LABORATORY
REPORT
FLUID
MECHANICS LABORATORY SKPU 1711
EXPERIMENT 1 :24th February 2014
FRICTION LOSSES IN PIPES
MUHAMMAD KHAIRIL IKRAM(A13KP0047) AKMAL FAIZ BIN ABDUL RAHIM (A13KP0008) ABDUL WAHAB (A13KP4006) KSATRIYA ANANTAYUTYA (A13KP4001)
1
Report summary: The experiment was undertaken to measure the head lost in the pipe due to shear stress between the fluid and the wall of the pipe. Different flow rates were introduced along with a different diameters and roughness of the pipes. Therefore we measured the friction factor of the pipes using our measurements. Fluid velocity was also studied and related to the diameter, flow rate and roughness of the pipe during the experiment. As the flow rate, Q was changed, the values for the inlet and outlet, H1 and H2 were measured. The Flow rate was changed to a range of different values and hence the respective values of H1 and H2 were recorded. The procedure was repeated for the for the different pipes which include, rough, smooth, sudden contraction and sudden enlargement pipes. Reynolds number was used to understand the variation of the flow between the laminar and the turbulent flows. As the Laminar flow (f) can be known by analysis while the turbulent flow (f) is found experimentally. As the frictional factor increased the Reynolds number decreased, this shows the inverse proportion between the friction factor (f) and the Reynolds number. The head loss was also found to increase with increase in the velocity. As during the sudden enlargement, the minor loss was also increased. To conclude, we chiefly studied the head losses in the pipes as along pipes of different diameters and roughness. There were few improvements required which include the forming of bubble along the inlets which gave inconsistent readings and there were few leaking inlets which affected the value of the flow rate. With these errors taken into consideration, the experimental results would be better.
2
THEORY In Bernoulli’s equation as shown below, hf represents the head loss due to the friction between the fluid and the internal surface of the constant diameter pipe as well as the friction between the adjacent fluid layers p1/g + V1²/2g + Z1 = p2/g + V2²/2g + Z2 + hf (1)
This will result in a continuous change of energy from a valuable mechanical form (such as kinetic or potential energies) to a less valuable thermal form that is heat. This change of energy is usually referred to as friction head loss, which represents the amount of energy converted into heat per unit weight of fluid. The head losses (hf) in pipe due to friction can be determined using Darcy-Weisback equation;
Turbulent flow
(2)
Laminar flow (3) Where: f = Friction factor L = Length V = Mean velocity (Q/A) 3
g = Gravity D = Constant diameter
The friction head loss for both laminar and turbulent flows can be expressed by similar formulas although the original derivation of each one is different: (4)
In laminar flow, the friction factor is only a friction of Reynolds number while for turbulent flow it is a function of Reynolds (Re) number and the relative roughness of the pipe. Re = VD /
(5)
Where : density, V: average velocity, D: Pipe inside diameter, : Viscosity.
Based on the nature of the flow, friction factor (f) can be estimated using the following correlations
Laminar flow
f = 64/Re
(6)
Turbulent Flow
f =0.316 x Re -0.25
(7)
Equation (7) is Blausius Equation and only valid for smooth pipe and 3000
hf= KVn
(8)
Where K is a loss coefficient and n ranges from 1.7 to 2.0 (depending on the value of Re and ks/D).This equation can be written as Log hf= Log K + n Log V
(9)
In order to find K and n experimentally, using graph
Experimentally, one can obtain the head loss by applying energy equation between any two points along a constant diameter pipe. This is done in Eq.1 and by noticing that the pipe is horizontal and the diameter is constant. The pressure heads of a fluid between 2 points, h1 and h2 are measured by using Piezometer tubes. The total head loss can be determined experimentally by applying the Bernoulli’s equation as follows: hf= (P1 – P2)/ g = h1 – h2
(10)
Energy losses are proportional to the velocity head of the fluid as it flows around an elbow, through an enlargement or contraction of the flow section, or through a valve. Experimental values for energy losses are usually reported in terms of a resistance or loss coefficient K as follows: hL= KV2/2g
(11)
where hL is the minor loss, K is the resistance or loss coefficient, and V is the average velocity of flow in the pipe in the vicinity where the minor occurs. The resistance or loss coefficient is dimensionless because it represents a constant of proportionality between the energy loss and the velocity head. The magnitude of the resistance coefficient depends on the geometry of the device that causes the loss and sometimes on the velocity of flow.
5
Minor losses at sudden enlargement When a fluid flows from a smaller pipe into a larger pipe through a sudden enlargement, its velocity abruptly decreases, causing turbulence, which generates an energy loss. P1V1
P2V2
1 2 Where, V1 = Velocity at small cross-section (upstream) V2 = Velocity at large cross-section (downstream)
The minor loss (hf) due to sudden enlargement of the pipe can be estimated by integrating the momentum, continuity and Bernoulli equations between positions 1 and 2 to give (12) Substituting again for the continuity equation to get an expression involving the two areas, (i.e V2 = V1 (A1/A2) gives hL = KV12/2g
(13)
Where, K= (1-A1/A2)2 = (1–(D1/D2)2)2
6
Minor losses at sudden contraction When a fluid flows from a larger pipe into a smaller pipe through a sudden contraction, the fluid streamlines will converge just downstream of the smaller pipe, known as vena contraction phenomena, creating a turbulence region from the sharp corner of the smaller pipe and extends past the vena contracta, which subsequently generates an energy loss.
V1
V2
1
In a sudden contraction, flow contracts from point 1 to point 1’, forming a vena contraction. It is possible to assume that energy losses from 1 to 1’ are negligible (no separation occur s in contracting flow) but that major losses occur between 1’ and 2 as the flow expands again
7
If the vena contracta area is A1=Ac, then the minor loss (hL) can be estimated by integrating the momentum, continuity and Bernoulli equations between positions 1 and 2 to give hL= (1-Ac/A2)2 V22/2g
(14)
The above equation is commonly expressed as a function of loss coefficient (K) and the average velocity (V2) in the smaller pipe downstream from the contraction as follows; hL = KV2 /2g
(15)
where K = (1 – Ac/A2)2 As the difference in pipe diameters gets large (A 1/A20) then this value of K will tend towards 0.5 which is equal to the value for entry loss from a reservoir into a pipe. The value of K depends upon the ratio of the pipe diameters (D2/D1) as given below;
8
d2/d1 K
0 0.5
0.1 0.45
0.2 0.412
0.3 0.39
0.4 0.36
0.5 0.33
0.6 0.28
0.7 0.15
0.8 0.15
0.9 0.06
1.0 0
Minor Losses at elbow or bend pipe Losses in fittings such as elbow, valves etc have been found to be proportional to the velocity head of the fluid flowing. The energy loss is expressed in the general form, hL= KV2/2g
(16)
Where, K = Loss coefficient (dependent on the ratio of total angle of bending to radius of bending (R/d) of the curves as the bending occurs)
Experimental determination of total head loss In the experiment the pressure heads before & after a fluid undergoing sudden change in pipe diameter or flow direction, h1 and h2 are measured by using Piezometer tubes. The total head loss (major and minor losses) can be determined experimentally by applying the Bernoulli’s equation as follows: 9
p1 /ρg + v1² / 2g + z1 = p2/ρg + v1² / 2g + z2 + hL
(17)
h1+ v1² / 2g + z1= h2 + v1² / 2g + z2 + hL
(18)
and since z1 = z2 , then
(19) Linear Pipe 1 2
Part A (Rough)
Diameter(mm) 25.0
Length(mm) 1030
B (Smooth) A (Rough) B (Smooth)
23.5 14.0 13.3
1030 1030 1030
Note 1: Q (m3/s) = Q (l/min) x 1.667 x 10-5 Note 2: Reynolds Number for Linear Pipe (At room Temperature = 27°C)
Pipe 1A Pipe 1B
: Re = 29.2 x 103 x V : Re = 27.5 x 103 x V
Pipe 2A Pipe 2B
: Re = 16.4 x 103 x V : Re = 15.5 x 103 x V
Table of Water Dynamic Viscosity and Density at Different Temperatures Temperature (oC) 0 5 10 15 20 25 30 40 50
(kg/m3) 999.8 1000.0 999.7 999.1 998.2 997.0 995.7 992.2 988.0
(x 10-3 Ns/m2) 1.781 1.518 1.307 1.139 1.002 0.890 0.798 0.653 0.547 10
60 70 80 90 100
983.2 977.8 971.8 965.3 953.4
0.466 0.404 0.354 0.315 0.282
EXPERIMENTAL PROCEDURE A)
Experiment with Pipe 2A: Rough Surface 1. The water manometer’s rubber tube was connected to the inlet flowing pressure (H1) and the outlet flowing pressure (H2). 2. The flow rate (Q) was reduced until it reached 26 liter/minute by closing the control valve. At the same time, the outlet valves of pipes 1 and 4 were closed while pipe 2 was opened. 11
3. Q was readjusted to 26 liter/minute and five Q were determined from value of 26 to 12 liter/minute. The values of H1 and H2 were recorded in millimeter as Q was adjusted. B)
Experiment with Pipe 2B: Smooth Surface 1. The manometer rubber tube from H2 of rough surface of pipe 2A was moved to H1 of smooth surface of pipe 2B. 2. The control valve was slowly opened until flow rate (Q) reached 26 liter/minute. Air bubbles present were removed to the manometer glass tube. 3. Five Qs were determined. The values of H1 and H2 were recorded in millimeter as Q was adjusted.
C)
Experiment with Pipe 1A: Rough Surface 1. The manometer rubber tubes of H1 and H2 of pipe 2B were moved to the rough surface of pipe 1A. 2. The outlet valve of pipe 1 was opened first before the outlet valve of pipe 2 was closed. 3. The control valve was slowly opened until Q reached 42 liter/minute. Air bubbles present were removed to the manometer glass tube. 4. Q was readjusted to appropriate maximum value of 42 liter/minute and five different Q from 42 to 12 liter/minute were determined. The values of H1 and H2 were recorded in millimeter as Q was adjusted.
12
D)
Experiment with Pipe 1B: Smooth Surface 1. The manometer rubber tube from H2 of rough surface of pipe 1A was moved to H1 of smooth surface of pipe 1B. 2. The control valve was slowly opened until Q reached maximum value of 42 liter/minute. Air bubbles present were removed to the manometer glass tube. 3. Five different Qs were determined similar to pipe 1A. The values of H1 and H2 were recorded in millimeter as Q was adjusted.
E)
Experiment with Pipe 4: Sudden Enlargement 1. The manometer rubber tubes of H1 and H2 of pipe 1B were moved to the Sudden Enlargement section of pipe 4. 2. The outlet valve of pipe 4 was opened before the outlet valve of pipe 1 was closed. 3. The control valve was slowly opened until Q reached 30 liter/minute. Air bubbles present were removed to the manometer glass tube. 4. Q was readjusted to 30 liter/minute and five Qs were determined from the maximum value of 30 to 12 liter/minute. The values of H1 and H2 were recorded in millimeter as Q was adjusted.
F)
Experiment with Pipe 4: Sudden Contraction 1. The manometer rubber tube from H1 of Sudden Enlargement of pipe 4 was moved to H2 of Sudden Contraction of pipe 4. 2. The control valve was slowly opened until Q reached 30 liter/minute. Air bubbles present were removed to the manometer glass tube. 3. Q was readjusted to appropriate value of 30 liter/minute and five different Qs were determined from the maximum value of 30 to 12 liter/minute. The values of H1 and H2 were recorded in millimeter as Q was adjusted.
13
G)
Experiment with Pipe 4: 90o Bend 1. The manometer rubber tube from H1 of Sudden Contraction of pipe 4 was moved to H2 of 90o bend of pipe 4. 2. The control valve was slowly opened until Q reached 30 liter/minute. Air bubbles present were removed to the manometer glass tube. 3. Q was readjusted to appropriate value of 30 liter/minute and five different Qs were determined from the maximum value of 30 to 12 liter/minute. The values of H1 and H2 were recorded in millimeter as Q was adjusted.
H)
Experiment with Pipe 4: Elbow 1. The manometer rubber tube from H1 of 90o bend of pipe 4 was moved to H2 of elbow of pipe 4. 2. The control valve was slowly opened until Q reached 30 liter/minute. Air bubbles present were removed to the manometer glass tube. 3. Q was readjusted to appropriate value of 30 liter/minute and five different Qs were determined from the maximum value of 30 to 12 liter/minute. The values of H1 and H2 were recorded in millimeter as Q was adjusted.
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Experimental data and analysis ftheo Pipe
2A
2B
hf.theo
hf.exp
fexp
h=h1-h2)
(Eq. 10)
26
4.33
920
35
4.91
0.882
14.46
(Eq 6 or (Eq. 4) Eq. 7 or Moody diagram) 0.162 0.473
22
3.67
770
155
4.91
0.747
12.25
0.168
0.352
0.615
0.294
18
3.00
660
240
4.91
0.611
10.02
0.177
0.248
0.420
0.300
14
2.33
565
320
4.91
0.475
7.790
0.189
0.160
0.245
0.290
12
2.00
530
350
4.91
0.407
6.670
0.196
0.122
0.180
0.289
26
4.33
915
185
4.34
0.998
15.47
0.159
0.625
0.730
0.186
22
3.67
780
245
4.34
0.846
13.11
0.166
0.469
0.535
0.189
18
3.00
660
300
4.34
0.691
10.71
0.174
0.328
0.360
0.191
14
2.33
570
350
4.34
0.537
8.320
0.185
0.211
2.220
0.193
12
2.00
535
370
4.34
0.461
7.150
0.193
0.162
0.165
0.197
Q (1/min)
Q x 10-4 (m3/s)
h1 (mm)
h2 (mm)
A 2 (m x10-4)
V (m/s)
Re (x 103)
(m)
f
2 Dgh f ,exp
0.885
0.303
LV 2
15
Pipe
1A
1B
Q x 10-4 (m3/s)
Q (1/min)
h1 (mm)
h2 (mm)
A (m x10-4) 2
V (m/s)
Re (x103)
ftheo
hf.theo
hf.exp
fexp
(Eq 6 or Eq. 7 or Moody diagram)
(Eq. 4)
h=h1-h2)
(Eq. 10)
(m)
f
2 Dgh f ,exp
28
4.67
390.2
300
4.91
0.951
28.33
0.137
0.260
0.09
0.047
24
4.00
373
315
4.91
0.815
24.29
0.142
0.198
0.06
0.043
20
3.33
360
330
4.91
0.678
20.20
0.149
0.144
0.03
0.031
16
2.67
353
340
4.91
0.544
16.21
0.157
0.098
0.013
0.021
12
2.00
349
345
4.91
0.407
12.13
0.169
0.059
0.004
0.011
28
4.67
384
305
4.34
1.076
29.59
0.135
0.349
0.079
0.031
24
4.00
370
315
4.34
1.168
32.12
0.132
0.402
0.055
0.018
20
3.33
365
317
4.34
1.402
38.56
0.126
0.553
0.048
0.011
16
2.67
363
320
4.34
1.749
48.10
0.120
0.820
0.043
0.006
12
2.00
365
325
4.34
2.335
64.21
0.111
1.352
0.04
0.003
LV 2
Table for Data of Sudden Enlargement Pipe Q (1/min)
Qx10-4 (m3/s)
h1 (mm)
h2 (mm)
h (m)
A1 (m2x10-4)
A2 (m2x10-4)
V1 (m/s)
V2 (m/s)
hL,theo (m) Eq. 2
hL,exp (m) Eq. 9
K hL,exp /(V12/2g)
16
28
4.67
5356
525
0.01
1.39
4.26
3.360
1.096
0.261
0.524
0.911
24
4.00
490
485
0.005
1.39
4.26
2.878
0.939
0.192
0.382
0.905
20
3.33
445
440
0.005
1.39
4.26
2.396
0.728
0.133
0.266
0.909
16
2.67
405
400
0.005
1.39
4.26
1.921
0.627
0.085
0.173
0.920
12
2.00
365
363
0.002
1.39
4.26
1.439
0.469
0.048
0.096
0.910
K
Table for Data of Sudden Contraction Pipe Q (1/min)
Qx10-4 (m3/s)
h1 (mm)
h2 (mm)
h (m)
A2 2 (m x10-4)
A2 2 (m x10-4)
V1 (m/s)
V2 (m/s)
hL,theo (m) Eq. 5
hL,exp (m) Eq. 9
hL,exp /(V22/2g)
28
4.67
845
280
0.565
4.26
1.39
1.096
3.360
0.288
0.051
0.089
24
4.00
765
300
0.465
4.26
1.39
0.939
2.878
0.211
0.088
0.208
20
3.33
635
335
0.300
4.26
1.39
0.782
2.396
0.146
0.039
0.133
16
2.67
560
340
0.220
4.26
1.39
0.627
1.921
0.094
0.052
0.276
12
2.00
485
360
0.125
4.26
1.39
0.469
1.439
0.053
0.031
0.294
V (m/s)
hL,theo (m) Eq. 6
hL,exp (m) Eq. 9
K
Table for Data of 90o Bend Pipe Q (1/min)
Qx10-4 (m3/s)
h1 (mm)
h2 (mm)
h (m)
A 2 (m x10-4)
hL,exp /(V2/2g)
17
28
4.67
825
2201
0.605
1.27
3.677
0.262
1.294
1.878
24
4.00
735
250
0.485
1.27
3.150
0.192
0.991
1.960
20
3.33
640
295
0.345
1.27
2.622
0.133
0.695
1.983
16
2.67
550
330
0.220
1.27
2.102
0.086
0.445
1.976
12
2.00
475
355
0.120
1.27
1.575
0.048
0.246
1.946
hL,exp (m) Eq. 9 1.469
K hL,exp /(V2/2g) 2.132
Table for Data of Elbow Pipe Q (1/min)
Qx10-4 (m3/s)
h1 (mm)
h2 (mm)
h (m)
A 2 (m x10-4)
V (m/s)
28
4.67
860
80
0.780
1.27
3.677
hL,theo (m) Eq. 6 0.262
24
4.00
755
155
0.600
1.27
3.150
0.192
1.106
2.187
20
3.33
640
230
0.410
1.27
2.622
0.133
0.760
2.169
16
2.67
545
295
0.250
1.27
2.102
0.086
0.475
2.109
12
2.00
475
340
0.135
1.27
1.575
0.048
0.261
2.064
18
19
GRAPH RESULT:
20
21
22
23
24
25
26
27
28
29
30
31
RESULTS AND DISCUSSION 1.value of n: n = (log hf 1 - log hf 2 ) / (log V1 - log V 2 ) pipe 2A: (log 0.84 – log 0.32)/ (log 0.84 – log 0.46) = 1.4688 pipe 2B: (log 0.54 – log 0.16)/ (log 0.82 – log 0.44) = 1.0525 pipe 1A: (log 0.075 – log 0.01)/ (log 0.9 – log 0.5) = 0.1612 pipe 1B: (log 0.05 – log 0.04)/ (log 01.35 – log 2.1) = 0.0234 Graph of ftheo and fexp versus Re In the graph of ftheo and fexp versus Re for pipe 2A, the graph of fexp is a straight line with postitive gradient. Meanwhile, the graph of ftheo for 2A is a straight line with negative gradient. For pipe 2B, both graphs of fexp and ftheo is a straight line with negative gradient. The difference between fexp and ftheo is very small. For pipe 1A, graph of fexp is a straight line with positive gradient and graph of ftheo is a straight line with negative gradient. In pipe 1B, both fexp and ftheo is a straight line with negative gradient, also with a very small difference between ftheo and fexp. For all graphs, there are some inaccuracies and marginal difference of values that causing the fexp differ from the ftheo. These errors may be occurred due to the bubble inside the pipe that can cause great difference of measurement, and also because of the flow rate of water source that keep changing inconsistently during the experiment.
32
Value of the slope of straight line, n. Slope of the graph 2A have a value of 1.4688. While in the graph 2B, the value of n is 1.0525. In the graph 1A, the value of the slope is 0.1612 and in the graph of 1B, the value of n is 0.0234. Pipe 2A and 1A are the pipes with rough surfaces and 2B and 1B are the pipes with smooth surfaces. Therefore, from these values, we can conclude that when the rougher the surface, the higher the slope of the graph (n). These difference of the value of n occur because when the surface of the pipe is rough, the friction is also high. From the graphs that has been plotted, we can get the value of loss coefficient (K). The value of loss coefficient (K) are influenced by the size of the diameter, pipe roughness and fluid velocity. From the experiment, the smaller the size of pipe diameter, the greater the value of loss coefficient. While the rougher the pipe, the greater the value of loss coefficient. Graph of Sudden Enlargement), Graph of Sudden Contraction, Graph of 90º bend, and Graph of Elbow pipe. All the graphs plotted are straight line and having positive gradient. There are significant differences between the experimental and the theoretical results in all these 4 graphs. These differences may be occurring due to the errors happen during the experiment. Some of the noticeable errors during the experiment are the inconsistent flow rate of the water source. Besides, there are bubbles in the measuring tubes that cause big inaccuracies in measuring the water level. The effect of fluid flow rate will affect the energy loss directly. The larger the fluid flow rate, the larger the energy loss of fluid. Graph of hLexp versus V21/2g for sudden enlargement, sudden contraction, 90˚ bend pipe and elbow pipe. All the graph plotted are all straight line with positive gradient. The value of loss coefficeient (K) is obtained from the slope of the graph. The value of K for sudden enlargement pipe is 0.9999, while the value of K for sudden contraction is 0.2616. The value of K for 90º bend pipe is 0.9983 while for the value of K for elbow pipe is 0.9054. We can see that the value of K is different for each value of graph. Sudden enlargement 33
graph has the highest value of K, while for sudden contraction graph has the lowest. The different pipe geometry will cause the difference in the value of loss condition and lead to the difference of the energy loss in pipe. The experiemental value of K obtained for the experiments of sudden enlargement, sudden contraction, 90º bend pipe and elbow pipe are all different from the theoritical value of K calculated. This occurs because there errors happen during the experiment. In addition, the might not be equal to 27 ˚ C since the value of the proposed Ktheo should be at 27 ˚ C. Overall From the experiment conducted, there are some of the errors that will affect the result of the experiment. While conducting, presence of air bubble in the tube that caused the height value of H1 and H2 have lower sensitivity. Unstable flow rate from the water source will cause the height value to be inaccurate. Furthermore, there are leakages in some point of the pipe causing the pressure of the water is not consistent and leads to the difference in the experimental and theoretical value. Therefore, some precautionary steps should be taken. Firstly, make sure that valve is tide enough in order to prevent leakage happen during the flow and also to make sure that the flow rate through the pipe is the same as the flow rate from the water meter. Furthermore, flow rate must be always constant during experiment by fully open the valve during every part of experiment. Smaller scale on water meter should be used. Other than that, every air bubble in the tube is removed. Hence, the reading should be taken repeatedly to minimize the errors. In avoiding parallax error, the eyes should be perpendicular to the scale. Last but not least, all water flow must be turn off before pipe changing. This is to make sure that water level does not exceed maximum level in the tube.
34
CONCLUSION In conclusion, all the objectives of the experiment are achieved. However, the result obtained in the experiment is inaccurate. This is due to difference in the experimental value and theoretical value. From the experiment, we can conclude that linear pipe with rough surface have larger energy losses than the energy losses in linear pipe with smooth surface. This occurs because friction in rough surface pipe is higher than the friction in smooth surface pipe. From the experiment, we also know that losses in pipe are also dependent on the diameter of the pipe. The smaller the diameter will have the greater losses. Besides, losses in pipe are also dependent on the flow rate. When the flow rate is higher, the losses will also be greater. Losses in sudden enlargement in pipe are greater than sudden contraction in pipe and 90° bend pipe. Losses in 90° bend pipe are greater than losses in sudden contraction in pipe. Ksudden enlargement > K90° bend > Ksudden contraction Hence, the precautionary steps should be taken to get the best result in order to avoid all the errors come out. Some of the steps are to make the flow rate of the water source consistent and remove the bubble from the tubes in the measurements.
35
REFERENCES A)
Rolf H. Sabersky, Allan J Acosta, Edward G. Hauptmann and E.M. Gates, "Fluid Flow-A First Course of Fluid Mechanics" (Fourth Edition), Prentice Hall Inc., 1999.
B)
R.V Giles, “Fluid Mechanics and Hydraulics” (Third Edition), McGrawHill Inc;
1994. C)
Lab Manual University Teknologi Malaysia.
36
Appendix Sample Calculation For pipe 1 and 2 (i)
(ii)
(iii)Reynolds Number for Pipe 1A
(iv)Turbulent flow,
(v)
(vi)
(vii) fexp,
37
Same method using for data of Pipe 1(B), 2(A) and 2(B) in determine of Reynolds Number:1B: Re = 27.5 x 103 x V 2A: Re = 16.4 x 103 x V 2B: Re = 15.5 x 103 x V Losses in Pipe of Sudden Enlargement Pipe (i)
(ii)h = h1 – h2 = 582-570 mm = 12 mm = 0.012 m (iii)
(iv)
(v)
(vi)
38
(vii)
Losses in Pipe of Sudden Contraction Pipe Note: Same method uses to find value of Q, h as shown in calculation of losses in pipe of sudden enlargement pipe. (i)
(ii)
(iii)
(iv)
(v)
Losses in Pipe for 900 Bend Pipe and Elbow Pipe Note: Same method uses to find value of Q, h as shown in calculation of losses in pipe of sudden enlargement pipe.
39
(i)
(iii)
(iv)
(v)
40
41
