metering fluids.docx

PAMANTASAN NG LUNGSOD NG MAYNILACollege of Engineering and Technology

Chemical Engineering Department

METERING FLUIDS

SUBMITTED BY:ANCHETA, Jeric P.HARO, April joy

ILAGAN, Elaine Jane P.SARSOZA, Andriane C.SUPREMO, Journel Ann

SUBMITTED TO:Engr. Denvert Pangayao

August 22, 2014

Metering fluids Page1



FLOWMETER

A flowmeter is a device for measurement of the quantity of fluid flowing per unit time, as in cubic feet per minute or pounds per second, or of the velocity of flow, as in feet per second.

Whatever the construction, a flowmeter if often calibrated by diverting the entire stream of fluid from its usual channel into a receiver arranged to permit accurate measurement of flow by weight or volume during a measured interval of time. A liquid may flow into a “weigh tank” mounted on scales or into a tank calibrated to indicate volume as a function of liquid depth. A gas may flow into a “gas holder,” an inverted tank floating in water or oil inside a larger tank. In a sense, all flowmeters are always calibrated in this way, for even a standard calibration meter must be checked by this method.

DIFFERENT TYPES OF FLOWMETER

1. MANOMETER

Definition and Uses of a Manometer

A manometer is an instrument for measuring the pressure acting on a column of fluid, especially one with a U-shaped tube of liquid in which a difference in the pressures acting in the two arms of the tube causes the liquid to reach different heights in the two arms. The word was derived from the French word “manomètre” equivalent to mano (Greek manós which means loose, rare, sparse) and mètre meaning meter. By the simplest, most basic definition, a manometer is a pressure-measuring instrument. However, there are different types of pressure that are commonly measured. Most pressure-measuring instruments are either designed to measure pressure as it relates to atmospheric pressure or pressure in a vacuum. Manometers fall under the category of measuring atmospheric pressure. A more precise definition of what is a manometer can be summed up as a liquid hydrostatic instrument.


http://dictionary.reference.com/browse/-meter



Physical Appearance of a ManometerManometers were the original pressure-measuring instruments because

pressure was once measured by its ability to displace a column of liquid. A manometer in its simplest form is just a piezometer tube that holds the measuring liquid. Nowadays, the most common form of a manometer is a U-shaped design. Manometers, as stated, measure pressure by displacing liquid, though not just any liquid. A manometer's gauge can either be analog or digital. Manometers are made of plastic or glass.Among manometer manufacturers, the preferred fluid is mercury because its density allows for the manufacturing of shorter and smaller manometers. Water is another popular option to use as fluid in a manometer. Even though water manometers are bigger in size than their mercury counterparts, the advantage of a water manometer is that water is non-toxic and easy to acquire. Often, you'll be able to spot water-based manometers because of the initials "W.C." that stands for "water column." Simpler, single tube manometers can only measure the pressure of a liquid, while U-shaped manometers are also able to measure gas pressure.

How does a Manometer WorksManometers work by measuring the difference between the liquid or gas

being measured against atmospheric pressure. First, liquid is placed inside the manometer, either mercury or water. When measuring gas pressure, gas will be pumped in through one end of the U-shaped manometer, then that end is sealed to keep the gas inside. The other end of the manometer is left open to allow atmospheric pressure level to do its function on the manometer's liquid. Both gas pressure and atmospheric pressure will push down on the liquid sitting at the bottom of the U-shape. If the liquid remains level across both ends, then the pressure the gas exerts is the same as that of the atmosphere. If the gas is heavier than the atmosphere, it will exert more pressure on the liquid and make it rise on the open end, past the equal point. If the liquid rises higher on the sealed end, it means atmospheric pressure is heavier than the gas.

Measuring with a ManometerManometers used to be the standard method for measuring pressure. This

became problematic once it became apparent that things like atmospheric pressure and fluid density can change the measurement of fluid displacement in a manometer. Also, temperature and even gravity tended to influence how high a column of fluid would be displaced inside a manometer. This is the reason why atmospheric pressure differences must be accounted for when doing studies that require precise measurements. Even though these small inaccuracies gave rise to vacuum systems, manometer measurements, also called manometric units, are still in use today. For example, blood pressure is still measured in millimeters of mercury, lung pressure in inches of water, and also natural gas pipeline pressures, which are noted as "inches W.C."




Disadvantages of ManometersA manometer's main advantage is its low cost. However, there are a few

disadvantages that come with a manometer that often limits their usefulness. For one, manometers tend to be bulky and rather large. This translates into a lack of portability, as they can't be disassembled into a more manageable size. Also, one must find an appropriate surface in which to place the manometer, as it needs to be level in order to provide accurate readings. Because of its fluid content, sometimes condensation may present inside the instrument, affecting readings. Also, manometers offer no over-range protection; should the pressure being tested far exceed that of the atmospheric pressure, which will cause fluid to spill out of the instrument.Manometers are very useful instruments for measuring pressure. They work by comparing pressure exerted by gas and liquids and comparing them to atmospheric pressure. Because of variation in atmospheric pressure, it is often necessary to measure atmospheric pressure versus standard atmospheric pressure to account for difference in pressure variances. While manometers are easy to use and affordable, their main disadvantages are lack of portability and bulky size.

Manometer types

1.Simple U-tube manometerMeasures the pressure of the liquids or gases. Bottom of the U-tube filled with manometric liquid which is of greater density and immiscible with the fluid to be measured.

2. Inverted U-tube manometerUsed for measuring pressure differences in liquids. The space abovethe liquid in the manometer is filled with air which can be admitted or expelled through the tap on the top, in order to adjust the level of the liquid in the manometer. For inverted U - tube manometer the manometric fluid is usually air.




3. U- tube with one leg enlargedBy making the diameter of one leg very large compared to other, movement in the large leg become very small. So it is only necessary to read the movement of liquid in the narrow leg.

4. Two fluid-U- tube manometerSmall differences in pressure in gases are often measured with this manometer in which two fluids were used.

5. Inclined U-tube manometerIn this type, one leg of a manometer is inclined in such manner that, for a small magnitude of Rm, the meniscus in the inclined tube must move a considerable distance along the tube.




DERIVATION OF THE EQUATION FOR MANOMETERAssume the shaded that the shaded portion of the U-tube is filled with liquid A having a density of ρa and that the arms of the U tube above the liquid are filled with liquid B having a density of ρb. Fluid B is immiscible with liquid A and less dense than A; it is often a gas such as air or nitrogen. (refer to the figure below)

A pressure ρa is exerted in one arm of the U tube and a pressure ρb in the other. As a result of the difference in the pressure ρa- ρb, the meniscus in one branch of the U tube is higher than the other, and the vertical distance between the two meniscus Rm, may be used to measure the difference in pressure. To derive a relationship between ρa- ρb, and Rm, start at point 1 where the pressure is ρa.

The pressure at point 2 is ρa + g (Zm+Rm)ρb. By the principles of hydrostatics, this is also the pressure at point 3. The pressure at point 4 is less than that at point 3 by the amount of gRmρa, and the pressure at point 5, which is ρb , is




still less the amount of gZmρb. These statement can be summarized by the equation:

Simplification of this statement gives,

Note that this relationship is independent of the distance Zm and of the dimensions of the tube, provided that pressures ρa and ρb are measured in the same horizontal plane. If the fluid B is a gas, ρB is usually negligible compared to ρA and may be omitted from the above equation.

Sample Problem:1. A manometer of U tube type is used to measure the pressure drop across an

orifice. Liquid A is mercury (density = 13, 590 kg/m3) and fluid B, flowing through an orifice and filling the manometer leads is brine, (density = 1,260 kg/m3). When the pressure at the taps are equal, the level of the mercury in the manometer is 0.9m below the orifice taps. Under operating conditions, the gauge pressure at the upstream tap is 0.14 bar; the pressure at the downstream tap is 250mmHg below atmospheric. What is the reading of the manometer in mm?

Solution: call the atmospheric pressure zero:

ρa = 0.14bar¿101325Pa1.01325 ¿̄ ¿ = 14,000 Pa

ρb = gZbρA

= 9.80665*(-250

1000)*13,590

ρb = 33,318.09338 PaSubstituting to the formula:

ρa- ρb = gRm (ρA- ρB)14,000 Pa + 33,318.09338 Pa = Rm * 9.80665 (13,590 – 1260) Rm = 391.33mm


ρa +g [((Zm+Rm)ρB - Rm ρA- ZmρB] =

ρb

ρa- ρb = gRm (ρA- ρB)



2. Pitot Tube

IntroductionThe Pitot tube was invented by the French engineer Henri Pitot in 1732 and was modified to its modern form in the mid-19th century by French scientist Henry Darcy. It is widely used to determine the airspeed of an aircraft, water speed of a boat, and to measure liquid, air and gas velocities in industrial applications. The pitot tube is used to measure the local velocity at a given point in the flow stream and not the average velocity in the pipe or conduit. Pitot tubes detect the flowing velocity at a single point (standard), at several points that lead into an averaging probe (multiported), or at many points across the section of a pipe or duct( area-averaging). Theory of operationIn Fig. 1, a sketch of this simple device is shown. One tube, the impact tube, has its opening normal to the direction of the flow, while the static tube has its opening parallel to the direction of flow.

The fluid flows into the opening at point 2; pressure builds up and then remains stationary at this point, called the stagnation point. The difference in the stagnation pressure ( also known as total pressure or the pitot pressure) at point 2 and the static pressure measured by the static tube represents the pressure rise associated with deceleration of the fluid. The manometer measures this small pressure rise.




The conversion from potential to kinetic energy takes place at the stagnation point, located at the Pitot tube entrance (see the schematic below. A pressure higher than the free-stream (i.e. dynamic) pressure results from the kinematic to potential conversion. This "static" pressure is measured by comparing it to the flow's dynamic pressure with a differential manometer.

If the fluid is incompressible, we can write the Bernoulli equation between point A, where the velocity v1 is undisturbed before the liquid decelerates, and point B, where the velocity V2 is zero:

v 1 22

-v 222

+(P1-P2)

P=0 (1)

Setting v2=0 and solving for v1,

v=Cp√ 2(P2−P1)ρ

(2)

Where:v=velocity v 1∈t he tube at point A∈m /sP2=stagnation pressureρ=density of t he flowing fluid at t he static pressure P1

C p=adimensionless coefficient ¿ take intoaccount deviations ¿ Eq . (1 )t hat generallyvariesbetweenabout 0.98∧1.0

NOTE: The above equation applies only to fluids that can be treated as incompressible. Liquids are treated as incompressible under almost all conditions. Gases under certain conditions can be approximated as incompressible.

The value of the pressure drop P1 –P2 or ∆P is related to ∆h, the reading on the manometer, as follows:

∆P=∆h (𝞺A- 𝞺B )g

Since the pitot tube measures velocity at only one point in the flow, several methods can be used to obtain the average velocity in the pipe. In the first method the velocity is measured at the exact center of the tube to obtain vmax . Then by using the graph for the ratio vave/vmax as a function of Reynolds number for pipes (Fig. 2.10-2 in Geankoplis), the vave can be obtained. Care should be taken to have the pilot tube at least 100 diameters downstream from any pipe obstruction.

Static Pressure MeasurementIn process fluids flowing through pipes or ducts, the static pressure is

commonly measured in one of the three ways: (1) through taps in the wall,(2) by static probes inserted into the fluid stream, or (3) by small apertures located on an aerodynamic body immersed in the flowing fluid.




Static pressure errors also depend on fluid viscosity, fluid velocity, and whether the fluid is compressible.

The total pressure develops at a point where the flow is isentropically stagnated, which is assumed to occur at the tip of a pitot tube or at a specific point on a bluff body immersed in the stream. Fig.2 illustrates a typical pitot tube, also showing the taps for sensing static pressure. Another variation is shown in Fig. 3.

Fig. 2. Typical pitot tube

Calculating ErrorWhen selecting a Pitot Static tube to be used in conjunction with any

manometer, it is necessary to select a tube with a constant close to unity, if errors in velocity are to be avoided. If data for a particular Pitot tube is not available, the constant C may be estimated. This constant is dependent on the spacing of the Pitot tubes' static pressure ports (see Fig. 4) from the base of the Pitot tube's tip and the stem's center line. Prandtl type Pitot tubes typically have constants C close to 1.

Advantageous of pitot tube (a) It is easy to remove pitot tube from pipe line.(b) Low permanent pressure loss in the pitot tube.(c) It is easy to install(d) Low cost

Disadvantages of the Pitot Tube1. Most designs do not give the average velocity directly2. With gases, the differential is very small at low velocities;

e.g., at 4.6 m/s (15.1 ft/s) the differential is only about 1.30 mm (0.051 in) of water (20C) for air at 1 atm (20C), which represents a lower limit for 1 percent error even when one uses a micromanometer with a precision of 0.0254 mm (0.001 in) of water.




Fig. 3. Schematic of an industrial device for sensing static and dynamic pressures in a flowing fluid

. Fig. 4. Cross-section of a Typical Static Tube

Sample problem:1. Air at 200f is forced through a long, circular flue 36 in. in diameter. A pitot-tube reading is taken at the center of the flue at a sufficient distance from flow disturbances to ensure normal velocity distribution. The pitot reading is 0.54 in. H2O, and the static pressure at the point of measurement is 15.25 in. H2O. The coefficient of the pitot tube is 0.98.

Calculate the fow of air, in cubic feet per minute, measured at 60F and a barometric pressure of 29.92 in Hg.

Solution:




The velocity at the center of the flue, which is that measured by the instrument,is calculated by Eq. (2), using the coefficient 0.98 to correct for imperfections in the flow pattern caused by the presence of the tube. The necessary quantities are as follows. The absolute pressure at the instrument is

p=29.92+ 15.2512.6

=31.04∈.Hg




3. Venturi Meter

A Venturi meter is a full-bore meter (fluid flow meter that operates on all fluid in the pipe or channel) that is usually inserted directly into a pipeline. If the fluid to be measured is flowing inside a closed conduit, a constriction in the channel will serve as the primary element of a flow meter. A short conical inlet section leads to a throat section, then to along discharge cone. Pressure taps at the start of the inlet section and at the throat are connected to a manometer or differentia; pressure transmitter.

In the upstream cone, the fluid velocity is increased and its pressure decreased. The pressure drop in this cone is used to measure the flow rate. In the discharge cone the velocity is decreased and the original pressure largely recovered. The angle of the discharge cone is made small between 5° and 15°, to prevent boundary layer separation and to minimize friction. Since there is no separation in a contracting cross section, the upstream cone can be made shorter than the downstream cone. Typically 90% of the pressure loss in the upstream cone is recovered.

Venturi Tube

Although venturi meters can be applied to the measurement of gas flow rates, they are most commonly used with liquids, especially large flows of water where, because of the large pressure recovery, a Venturi requires less power than other types of meters.

The basic equation for Venturi meters is obtained by writing the Bernoulli equation for incompressible fluids across the upstream cone. If Va and Vb are the average upstream and downstream velocities respectively, and ρ is the density of the fluid, the equation becomes:

α bV b2−α aV a

2=2(P¿¿a−Pb)

ρ(Equation1)¿

where: α = kinetic energy correction factor P = pressureρ = densityV =average fluid velocity




The continuity equation can be written, since the density is constant, as:

V a=(Db

Da

)2

V b=β2V b(Equation2)

where: Da = diameter of pipeDb = meter throat diameterβ = diameter ratio, Db/Da

Substituting the continuity expression to the Bernoulli statement for Venturi meters eliminates Va, hence, the equation becomes:

V b=1

√α b−β4α a√ 2(P¿¿a−Pb)

ρ(Equation3)¿

Equation 3 applies strictly to the frictionless flow of incompressible fluids. To account for the small friction loss between locations a and b, the equation above is corrected by introducing an empirical factor Cv and writing

V b=C v

√1−β4 √ 2(P¿¿ a−Pb)ρ

(Equation4 )¿

The small effects of the kinetic energy factors αa and αb are also taken into account in the definition of Cv. The coefficient Cv is determined experimentally. It is called the Venturi coefficient of which the effects of the approach velocity are not included. The effect of the approach velocity Va is accounted for by the term 1/√1−β4. When Db is less than 0.25Da, the approach velocity and the term β can be neglected, since the resulting error is less than 0.2%.

For a well-designed Venturi, the constant Cv is about 0.98 for pipe diameter of 2 – 8 in. and 0.99 for larger sizes.

The velocity through the Venturi throat Vb is not the quantity usually desired. The flow rates of practical interest are the volumetric and mass flow rates through the meter. The volumetric flow rate can be calculated as follows:

Q=V b Ab=C v Ab

√1−β4 √ 2(P¿¿a−Pb)ρ

(Equation5)¿

where:Q =volumetric flow rateAb = area of throat

The mass flow rate is obtained by multiplying the volumetric flow rate by the density:

m=Qρ=C v Ab

√1−β4 √2 ρ(P¿¿a−Pb)(Equation6)¿

where:m = fluid mass flow rate

Energy Balances on Venturi Meter




Applying the overall energy balance equation to Venturi meters if the tube is mounted horizontally in a pipeline (no difference in elevation, no work done and the operation is adiabatic) gives:

∆U+∆ (PV )=−∆(mV 2

2 )(Equation 7)

Equation 7 may be written for 1-kg mass:

∆U+∆ (PV )=m2

2 ( 1ρa

2 Aa2 −

1ρb

2 Ab2 )(Equation8)

where:U = specific internal energyV = specific volume

Rearranging equation 8 to compute for the mass flow rate gives:

m=√ 2(∆U+∆ (PV ))1

ρa2 Aa

2 −1

ρb2 Ab

2

=¿ √ 2(∆ H )

1ρa

2 Aa2 −

1ρb

2 Ab2

(Equation 9)

If the flowing fluid is incompressible or the pressure difference is so small that the density is almost constant, then:

m=√ 2 ρ2Ab

2(∆ H)

( Ab2

Aa2 )−1

(Equation 10)

If the enthalpies cannot be evaluated, the mechanical energy balance for Venturi meters gives:

∆ Pρ

+ ∆v2

2=−∑ F̂ (Equation11)

Computing for the mass flow rate using equation 11:ρ ¿

∆ P+ ρ ∆ v2

2=− ρ∑ F̂

∆ P+ ρ∆ ( m

ρA)

2

2=−ρ∑ F̂

m2

2ρ(

1

Ab2− 1

Aa2¿=−∆ P− ρ∑ F̂

m2=2 ρ(−∆ P−ρ∑ F̂ )

Ab2[( 1

Ab2−

1Aa

2 )]




m=√ 2 ρ(−∆ P−ρ∑ F̂ )

1−( Ab2

Aa2 )

(Equation 12)

The irreversibilities ∑ F̂ can be expressed as a fraction of the pressure difference ∆ P or

−∆ P−ρ∑ F̂=C v2 (−∆ P )(Equation 13)

Therefore, mass flow rate can be alternatively computed by:

m=C v Ab√ 2 ρ(−∆P)

1−( Ab2

Aa2 )

(Equation14)




4. Orifice Meter

Orifice Meter is an instrument that measures fluid flow by recording differential pressure across a restriction placed in the flow stream and the static or actual pressure acting on the system.

Parts of Orifice Meter

1. Orifice Plate – is a stainless steel thin (1/16 to ¼ in thichness) plate with a circular hole in the middle which is held between flanges of a pipe carrying the fluid whose flow rate is being measured.

Types of Orifice Plates

a. Concentric Orifice PlateThe orifice is equidistant to the inside diameter of the pipe. It is used for ideal liquid and gas and steam services. This orifice plate is best for beta ratio that fall between 0.15 to 0.75 for liquids and 0.2 to 0.7 for gases.

b. Eccentric Orifice PlateIt has a hole eccentric to the inside diameter. It shifts the edge of the orifice to the inside of the pipe wall. It is use for measuring containing solids, oil containing




water and wet steam. It has a bore offset from the center to minimize problems in services of solid-containing materials.

c. Segmental Orifice PlateThe circular section of the segmental orifice is concentric with the pipe. The segmental portion of the orifice eliminates damming of foreign materials on the upstream side of the orifice when mounted in a horizontal pipe. Depending on the type of fluid, the segmental section is placed on either the top or bottom of the horizontal pipe to increase the accuracy of the measurement.

2. Gasket – a material that is used to make a tight seal between the two flanges to make a joint fluid-tight connected.3. Flanges – the ribs where the gasket are connected for strong connection.4. Differential Pressure Sensor – openings are provided at two places near the orifice plate to measure the change in pressure (U-tube manometer, differential pressure gauge, etc.)

Operation of Orifice Meter

1. The fluid having uniform cross section of flow converges into the orifice plate’s opening in its upstream. When the fluid comes out of the orifice plate’s opening, its cross section is minimum and uniform for a particular distance and then the cross section of the fluid starts diverging in the downstream.2. At the upstream of the orifice, before the converging of the fluid takes place, the pressure of the fluid is maximum. As the fluid starts converging as it enter the orifice opening its pressure drops. When the fluid comes out of the orifice opening, its pressure is minimum and this minimum pressure remains constant in the minimum cross section area of fluid flow at the downstream.3. This minimum cross-sectional area of the fluid obtained at downstream from the orifice edge is called VENE CONTRACTA.




4. The differential pressure sensor attached between points 1 and 2 records the pressure difference (p1-p2) between these two points which becomes an indication of the flow rate of the fluid through the pipe when calibrated.

Mechanism of Measurement

Orifice plate is usually placed in a pipe in which fluid flows. When the fluid reaches the orifice plate, the fluid is forced to converge to go through the small hole; the point of maximum convergence actually occurs shortly downstream of the physical orifice at the so-called vena contracta point. As it does so, the velocity and the pressure change. Beyond the vena contracta, the fluid expands and the velocity and pressure change back to the original value. By measuring the difference in fluid pressure across tappings upstream and downstream of the plate, the volumetric and mass flow rates can be obtained from Bernoulli’s equation. Orifice plates are commonly used to measure flow rates in pipes, when the fluid is single-phase, well-mixed, having a continuous flow and occupies the entire pipe (precluding silt or trapped gas). The flow profile is even and well-developed

Calculation for Orifice Plate carrying liquid

A quantity called beta, β, that shows the relationship of the diameter of the orifice, DO, and the diameter of the pipe, D.

β=DO

DThe velocity at the point in the orifice, VO, can be computed using the overall

mechanical energy balance and continuity equation to get the final equation below.

V O=1

√1−β4 √−2 ΔPρ

Since the velocity computed above is the theoretical velocity a coefficient of discharge, CD is multiplied in the equation to get the true velocity.


http://en.wikipedia.org/wiki/File:Orifice.png



V O=CD

√1−β4 √−2 ΔPρ

From the computation of true velocity, we can compute for the mass flow rate.

QM=C D AO

√1−β4√−2 ρΔP

Calculation for Orifice Plate carrying gas

The gamma, γ and pressure ratio, r is used to compute for the correction factor, Y for the measurement of compressible flow of gases in an orifice.

γ=CpCv

r=( P2

P1)

Y=1−( 1−rγ ) (0.41+0.35 β4 ) ρg=M

P1

ZRT 1

QM=CD AOY

√1−β4√−2 ρΔP

Permanent pressure lossThe permanent pressure loss is much higher than for a venturi because of

the eddies formed when the jet expands below the vena contracta. This loss depends on β and is as follows:

P1−P4=(1−β2 )(P1−P2)

Advantages of Orifice Meter1. It is very cheap and easy method to measure flow rate.2. It has predictable characteristics and occupies less space.3. Can be used to measure flow rates in large variation of pipes.

Limitations of Orifice Meter1. The vena contracta length depends on the roughness of the inner wall of the pipe and the sharpness of the orifice plate. In certain cases it becomes difficult to tap the minimum pressure due to the above factor.2. Pressure recovery at downstream is poor, that is, overall loss varies from 40%-90% of the differential pressure.3. In the upstream straightening vanes are a must to obtain laminar flow conditions.4. Gets clogged when the suspended fluids flow. It is limited only to single phase fluids with continuous flow and must occupy the whole pipe.5. The orifice plate gets corroded and due to this after sometime, inaccuracy occurs. Moreover, the orifice plate has low physical strength. The materials used for maintaining orifice plate are stainless steel, phosper bronze and nickel.




5. Area meter

A variable area meter is a meter that measures fluid flow by allowing the cross sectional area of the device to vary in response to the flow, causing some measurable effect that indicates the rate.

In the orifice, nozzle, or venturi, the variation of flow rate through a constant area generates a variable pressure drop, which is related to the flow rate. Area meters consist of devices in which pressure drop is constant, or nearly so, and the area through which the fluid flows varies with flow rate. The area is related, through proper calibration, to the flow rate.

RotametersThe most important area meter is the

rotameter. It is an industrial flow meter used to measure the flow rate of liquids and gases. The rotameter is popular because it has a linear scale, a relatively long measurement range, and low pressure drop. It is simple to install and maintain.

The rotameter consists essentially of a gradually tapered glass tube mounted vertically in a frame with the large end up. The fluid flows upward through the tapered tube and suspends freely a float (which actually does not float but is completely submerged in the fluid). The float is the indicating element, and the greater the flow rate, the higher the float rides in the tube. The float response to flow rate changes is linear, and a 10-to-1 flow range or turndown is standard.

Principle of OperationThe rotameter’s

operation is based on the variable area principle: fluid flow raises a float in a tapered tube, increasing the area for passage of the fluid. The greater the flow, the higher the float is raised. The height of the float is




directly proportional to the flow rate. With liquids, the float is raised by a combination of the buoyancy of the liquid and the velocity head of the fluid. With gases, buoyancy is negligible, and the float responds to the velocity head alone. The entire fluid stream must flow through the annular space between the float and the tube wall. The float moves up or down in the tube in proportion to the fluid flow rate and the annular area between the float and the tube wall. The float reaches a stable position in the tube when the upward force exerted by the flowing fluid equals the downward gravitational force exerted by the weight of the float. A change in flow rate upsets this balance of the forces. The float then moves up and down, changing the annular area until it again reaches a position where the forces are in equilibrium. To satisfy the force equation, the rotameter float assumes a distinct position for every constant flow rate. The tube is marked in divisions, and the reading of the meter is obtained from the scale reading at the reading edge of the float, which is taken at the largest cross section of the float. A calibration curve must be available to convert the observed scale reading to flow rate. However, it is important to note that float position is gravity dependent; rotameters must be vertically oriented and mounted. Rotameters can be used for either liquid- or gas-flow measurement.

The bore of a glass rotameter tube is either an accurately formed plain conical taper or a taper with three beads, or flutes, parallel with the axis of the tube. In the first rotameters, angled notches in the top of the float made it rotate, but the float does not rotate in the most current designs. For opaque liquids, for high temperatures or pressures, or for other conditions where glass is impracticable, metal tubes are used. Metal tubes are plain tapered. Since in a metal tube the float is invisible, means must be provided for either indicating or transmitting the meter reading. This is accomplished by attaching a rod, called an extension, to the top or bottom of the float and using the extension as an armature. The extension is enclosed in a fluid-tight tube mounted on one of the fittings. Since the inside of this tube communicates directly with the interior of the rotameter, no stuffing box for the extension is needed. The tube is surrounded by external induction coils. The length of the extension exposed to the coils varies with the position of the float. This in turn changes the inductance of the coil, and the variation of the inductance is measured electrically to operate a control valve or to give a reading on a recorder. Also, a magnetic follower, mounted outside the extension tube and adjacent to a vertical scale, can be used as a visual indicator for the top edge of the extension. By such modifications the rotameter has developed from a simple visual indicating instrument using only glass tubes into a versatile recording and controlling device.

Floats may be constructed of metals of various densities from lead to aluminum or from glass or plastic. Stainless steel floats are common. Float shapes and proportions are also varied for different application.




Rotameters tend to have a nearly linear relationship between flow and position of the float, compared with a calibration curve for an orifice meter, for which the flow rate is proportional to the square root of the reading. The calibration of a rotameter, unlike that of an orifice meter, is not sensitive to the velocity distribution in the approaching stream, and neither long, straight, approaches nor straightening vanes are necessary.

Types of Rotameter Glass Tube Rotameters

The basic rotameter is the glass tube indicating-type. The tube is precision formed of borosilicate glass, and the float is precisely machined from metal, glass, or plastic. The metal float is usually made of stainless steel to provide corrosion resistance. The float has a sharp metering edge where the reading is observed by means of a scale mounted alongside the tube. The practical temperature limit for glass rotameters is 204°C (400°F), although operation at such high temperatures substantially reduces the operating pressure of the meter. There is a linear relationship between the operating temperature and pressure.

Metal Tube Flow meters

For higher pressures and temperatures beyond the practical range of glass tubes, metal tubes are used. These are usually manufactured in aluminum, brass, or stainless steel. The position of the piston determined by magnetic or mechanical followers that can be read from the outside of the metal metering tube. Similar to glass tube rotameters, the spring-and-piston combination determines the flow rate, and the fittings and materials of construction must be chosen as to satisfy the demands of the applications. These meters are used for services where high operating pressure or temperature, water hammer, or other forces would damage glass metering tubes.

Plastic Tube Rotameters




Plastic tubes are also used in some rotameter designs due to their lower cost and high impact strength. They are typically constructed of polycarbonate, with either metal or plastic end fittings. With plastic end fittings, care must be taken in installation, to not distort the threads. Rotameters with all plastic construction are available for applications where metal wetted parts cannot be tolerated, such as with deionized water or corrosives.

Theory and Calibration of RotametersFor a given flow rate, the equilibrium position of the float in a rotameter is

established by a balance of three forces: (1) the weight of the float, (2) the buoyant force of the fluid on the float, and (3) the drag force on the float. Force 1 acts downward, and forces 2 and 3 act upward. For equilibrium

FD gc=v f ρ f g−v f ρgWhere

FD=¿ drag forceg=¿ acceleration of gravitygc=¿ Newton’s law proportionality factorv f=¿ volume of floatρ f=¿ density of floatρ=¿ density of fluid

The equation for flow of fluid through an orifice can be applied to flow through a rotameter. The area of the orifice Ao is now the area of the annular opening between the largest cross section of the float and the wall of the tube at any point. The area of the pipe A1 is now the cross-sectional area of the rotameter tube just below the float. The pressure difference ( −∆ P ) can be expressed from a force balance across the float. The downward force exerted by the float, the weight of the float less the buoyant thrust upward, is balanced by the pressure difference across the float times the cross-sectional area of the float:

V f ( ρf−ρ ) ggc

=A f (−∆ P )

WhereV f=¿ volume of the floatρ f=¿density of the floatA f=¿ maximum cross-sectional area of the float

Then

(−∆P )=V f (ρ f−ρ ) g

A f gc




And substituting in equation 100: W=Co Ao√ 2gc ρ (−∆ P )

1−(Ao2/A1

2 ) ,

W=CR Ao√ 2 gρ ( ρf−ρ )V f

A f (1− Ao2

A12 )

Normally the ratio (Ao2/ A1

2 ) is quite small and the term (1−Ao

2

A12 ) approaches a value of

1.0 and is not included in the equation, leaving

W=CR Ao√ 2 gρ ( ρf− ρ )V f

A f

The coefficient of discharge CR is similar to its counterpart for orifices Co in that it is sensitive to viscosity and to the flow lines through the constriction. CR is a function of Reynolds number through the annular space Do v oρ /μ , where Do is equivalent diameter of the annular opening (D1−D f ) for circular tube and float.




ReferenceBrown, G. et.al. (1971). Unit Operations: Modern Asia Edition. Manila City: Cardinal Book StoreMcCabe, W. et.al. (2001). Unit Operations for Chemical Engineering. New York City: McGraw-HillGeankoplis, C. J. (2003). Principles of Transport Processes and Separation Processes. New Jersey: Prentice Hall


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