riser nipple B as follows:

Metric US measure QB-BT = kA(PB)1/2

= 185.4(1.12)1/2 = 196.2 lpm QB-BT = kA(PB)1/2

= 13.28(14.6)1/2 = 50.7 gpm Step 19. Compute the total flow and pressure at riser nipple B.

Metric US measure QB = QB-BT+QA-B = 196.2 + 184.5 = 380.7 lpm

QB = QB-BT + QA-B = 50.7 + 47.7 = 98.4 gpm

PB = 1.12 bar PB = 14.6 psi

215

Step 20. Calculate the friction loss through the feed main and riser between riser nipple B and the system Base of Riser (BoR). This can be calculated in one step, as all pipe is 100 mm (4 inch). First total up all pipe lengths and equivalent fitting lengths:

Fittings 100 mm pipe 4 in. pipe Actual pipe length 13.7 m 45 ft. elbow (top or riser) 2.7 m 9 ft. check valve 6.7 m 22 ft. butterfly valve 3.7 m 12 ft.

Total 26.8 m 88 ft.

Metric US measure FB-BoR = (L) fB-BoR = (26.8) 0.0009 = 0.02 bar

FB-BoR = (L) fB-BoR = (88) 0.0037 = 0.3 psi

Step 21. Calculate the elevation loss down the main riser using the formula:

Metric US measure FEL = L (0.0981 bar/m) FEL = L (0.433 psi/ft)

Note that L is positive for a drop and negative for a rise.

Metric US measure FEL@BoR = +4.6 (0.0981) = +0.45 bar

FEL@BoR = +15 (0.433) = +6.5 psi

216

Step 22. Compute the total flow and pressure at the Base of Riser nipple A.

Metric US measure QA = 380.7 lpm QA = 98.4 gpm pBoR = pB + FB-BoR + FEL@BoR = 1.12 + 0.02 + (+0.45) = 1.59 bar

pBoR = pB + FB-BoR + FEL@BoR = 14.6 + 0.3 + (+6.5) = 21.4 psi

In summary, to deliver a density of 4.5 mm/min (0.12 gpm/ft2) over the entire 55.74 m2 (600 ft2) the system requires 381 lpm (98 gpm) @ 1.59 bar (21 psi) at the base of riser.

217

References

LPC Rules for Automatic Sprinkler Installations Incorporating BS EN 12845. United Kingdom: Fire Protection Association (FPA), 2009. Print.

NFPA 13. Standard for the Installation of Sprinkler Systems. Quincy, MA; NFPA, 2013. Online.

NFPA 20; Standard for the Installation of Stationary Pumps for Fire Protection; Quincy, MA; NFPA, 2013. Online.

NFPA 25; Standard for the Inspection, Testing, and Maintenance of Water-Based Fire Protection Systems; Quincy, MA; NFPA, 2014. Online.

NFPA 70E; Standard for Electrical Safety in the Workplace®; Quincy, MA; NFPA, 2012. Online.

NFPA 291; Recommended Practice for Fire Flow Testing and Marking of Hydrants; Quincy, MA; NFPA, 2013. Online.

Cote, Arthur E., John Raymond Hall, Pamela A. Powell, Casey C. Grant, and Robert E. Solomon. Fire Protection Handbook. Quincy, MA: National Fire Protection Association, 2008. Print.

Klaus, Matthew J. Automatic Sprinkler Systems Handbook. Quincy, MA: National Fire Protection Association, 2014.

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© 2015 The Zurich Services Corporation. All rights reserved. The information in this publication was compiled by The Zurich Services Corporation from sources believed to be reliable for informational purposes only. All sample policies and procedures herein should serve as a guideline, which you can use to create your own policies and procedures. We trust that you will customize these samples to reflect your own operations and believe that these samples may serve as a helpful platform for this endeavor. Any and all information contained herein is not intended to constitute advice (particularly not legal advice). Accordingly, persons requiring advice should consult independent advisors when developing programs and policies. We do not guarantee the accuracy of this information or any results and further assume no liability in connection with this publication and sample policies and procedures, including any information, methods or safety suggestions contained herein. We undertake no obligation to publicly update or revise any of this information, whether to reflect new information, future developments, events or circumstances or otherwise. Moreover, The Zurich Services Corporation reminds you that this cannot be assumed to contain every acceptable safety and compliance procedure or that additional procedures might not be appropriate under the circumstances. The subject matter of this publication is not tied to any specific insurance product nor will adopting these policies and procedures ensure coverage under any insurance policy.

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