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H16Losses in Piping Systems

The equipment described in this manual is manufactured and distributed by

TECQUIPMENT LIMITED

Suppliers of technological laboratory equipment designed for teaching.

BONSALL STREET, LONG EATON, NOTTINGHAM, NG10 2AN, ENGLAND.

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SECTION 1.0

TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS

INTRODUCTION

One of the most common problems in fluid mechanics is the estimation of pressure loss. This apparatus enables pressure loss measurements to be made on several small bore pipe circuit components, typical of those found in central heating installations. This apparatus is designed for use with the TecQuipment Hydraulic Bench H1, although the equipment can equally well be supplied from some other source if required. However, al1 future reference to the bench in this manual refers directly to the TecQuipment bench.

1.1 Description of Apparatus

The apparatus, shown diagrammatically in Figure 1.1, consists of two separate hydraulic circuits, one painted dark blue, one painted light blue, each one containing a number of pipe system components. Both circuits are supplied with water from the same hydraulic bench. The components in each of the circuits are as follows:

Dark Blue Circuit

Light Blue Circuit

1. Gate Valve 2. Standard Elbow 3. 90° Mitre Bend 4. Straight Pipe 5. Globe Valve 6. Sudden Expansion

7. Sudden Contraction 8. lS0mm 90° Radius Bend 9. 100mm 90° Radius Bend 10. 50mm 90° Radius Bend 3.4.

Key to Apparatus Arrangement

A Straight Pipe 13.7mm Bore B 90° Sharp Bend (Mitre) C Proprietary 90° Elbow D Gate Valve E Sudden Enlargement - 13.7mrn/26.4mm F Sudden Contraction - 26.4mrn/13.7rnrn G Smooth 90° Bend 50mm Radius H Smooth 90° Bend 100mrn Radius J Smooth 90° Bend lS0mm Radius K Globe Valve L Straight Pipe 26.4mm Bore

In all cases (except the gate and globe valves) the pressure change across each of the components is measured by a pair of pressurized Piezometer tubes. In the case of the valves pressure measurement is made by U-tubes containing mercury.

SECTION 2.0 THEORY

Figure 2.1

Figure 2.2

Figure 2.3

For an incompressible fluid flowing through a pipe the following equations apply:

Q=V 1 A1=V 2 A2 (Continuity)

z1+P1

ρg+

V 12

2 g=z2+

P2

ρg+

V 22

2 g+hL1−2 (Bernoulli)

Notation: Q Volumetric flow rate (m3/s) V Mean Velocity (m/s)A Cross sectional area (m3) Z Height above datum (m)

P Static pressure (N/m2) hL Head Loss (m) ρ Density (kg/m3) g Acceleration due to gravity (9.81m/s2)

2.1 Head Loss

The head loss in a pipe circuit falls into two categories: (a) That due to viscous resistance extending throughout the total length of the circuit, and; (b) That due to localized effects such as valves, sudden changes in area of flow, and bends.

The overall head loss is a combination of both these categories. Because of mutual interference between neighboring components in a complex circuit the total head loss may differ from that estimated from the losses due to the individual components considered in isolation.

Head Loss in Straight Pipes

The head loss along a length, L, of straight pipe of constant diameter, d, is given by the expression:

hL=4 fLV 2

2 gd

where f is a dimensionless constant which is a function of the Reynolds number of the flow and the roughness of the internal surface of the pipe.

Head Loss due to Sudden Changes in Area of Flow

Sudden Expansion: The head loss at a sudden expansion is given by the expression:

hL=(V 1−V 2 )2

2g


Sudden Contraction: The head loss at a sudden contraction is given by the expression:

hL=K V 2

2

2 g

where K is a dimensionless coefficient which depends upon the area ratio as shown in Table 2.1. This table can be found in most good textbooks on fluid mechanics.

A2/A1 0 0.1 0.2 0.3 0.4 0.6 0.8 1.0K 0.50 0.46 0.41 0.36 0.30 0.18 0.06 0

Table 2.1 Loss Coefficient For Sudden Contractions

Head Loss Due To Bends

The head loss due to a bend is given by the expression:

hL=K BV 2

2 g

where K is a dimensionless coefficient which depends upon the bend radius/pipe radius ratio and the angle of the bend.

Note: The loss given by this expression is not the total loss caused by the bend but the excess loss above that which would be caused by a straight pipe equal in length to the length of the pipe axis.

See Figure 4.5, which shows a graph of typical loss coefficients.

Head Loss due to Valves

The head loss due to a valve is given by the expression:

hB+K V 2

2 g

where the value of K depends upon the type of valve and the degrees of opening.

Table 2.2 gives typical values of loss coefficients for gate and globe valves.

Globe Valve, Fully Open 10.0

Gate Valve, Fully Open 0.2

Gate Valve, Half Open 5.6Table 2.2

2.2. Principles of Pressure Loss Measurements

Figure 2.4 Pressurised Piezometer Tubes to Measure Pressure Loss between Two Points at Different Elevations

Considering Figure 2.4, apply Bernoulli's equation between points 1 and 2:

z+P1

ρg+

V 12

2 g=

P2

ρg+

V 22

2 g+hL

but:

V 1=V 2 (2-1)

therefore

hL=z+( P1−P2 )

ρg (2-2)

Consider Piezometer tubes:

P=P1+ρ g [ z−( x+ y ) ] (2-3)

also

P=P2−ρgy (2-4)

giving

x=z+( P1−P2 )

ρg (2-5)

Comparing Equations (2-2) and (2-5) gives

hL=x (2-6)

2.2.1 Principle of Pressure Loss Measurement

Considering Figure 2.5, since points 1 and 2 have the same elevation and pipe diameter:

P1−P2

ρ( H¿¿2O) g¿ = hL (2-7)

Consider the U-tube. Pressure in both limbs of the U-tube is equal at level 00. Therefore equating pressure at 00:

P2−ρH 2 O g ( x+ y )+ρH 2O gx=P1− ρH 2 O g1 y1 (2-8)


Figure 2.5 U- Tube Containing Mercury used to measure Pressure Loss across Valves

giving P1−P2=xg (ρHg−ρ H 2O)

(2-9)

hence: P1−P2

ρH 2 O g=x(s−1)

(2-10)

Considering Equations (2-7) and (2-10) and taking the specific gravity of mercury as 13.6:

hL = 12(2-11)

SECTION 3.0


INSTRUCTIONS FOR USE

(1) Connect the hydraulic bench supply to the inlet of the apparatus and direct the outlet hose into the hydraulic bench weighing tank.

(2) Close the globe valve, open the gate valve and admit water to the Dark Blue circuit by starting the pump and opening

the outlet valve on hydraulic bench.

(3) Allow water

to flow for two or three minutes.

(4) Close the gate valve and manipulate all of the trapped air into the air space in piezometer tubes. Check that the piezometer tubes all indicate zero pressure difference.

(5) Open the gate valve and by manipulating the bleed screws on the U- tube fill both-limbs with water ensuring no air remains.

(6) Close the gate valve, open the globe valve and repeat the above procedure for the Light Blue circuit.

The apparatus is now set up for measurement to be made on the components in either circuit.

The-datum position of the piezometer can be adjusted to any desired position either by pumping air into the manifold with the bicycle pump supplied, or by gently allowing air to escape through the manifold valve. Ensure that there are no water locks in these manifolds as these will tend to suppress the head of water recorded and so provide incorrect readings.

3.1 Filling the Mercury Manometer

Important: Mercury and its vapors are poisonous and should be treated with great care. Any local regulations regarding the handling and use of mercury should be strictly adhered to.


Due to regulations concerning the transport of mercury, TecQuipment Ltd. are unable to supply this item. To fill the mercury manometer, it is recommended that a suitable syringe and catheter tube are used (not supplied) and the mercury acquired locally.

If you are wearing any items of gold or silver, remove them.

Remove the manometer from the H16 before filling with mercury. The object is to fill the dead-ended limb with a continuous column of mercury and then invert the column so that a vacuum is formed in the closed end of the tube.

Hold the manometer upside down and support it fir

mly. Thread a suitable catheter tube into the manometer tube, ensuring the catheter tube end touches the sealed end of the glass column. Fill a syringe with 10ml of mercury and connect to the catheter tube. Slowly fill the glass column using the syringe, and as the mercury fills the column, withdraw the tube ensuring there are no air bubbles left. Fill up to the bend and return the manometer to its normal position. The optimum level for the mercury is 400mm from the bottom of the U-Tube.

When the manometer has the correct amount of mercury in it, a small quantity of water should be poured into the reservoir to cover the mercury and so prevent vapors from escaping into the air.

3.2 Experimental Procedure

The following procedure- assumes that pressure loss measurements are to bemade on all the circuit components.

Fully open the water control valve on the hydraulic bench. With the globe valve closed, fully open the gate valve to obtain maximum flow through the Dark Blue circuit. Record the readings on the piezometer tubes and the U- tube. Collect a sufficient quantity of water in the weighting tank to ensure that the weighing takes place over a minimum period of 60 seconds.

Repeat the above procedure for a total of ten different flow rates, obtained by closing the gate valve, equally spaced over the full flow range.


With simple mercury in glass thermometer record the water temperature in the sump tank of the bench each time a reading is taken.

Close the gate valve, open the globe and repeat the experimental procedure for the Light Blue circuit.

Before switching off the pump, close both the globe valve and the gate valve. This procedure prevents air gaining access to the system and so saves time in subsequent setting up.

.-

SECTION 4.0

4.1 Results


TYPICAL SET OF RESULTS AND CALCULATIONS

Basic Data

Bend Radii

Pipe Diameter (internal) Pipe Diameter [between sudden expansion

(internal) and contraction] Pipe Material Distance between pressure tappings for straight pipe and bend experiments

90° Elbow (mitre) 90° Proprietary elbow 90° Smooth bend 90° Smooth bend 90° smooth bend

= 13.7mrn

= 26.4mrn Copper Tube

= 0.914m

=0 = 12.7mm = 50mm = 100mm = 150mm

4.1.1 Identification of Manometer Tubes and Components

Manometer Tube Number

Unit

1 Proprietary Elbow Bend23 Straight Pipe45 Mitre bend67 Expansion89 Contraction1011 150mm bend1213 100mm bend1415 50mm bend16


4.2 Straight Pipe Loss

The object of this experiment is to obtain the following relationships:

(a) Head loss as a function of volume flow rate; (b) Friction Factor as a function of Reynolds Number.

Test Time To Piezometer Tube Readings (cm) U-Tube

Number Collect 18 kg Water (cm) HgWater

(s) 1 2 3 4 5 6 Gate-Valve

1 63.0 51.0 14.0 49.5 16.3 86.9 29.2 29.4 28.6*

2 65.4 52.5 18.2 50.3 19.5 87.5 33.2 31.9 25.93 69.4 51.9 21.6 49.7 21.6 86.5 37.3 33.8 24.04 73.9 52.2 25.1 49.2 24.0 85.5 41.7 35.8 22.05 79.9 53.1 29.4 48.6 27.0 84.2 47.1 38.1 19.56 88.8 53.4 33.4 48.0 29.7 83.0 52.1 40.5 17.07 99.8 53.2 36.5 46.6 31.7 81.6 56.8 42.7 14.88 111.0 52.6 39.2 46.1 33.7 80.0 59.8 44.0 13.59 146.2 52.6 44.4 54.4 37.7 78.4 66.1 47.3 10.310 229.8 52.9 49.1 45.0 41.5 77.4 72.0 50.3 7.3

* Fully Open Water Temperature 23°C

Table 4.1 Experimental Results for Dark Blue Circuit

Specimen Calculation

From Table 4.1, test number 1

Mass flow rate ¿1863

¿0.286 kg /sHead loss ¿0.332 m water


Volume flow rate (Q) ¿ Mass Flow RateDensity

¿0.286103

¿286 ×10−6 m3 / s

Area of flow (A) ¿π4

×13.72

¿147.3 mm2

Mean Velocity (V) ¿QA

¿ 286 ×10−6

147.310−6

¿1.94 m /s

Reynolds Number (Re) ¿V × dv

For water at 23°C ¿9.40 ×10−7 m2/ s

Therefore Re ¿ 1.94 ×13.7 ×10−3

9.40 ×10−7

¿2.83 ×104

Friction Factor (f) ¿hL × 2 gd4 L V 2

¿ 0.332× 2× 9.81× 13.7 ×10−3

4× 914 x10−3 ×1.942

¿0.0065

Figure 4.1 shows the head loss - volume flow rate relationship plotted as a graph of log hL against log Q.

The graph shows that the relationship is of the form hL α Qn with n = 1.73


This value is close to the normally accepted range of 1.75 to 2.00 for turbulent flow. The lower value n is found as in this apparatus, in comparatively smooth pipes at comparatively low Reynolds Number.

Figure 4.2 shows the Friction Factor - Reynolds Number relationship plotted as a graph of friction factor against Reynolds Number. The graph also shows for comparison the relationship circulated from Blasius's equation for hydraulically smooth pipes.

Blasius's equation:

f ¿0.0785ℜ1 /4 In the range 104 < Re < 105

As would be expected the graph shows that the friction factor for the copper pipe in the apparatus is greater than that predicted for a smooth pipe at the same Reynolds Number.

Figure 4.1 Head Loss - Volume Flow Rate

5.TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS

Figure 4:2 Friction Factor - Reynolds Number


Test Time To Piezometer Tube Readings (cm) V-Tube


(s) 7 8 9 10 11 Globe Valve

11 73.2 38.7 43.5 42.5 12.1 38.3 37.4 20.2

12 76.8 39.2 43.5 42.5 22.1 38.5 38.5 19.013 82.6 39.1 43.0 42.2 24.5 38.3 40.2 17.414 95.4 39.4 42.0 41.5 28.5 38.3 43.0 14.715 102.6 39.7 42.2 41.7 30.2 38.0 44.0 13.616 130.8 40.0 41.5 41.1 33.8 37.3 46.5 11.717 144.6 40.4 41.5 41.2 35.2 37.5 47.5 10.118 176.9 40.7 41.4 41.2 37.0 37.3 49.1 8.619 220.8 41.0 41.5 41.4 38.6 37.4 50.2 7.520 277.8 41.2 41.6 41.6 39.6 37.5 51.4 6.5

Table 4.2(a) Experimental Results For Light Blue

Circuit

4.3 Sudden Expansion

The object of this experiment is to compare the measured head rise across a sudden expansion with the rise calculated on the assumption of:

(a) No head loss; (b) Head loss given by the expression:

hL=(V 1−V 2 )2

2g

Test Time To Piezometer Tube Readings (cm) V-Tube


(s) 12 13 14 15 16 Globe Valve

11 73.2 12.1 35.0 7.2 32.1 3.8 37.4 20.2

12 76.8 14.1 34.9 9.7 32.5 6.0 38.5 19.013 82.6 17.0 34.9 12.6 31.6 8.6 40.2 17.414 95.4 22.0 34.5 17.6 31.5 13.7 43.0 14.7

15 102.6 23.6 34.2 19.4 30.7 15.2 44.0 13.616 130.8 28.0 33.4 23.7 29.6 19.5 46.5 11.717 144.6 29.7 33.4 25.5 29.8 21.4 47.5 10.118 176.9 31.9 33.2 27.7 29.4 23.5 49.1 8.619 220.8 33.6 33.3 39.4 29.5 25.4 50.2 7.520 227.8 35.0 33.4 30.9 29.5 26.8 51.4 6.5

Table 4.2(b) Experimental Results For Light B

lue Circu

it (continued)



From Table 4.2 test number 11.

Measured head rise = 48mm

(a) Assuming no head loss

h2−h1=(V 1

2−V 22)

2 g

(Bernoulli) Since

A1 V 1=A2 V 2

h2−h1=V 12[1−( A1/ A2 )2

2 g ]¿V 1

2[1−(d1/d2)4

2 g ]From the table,

V 1=QA1

(Continuity)

¿ 1873.2×103×147.3 ×10−6

= 1.67m/s

therefore h2 - h1

= 1.672[ 1−(13.7 /26.4)4

2 × 9.81 ]= 0.132m


Therefore head rise across the sudden expansion assuming no head loss is 132mm water.

(b) Assuming

hL=(V 1−V 2 )2

2g

h2−h1=(V 1

2−V 22)

2g−hL

(Bernoulli)

¿(V 1

2−V 22 )

2 g −(V 1−V 2 )2

2 g

On rearranging and inserting values of d. = 13.7mm and d2 = 26.4mm, this reduces to

h2−h1=0.396 V 1

2

2 g

which when V1 = 1.67m/ s

gives h2−h1=0.0562 m

Therefore head rise across the sudden expansion assuming the simple expression for head loss is 56mm water.

Figure 4.3 shows the full set of results for this experiment plotted as a graph of measured head rise against calculated head rise.

Comparison with the dashed line on the graph shows clearly that the head rise across the sudden expansion is given more accurately by the assumption of a simple head loss expansion than by the assumption of no head loss.


Figure 4.3 Head Rise Across a Sudden Enlargement

4.4 Sudden Contraction

The object of this experiment is to compare the measured fall in head across a

sudden contraction, with the fall calculated in the assumption of:

(a) No head loss; (b) Head loss given by the expression

hL=K V ❑

2

2 g



From Table 4.2, test number 11.

Measured head fall = 221mm water

(a) Assuming no head loss

Combining Bernoulli's equation and the continuity equation gives:

h2−h1=V 22[ 1−(d1/d2)

4

2 g ]¿0.927

V 22

2g

Which when V2 = 1.67m/s gives

h2−h1=0.132 m

Therefore head fall across the sudden contraction assuming no head loss is 132mm water.

(b) Assuming

hL=K V 2

2

2g

h2−h1=V 22[ 1−(d1/d2)

4

2 g+hL ]

¿V 22[ 1−(d1/d2)

4

2 g+K V 2

2

2 g ]


From Table 1, when A2

A1=0.27

K = 0.376

giving

h2−h1=0.927V 2

2

2 g+0.376

V 22

2 g

¿1.303V 2

2

2 g

Which when V2 = 1.67m/s gives

h1 – h2 = 0.185m _

Therefore head fall across the sudden contraction assuming loss coefficient of 0.376 is 18.5cm water.

Figure 4.4 shows the full set of results for this experiment plotted as a graph of measured head fall against calculated head fall.


Figure 4.4 Head Decrease across a Sudden Contraction

The graph shows that the actual fall in head is greater than predicted by the accepted value of loss coefficient for this particular area ratio. The actual value of loss coefficient can be obtained as follows:

Let hm = measured fall in head and K' = actual loss coefficient

then

hm=0.927 V ❑2

2g+ K ' V ❑

2

2g

Calculated decrease in head (cm of water)


hence K '=h× 2× g

V 22 −0.927

which when

4.5 Bends

v2 = 1.67 m/s gives K' = 0.63

The aim here is to measure the loss coefficient for five bends. There is some confusion over terminology, which should be noted; there are the total bend losses (KL hL) and those due solely to bend geometry, ignoring frictional

losses (KB, hB).

i.e.

K B=2 gV 2 (Total measured head loss - straight line loss) i.e.

K=2 gV 2 (Head gradient for bend - k x head gradient for straight pipe)

Where k = 1 for KB

For either,

K=1−2 Pi2 L

h=K V 2

2 g

Plotted on Figure 4.5 are experimental results for KB and KL for the 5 types of bends and also some tabulated data for KL. The last was obtained from 'Handbook of Fluid Mechanics' by VL Streeter. It should be noted though, that these results are by no means universally accepted and other sources give different values. Further, the experiment assumes that the head loss is independent of Reynolds Number and this is not exactly correct. 6.

Figure 4.5 Graph of Loss Coefficient

Is the form of Kg what you would expect? Does putting vanes in an elbow

have any effect? Which do you consider more useful to measure, KL or KB?

4.6 Valves

The object of this experiment is to determine the relationship between loss

coefficient and volume flow rate for a globe type valve and a gate type valve.


hL=K V ❑

2

2 g

Globe Valve

From Table 4.2, test number 11.

Volume flow rate = 246 ×10−6 m3/ s (valve fully open)U-tube reading = 172 mm mercury

Therefore hL = 172 ×12.6

= 2.17 m water

Velocity (V) = 1.67 m /s

Giving K = 2.17 ×2 ×9.81

1.672

= 15.3

Figure 4.6 shows the full set of results for both valves in the form of a graph of loss coefficient against percentage

volume flow.

TECQUIPMENT H16 LOSSES IN PIPING SYSTEMSPercentage Flow Rate

Figure 4.6 Loss Coefficients for Globe and Gate Valves

7.

8.


Normal manufacturing tolerances assume greater importance when the physical scale is small. This effect may be particularly noticeable in relation to the internal finish of the tube near the pressure tappings. The utmost care is taken during manufacturing to ensure a smooth uninterrupted. Bore of the tube in the region of each pressure tapping, to obtain maximum accuracy of pressure reading.

Concerning again all published information relating to pipe systems, the Reynolds Numbers are large, in the region of 1 x 105 and above. The maximum Reynolds Number obtained in these experiments, using the hydraulic bench, HI, is 3 x 104 although this has not adversely affected the results. However, as previously stated in the introduction to this manual, an alternative source of supply (provided by the customer) could be used if desired, to increase the flow rate. In this case an alternative flow meter would also be necessary.

The three factors discussed very briefly above are offered as a guide to explain discrepancies between experimental and published results, since in most cases all three are involved, although much more personal investigation is required by the student to obtain maximum value from using this equipment.

In conclusion the genera

l trends and magnitudes obtained give a valuable indication of pressure loss from the various components in the pipe system. The student is therefore given a realistic appreciation of relating experimental to theoretical or published information.

SECTION 5.0 GENERAL REVIEWS OF THE EQUIPMENT AND RESULTS

An attempt has been made in this apparatus to combine a large number of pipe components into a manageable and compact pipe system and so provide the student user with the maximum scope for investigation. This is made possible by using small bore pipe tubing. However, in practice, so many restrictions, bends and the like may never be encountered in such short pipe lengths. The normally accepted design criteria of placing the downstream pressure tapping 30-50 pipe diameters away from the obstruction i.e. the 90° bends, has been adhered to. This ensures that this tapping is well away from any disturbances due to the obstruction and in a region where there is normal steady flow conditions. Also sufficient pipe length has been left between each component in the circuit; to obviate any adverse influence neighboring components may tend to have on each other.

Any discrepancies between actual experimental and theoretical or published results may be attributed to three main factors:

(a) Relatively small physical scale of the pipe work; (b) Relatively small pressure differences in some cases; (c) Low Reynolds Numbers.

The relatively small pressure differences, although easily readable, are encountered on the smooth 90° bends and sudden expansion. The results on these components should therefore be taken with most care to obtain maximum accuracy from the equipment. The results obtained however, are quite realistic as can be seen from their comparison with published data, as shown in Figure 4.5. Although there is wide divergence even amongst published data, refer to page 472 of “Engineering Fluid Mechanics”, it is interesting to note that all curves seem to

show a minimum value of the loss coefficient 'K' where the ratio"rd " is between 2 and 4. It is

important to realize and remember throughout the review of the results that all published data have been obtained using much larger bore tubing (76mm and above) and considering each component in isolation and not in a compound circuit.

. by Charles Jaeger and published by Blackie and Son L

€¦ · web viewremove the manometer from the h16 before filling with mercury. the object is to...

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