H16 Losses in Piping Systems
PE/djb/0501
CONTENTS Section 1
Page INTRODUCTION Description of the Apparatus
2
THEORY Head Loss Head Loss in Straight Pipes Head Loss due to Sudden Changes in Area of Flow Head Loss due to Bends Head Loss due to Valves
Principles of Pressure Loss Measurement Principles of Pressure Loss Measurement
3
INSTRUCTIONS FOR USE Filling the Mercury Manometer Experimental Procedure
4
TYPICAL SET OF RESULTS AND CALCULATIONS Results Identification of Manometer Tubes and Components Experiment 1: Straight Pipe Loss Experiment 2: Sudden Expansion Experiment 3: Sudden Contraction Experiment 4: Bends Experiment 5: Valves
1-1 1-1 2-1 2-1 2-1 2-1 2-2 2-2 2-2 2-2 3-1 3-1 3-1 4-1 4-1 4-1 4-2 4-4 4-6 4-8 4-9
5
GENERAL REVIEW OF THE EQUIPMENT AND RESULTS
5-1
6
H16p ROUGH PIPE ASSEMBLY
6-1 6-1 6-2 6-2 6-4 6-4 6-4 6-4
Installation Dimensions Range of Experiments Theory Flow Rate
Experimental Procedure Typical Test Results
i
TQ Losses in Piping Systems
ii
SECTION 1 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 household central heating installations. This apparatus is designed for use with the TQ Hydraulic Bench H1, although the equipment may be supplied from another source, providing it has an accurate means of mass flow rate measurement. All reference to ‘the bench’ in this manual refers directly to the TQ Hydraulic Bench.
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 detailed at Figure 1.1. In all cases (except the gate and globe valves), the pressure change across each of the components is measured by a pair of pressurised piezometer tubes. In the case of the valves, pressure measurement is made by U-tube Manometers containing mercury.
Figure 1.1 Arrangement of the apparatus
Dark Blue Circuit
Light Blue Circuit
A) Straight pipe 13.7 mm bore B) 90° Sharp bend (mitre); C) Proprietary 90° elbow D) Gate valve
E) Sudden expansion - 13.6 mm / 26.2 mm F) Sudden contraction - 26.2 mm / 13.6 mm G) Smooth 90° bend 50.8 mm radius H) Smooth 90° bend 100 mm radius J) Smooth 90° bend 152 mm radius K) Globe Valve L) Straight Pipe 26.4mm
Page 1-1
TQ Losses in Piping Systems
Page 1-2
SECTION 2 THEORY where f is a dimension 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 i) Sudden Expansion The head loss at a sudden expansion is given by the expression: hL
=
(V1 − V 2 )
2
2g
Figure 2.1 For an incompressible fluid flowing through a pipe the following equations apply: Q
=
V1 A1
=
V2 A2
(Continuity)
Figure 2.2 Expanding pipe Z 1
+
p1
ρg
+
2 V 1
2g
=
Z 2
+
P2
ρg
+ V22 + hL1− 2 (Bernoulli)
Notation: 3 Volumetric flow rate (m /s); Q V Mean velocity (m/s); 2 Cross sectional area (m ); A Height above datum (m); z 2 Static pressure (N/m ); p hL Head loss (m); ρ Density (kg/m3); 2 Acceleration due to gravity (9.81 m/s ). g
ii) Sudden Contraction
Figure 2.3 Contracting pipe The head loss at a sudden contraction is given by the expression:
Head Loss
hL
The head loss in a pipe circuit falls into two categories:
The overall head loss is a combination of both these categories. Because of mutual interference between neighbouring 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
hL
=
2g
where K is a dimension 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.
a) That due to viscous resistance extending throughout the total length of the circuit b) That due to localised effects such as valves, sudden changes in area of flow and bends.
The head loss along a length, L, of straight pipe of constant diameter, d , is given by the expression:
=
K V 22
A2/A1
K
0
0.50
0.1
0.46
0.2
0.41
0.3
0.36
0.4
0.30
0.6
0.18
0.8
0.06
1.0
0
Table 2.1 Loss coefficients for sudden contractions
4 f LV 2 2 gd
Page 2-1
TQ Losses in Piping Systems
Head Loss due to Bends
z +
The head loss due to a bend is given by the expression: hB
p1
ρg
2
+
V 1
2g
p2
=
ρg
2
+
V 2
2g
K B V 2
=
+ hL (2-1)
2g
but:
where K is a dimensionless coefficient which depends upon the bend radius/pipe radius ratio and the angle of the bend.
=
V1
V 2 (2-2)
Therefore 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.
=
hL
z+
ρg
Consider piezometer tubes:
See Figure 4.5, which shows a graph of typical loss coefficients.
=
p1
+ ρg [z − ( x + y)] (2-4)
also
Head Loss due to Valves
p
=
p2
The head loss due to a valve is given by the expression:
+
p2 ) (2-3)
p
hL
( p1 −
− ρgy (2-5)
2
KV
giving:
2g x
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
5.6
=
z
+
( p1 −
p2 )
ρg (2-6)
Table 2.2
Principles of Pressure Loss Measurement
Figure 2.5 U-tube containing mercury used to measure pressure loss across valves Consider Figure 2.5; since 1 and 2 have the same elevation and pipe diameter:
Figure 2.4 Pressurised piezometer tubes to measure pressure loss between two points at different elevations
p1
−
p2
ρH O g
=
hL
2
(2-7)
Considering Figure 2.4, apply Bernoulli’s equation between 1 and 2:
Consider the U-tube. Pressure in both limbs of U-tube are equal at level 00. Therefore equating pressure at 00:
Page 2-2
TQ Losses in Piping Systems
− ρ H O g ( x + y) ρ Hg g x =
p2
2
p1
− ρ H O g1 y1 2
(2-8)
Considering Equations (2-6) and (2-10) and taking the specific gravity of mercury as 13.6: hL
giving: p1
−
p2
=
xg
(ρ
Hg
− ρH O ) 2
hence:
−
p2
ρH O g
=
12.6 x (2-11)
(2-9)
p1
=
x ( s − 1)
2
(2-10)
Page 2-3
TQ Losses in Piping Systems
Page 2-4
SECTION 3 INSTRUCTIONS FOR USE 1. Connect the hydraulic bench supply to the inlet of the apparatus, directing the outlet hose into the hydraulic bench weighing tank. 2. Close globe valve, open gate valve and admit water to the Dark Blue circuit, starting the pump and opening the outlet valve on the hydraulic bench. 3. Allow water to flow for two to three minutes. 4. Close gate valve and manipulate all trapped air into air space in piezometer tubes. Check that all piezometer tubes indicate zero pressure difference. 5. Open the gate valve and by manipulating bleed screws on the U-tube, fill both limbs with water ensuring that no air remains. 6. Close gate valve, open globe valve and repeat the above procedure for the Light Blue circuit . Both circuits are now ready for measurements. The datum position of the piezometer can be adjusted to any desired position either by pumping air into the manifold with the hand 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.
Figure 7 Filling the manometers
Unscrew the caps at the top of the manometer to purge any trapped air. Replace caps immediately.
Filling the Mercury Manometers
Experimental Procedure
Important Mercury and its vapour 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, TQ Ltd are unable to supply this item. To fill the mercury manometers, it is recommended that a suitable syringe and catheter tube are used (not supplied) and the mercury acquired locally. Approximately 1Kg of Mercury is sufficient. Remove any items of gold or silver jewellery. Unscrew the two caps at the top of the manometer. Thread a suitable catheter tube into the manometer tube, ensuring the catheter tube end touches the end of the manometer column. Fill a syringe with 10 ml of mercury and connect to the catheter tube. Slowly fill the manometer using the syringe, and as the mercury fills the columns, withdraw the tube ensuring there are no air bubbles left. The optimum level for the mercury is 400 mm from the bottom of the U-tube. When the manometer has the correct amount of mercury in it, water should be added to the reservoir, covering the mercury and preventing vapour from escaping into the air.
The following procedure assumes that pressure loss measurements are to be made on all the circuit components. Open fully the water control valve on the hydraulic bench. With the globe valve closed, open the gate valve fully 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 weigh 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 an accurate 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 experiment 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.
Page 3-1
TQ Losses in Piping Systems
Page 3-2
SECTION 4 TYPICAL SET OF RESULTS AND CALCULATIONS Results
Identification of Manometer Tubes and Components
Basic Data Pipe diameter (internal) Pipe diameter [between sudden expansion (internal) and contraction] Pipe material Distance between pressure tappings for straight pipe and bend experiments
13.7 mm
Manometer tube number
Unit
26.4 mm
1
Proprietary elbow bend
2 Copper tube
3
Straight pipe
4
0.914 m
5
Mitre bend
6
Table 4.1
7
Expansion
8
Bend Radii
9
Contraction
10
90° Elbow (mitre)
0
90° Proprietary elbow
12.7 mm
90° Smooth bend
50.8 mm
90° Smooth bend
100 mm
14
90° smooth bend
152 mm
15
11
152 mm bend
12 13
16
Table 4.2 Table 4.3
Page 4-1
100 mm bend 50.8 mm bend
TQ Losses in Piping Systems
Experiment 1: Straight Pipe Loss The object of this experiment is to obtain the following relationships:
Re =
a) Head loss as a function of volume flow rate; b) Friction Factor as a function of Reynolds number.
9.40 × 10
Friction Factor ( f ) =
Specimen Calculations From Table 4.4, test number 1 Mass flow rate
1.94 × 13.7 × 10
f =
−3
−7
= 2.83 × 10
4
hL × 2 gd
4 LV 2
0.332 × 2 × 9.81 × 13.7 × 10 4 × 914 × 10
−3
2 × 194 .
−3
= 0.0065
= 18/63 = 0.286 kg/s
Head loss
= 0.332 m water
Volume flow rate (Q)
= Mass flow rate/density 0286 . –6 3 = = 286 × 10 m /s 3 10
Area of flow (A)
=
Mean velocity (V )
= =
π
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 n hL α Q 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.
× 13.7 2 = 147.3 mm2
4 Q A
286 × 10 −6 147.3 × 10
−6
= 1.94 m/s
Blasius’s equation:
Reynolds number ( Re)
d = V
For water at 23°C ν
= 9.40 × 19 m /s
f
ν
–7
=
0.0785 14
Re
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.
2
Therefore,
Test
Time to collect 18 kg
Piezometer tube readings (cm) water
number
water (s)
1
2
3
4
5
6
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
25.9
3
69.4
51.9
21.6
49.7
21.6
86.5
37.3
33.8
24.0
4
73.9
52.2
25.1
49.2
24.0
85.5
41.7
35.8
22.0
5
79.9
53.1
29.4
48.6
27.0
84.2
47.1
38.1
19.5
6
88.8
53.4
33.4
48.0
29.7
83.0
52.1
40.5
17.0
7
99.8
53.2
36.5
46.6
31.7
81.6
56.8
42.7
14.8
8
111.0
52.6
39.2
46.1
33.7
80.0
59.8
44.0
13.5
9
146.2
52.6
44.4
54.4
37.7
78.4
66.1
47.3
10.3
10
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 4.4 Experimental results for dark blue circuit
Page 4-2
U-tube (cm) Hg Gate-valve
TQ Losses in Piping Systems
Figure 4.1 Head loss versus volume flow rate
Figure 4.2 Friction factor versus Reynolds number
Page 4-3
TQ Losses in Piping Systems
Experiment 2: 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
Test
Time to collect 18 kg
number
water
(V1 V 2 )
=
2
2g
Piezometer tube readings (cm) water
U-tube (cm) Hg
(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
19.0
13
82.6
39.1
43.0
42.2
24.5
38.3
40.2
17.4
14
95.4
39.4
42.0
41.5
28.5
38.3
43.0
14.7
15
102.6
39.7
42.2
41.7
30.2
38.0
44.0
13.6
16
130.8
40.0
41.5
41.1
33.8
37.3
46.5
11.7
17
144.6
40.4
41.5
41.2
35.2
37.5
47.5
10.1
18
176.9
40.7
41.4
41.2
37.0
37.3
49.1
8.6
19
220.8
41.0
41.5
41.4
38.6
37.4
50.2
7.5
20
227.8
41.2
41.6
41.6
39.6
37.5
51.4
6.5
Table 4.2(a) Experimental results for light blue circuit Test
Time to collect 18 kg
number
water
Piezometer tube readings (cm) water
U-tube (cm) Hg
(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
19.0
13
82.6
17.0
34.9
12.6
31.6
8.6
40.2
17.4
14
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
13.6
16
130.8
28.0
33.4
23.7
29.6
19.5
46.5
11.7
17
144.6
29.7
33.4
25.5
29.8
21.4
47.5
10.1
18
176.9
31.9
33.2
27.7
29.4
23.5
49.1
8.6
19
220.8
33.6
33.3
39.4
29.5
25.4
50.2
7.5
20
227.8
35.0
33.4
30.9
29.5
26.8
51.4
6.5
Table 4.2(b) Experimental results for light blue circuit (continued) Specimen Calculation
= From Table 4.2 test number 11 measured head rise = 48 mm.
h2
− h1 =
2 2
V 1
− V 22 ) 2g
(Bernoulli)
=
= =
since A1V1
(1 − (d
d 2 ) 4
1
)
2g
From the table,
a) Assuming no head loss
(V
2 V 1
=
A2V 2 (Continuity)
Q A1
18 73.2 × 10
3
×
147.3 × 10
−6
1.67 m / s
therefore h2
− h1 =
2 V 1
(1 − ( A
1
A2 )
2
)
(1 − (13.7 26.4) ) = 0.132 m 4
h2
2g
Page 4-4
− h1 =
1.67 2
2 × 9.81
TQ Losses in Piping Systems
Therefore head rise across the sudden expansion assuming no head loss is 132 mm water.
which when
b) Assuming
gives
hL
h2
=
(V1 − V 2 )
2
h2
2g
− h1 = =
(V
− V 22 ) (Bernoulli) 2 g − hL 2 1
(V
2 1
− V 22 ) 2g
−
(V1 − V 2 )
2
2g
or rearranging and inserting values of d 1 = 13.7 mm and d2 = 26.4 mm, this reduces to h2
− h1 =
V 1
2 0396 . V 1
=
1.67 m / s
− h1 =
00562 m .
Therefore head rise across the sudden expansion assuming the simple expression for head loss is 56 mm 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, rather than by the assumption of no head loss.
2g
Figure 4.3 Head rise across a sudden enlargement
Page 4-5
TQ Losses in Piping Systems
Experiment 3: 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:
From Table 2.1, when: A2 A1
a) No head loss, b) Head loss given by the expression:
=
hL
=
0.27
K = 0.376
giving:
KV 2
2g
h1
− h2 =
0927 .
=
1303 .
Specimen Calculation
From table 4.2 test number 11 measured head fall = 221 mm water.
V 22
2g
+ 0376 .
V 22
2g
2
V 2
2g
Which when: a) Assuming no head loss: combining Bernoulli’s equation and the continuity equation gives:
h2
− h1 =
V 22
1 − (d / d )4 2 1 2g
(
)
V 2 = 1.67 m/s
gives:
h1 – h2 = 0.185 m
Therefore head fall across the sudden contraction assuming loss coefficient of 0.376 is 18.5 cm water.
2
= 0.927
V 2
Figure 4.4 shows the full set of results for this experiment plotted as a graph of measured head fall against calculated head fall. 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:
2g
Which when V 2 = 1.67 m/s
gives h1 – h2 = 0.132 m
Therefore head fall across the sudden contraction assuming no head loss is 13 2 mm water.
Let hm = measured fall in head and K ’ = actual loss coefficient, then: hm
b) Assuming hL
h2
= − h1
KV 22
=
0927 .
=
2hg
4 2 1 − (d 2 / d 1 ) = V 2 2 g + hL
=
2g
+
K ′V
2
2g
hence
2g
2 V 2
2
V
K ′
2
V 2 2
− 0927 .
which when V = 1.67 m/s gives K ’ = 0.63
1 − (d / d )4 2 1 2 2 g + ( KV2 / 2 g )
Page 4-6
TQ Losses in Piping Systems
Figure 4.4 Head decrease across a sudden contraction
Page 4-7
TQ Losses in Piping Systems
Experiment 4: Bends The purpose 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 (K L hL)and those due solely to bend geometry, ignoring frictional losses ( K B, hB).
=
K B
2g 2
V
(Total measured head loss – straight line loss) i.e. K
=
2g 2
V
(Head gradient for bend - k × head gradient for straight pipe) Where k = 1 for K B k
=
For either,
1−
πr 2 L
h
=
V 2 K 2g
Plotted on Figure 4.5 are experimental results for K B and K L for the five types of bends and also some tabulated data for K L. 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. Is the form of K B what you would expect? Does putting vanes in an elbow have any effect? Which do you consider more useful to measure, K L or K B?
Figure 4.5 Graph of loss coefficient
Page 4-8
TQ Losses in Piping Systems
Experiment 5: 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.
Therefore hL
= 172 × 12.6 = 2.17 m water
Velocity (V )
= 1.67 m/s
Giving K
= 2.17 × 2 × 9.81/1.67 = 15.3
Specimen Calculation hL
=
2
KV
2
2g Figure 4.6 shows the full set of results for both valves in the form of a graph of loss coefficient against percent volume flow.
Globe Valve From Table 4.2, test number 11.
Volume flow rate = 246 × 10 m /s (valve fully open); U-tube reading = 172 mm mercury. –6
3
Figure 4.6 Loss coefficient for globe and gate valves
Page 4-9
TQ Losses in Piping Systems
Page 4-8
SECTION 5 GENERAL REVIEW 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 neighbouring 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 the utmost 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 4.6. Although there is wide divergence even amongst published data, refer to page 472 of ‘Engineering Fluid Mechanics’ by Charles Jaeger and published by Blackie and Son Ltd, it is interesting to
note that all curves seem to show a minimum value of the loss coefficient ‘K ’ where the ratio r/d is between 2 and 4. It is important to realise and remember throughout the review of the results that all published data have been obtained using much larger bore tubing (76 mm and above) and considering each component in isolation and not in a compound circuit. 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 tappings, 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 × 105 and above. The maximum Reynolds number obtained in these experiments, using the hydraulic bench, H1, is 3 × 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 flowmeter 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 general 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.
Page 5-1
TQ Losses in Piping Systems
Page 5-2
