Contents Abstract ......................................................................................................................................................... 2 Objectives ..................................................................................................................................................... 2 Theoretical background ................................................................................................................................ 2 Experimental setup ....................................................................................................................................... 4 Procedure...................................................................................................................................................... 5 Data reduction procedure............................................................................................................................. 6 Experimental results ..................................................................................................................................... 8 Discussion.................................................................................................................................................... 11 References .................................................................................................................................................. 13 Appendix ..................................................................................................................................................... 13 Sample calculation ...................................................................................................................................... 19
LIST OF TABLES Table 1: Test 1Measurement ...................................................................................................................... 13 Table 2: Test 2 measurement ..................................................................................................................... 14 Table 3: Test 3 measurement ..................................................................................................................... 14 Table 4: Test 1 result ................................................................................................................................... 15 Table 5: Test 2 result ................................................................................................................................... 16 Table 6: Test 3 result ................................................................................................................................... 18
LIST OF FIGURES Figure 1: Minor loss in pipes ......................................................................................................................... 4 Figure 2: Experimental setup ........................................................................................................................ 5 Figure 3: Moody's friction chart ................................................................................................................... 7 Figure 4: Minor loss factor for a diffuser ...................................................................................................... 8 Figure 5: Pressure head variation ................................................................................................................. 9 Figure 6: Static and kinetic pressure at each location ................................................................................ 10 Figure 7: Friction factor............................................................................................................................... 11 Figure 8: Uncertainty analysis input ........................................................................................................... 11 Figure 9: Uncertainty result ........................................................................................................................ 12
Abstract Pressure loss in a pipe generally occurred due to friction properties in pipe or in fluid. This tends to loss of energy (head) in the fluid flow. The minor factor also plays a big role in the pipe flow to reduce the total fluid energy. This lab report is compared both theoretical and experimental friction as well as the minor loss factor and found out that the value obtained from the lab result is more than the values obtained from the references. It is found that the energy loss in the lab experiment is more than theoretical aspects. Different parts of the piping systems like straight pipe, elbow, bend, valves, are considered in the lab report and each analysis for the minor loss friction is also performed. The graph is plotted based on the pressure loss with location showing that the pressure loss is increases with location and depend upon the minor loss of head the pressure drop increases with location.
Objectives
To analyze the major and minor loss factor in a piping system: Understanding this section helps to design a piping system with least head loss. This gives the idea to optimize the piping system with the available pipe connections.
To understand the energy loss taking place in different geometries: To perform the energy transfer as in the case of potential energy to kinetic energy a better piping system with least energy loss has to be designed. (ex: penstock to turbine)
To compare the experimental and theoretical results: This helps to identify the present design performance. It also makes sure whether the design has to modify or not.
Theoretical background When a fluid is flowing through a pipe head loss in the water takes place due to friction between the pipe surface and fluid. The head loss depends upon the friction factor, velocity, the shape of the pipe. The head loss in a pipe is divided in to two main categories. One is major loss and the other is minor loss. Major loss is generally takes place in long pipe due to friction. The head loss in a pipe can be calculated by the formula
v2 L Ploss,major f 2 D
(Bansal, 2012)
f is the friction factor, v is the velocity, L is the length of the pipe, D is the diameter of the pipe, ρ is the density of the fluid flowing through the piping system. When a fluid is flowing over a solid surface the velocity at the location close to the surface is zero and this condition is called no slip condition. The velocity of a fluid layer increases from the solid surface to the free stream fluid. The layer where the velocity gradient exists is called boundary layer region. The fluid in this region will have rotation flow because of one fluid layer is flowing over the other. The region other than boundary layer region is called in-viscid region. In this region velocity of fluid is maximum. The presence of boundary layer due to friction creates major flow in pipes. The other loss of head in pipe is due to minor flow effects. Minor loss is due to the physical shape of the piping system. Minor loss is calculated by the formula Ploss,min or
v2 K 2
(Bansal, 2012)
K is the minor loss factor and is different for different piping systems. Different piping system with minor loss factor is given in the image below.
Figure 1: Minor loss in pipes
(Yunus, 2011)
Sudden expansion or contraction in fluid flow changes the velocity of fluid flow and forms eddies in the fluid.
Experimental setup The experimental setup consists of piping network consists of different arrangements to control and direct the fluid flow.
Figure 2: Experimental setup
Arrangement consists of pipes and direction joints which directs the flow. A manometer is connected used to measure the pressure head. Each minor arrangement in the piping network is equipped with flow passages to measure the pressure head available. The 6 fold pressure gauge panel is a 6 level tubes made of glass with a millimeter scale behind it measure a range of 300 mm H2O. All levels tubes are connected to each other at the top end and have a joint vent valve. When the vent valve is closed, the differential pressure is measured with the vent valve. The measuring points are connected to the bottom end of the level tubes with quick release hose couplings. The first level tube has a drainage valve at the bottom tube.
Procedure Measure the length of the pipe. Note down the each pipe fittings diameter given in the lab manual. Allow the water to flow through the piping network. The discharge of the water is controlled by a controlling valve. After controlling the flow, water is allowed to pass through the
whole piping network. Manometer is filled with H2O make sure that the manometer valves are closely tighten and no presence of air in the manometer. Once the piping system is filled completely measure the water head at different junctions of the piping system. Connect the manometer to the respective parts to measure the head difference across the parts. During the pressure measurement the volume flow rate has to be constant. Note down the manometer reading at different locations and repeat the procedure for two more volume flow rates. Based on the discharge value and diameter at each location calculate velocity. From the pressure difference reading and velocity change the total pressure loss is determined. Substituting the pressure difference to the corresponding major or minor loss the friction factor (f)/minor loss factor (K) is determined.
Data reduction procedure The available water head in the a pipe flow is expressed as 𝑃𝑇𝑜𝑡𝑎𝑙 = 𝑃𝑠𝑡𝑎𝑡𝑖𝑐 + 𝑃𝑘𝑖𝑛𝑒𝑡𝑖𝑐 + 𝑃𝑃𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 Since the experimental setup is horizontal the potential head is zero. The equation becomes 𝑃𝑇𝑜𝑡𝑎𝑙 = 𝑃𝑠𝑡𝑎𝑡𝑖𝑐 + 𝑃𝑘𝑖𝑛𝑒𝑡𝑖𝑐 Static pressure effect represents the pressure due to the height of water and the kinetic pressure effect is due the velocity of water. According to Bernoulli the total energy in a streamlined flow is constant. Thus if no loss of energy takes place the P total will be same everywhere in the pipe flow. Considering the head loss the equation can be over write as 𝑃𝑇𝑜𝑡𝑎𝑙 = 𝑃𝑠𝑡𝑎𝑡𝑖𝑐 + 𝑃𝑘𝑖𝑛𝑒𝑡𝑖𝑐 + 𝑃𝑙𝑜𝑠𝑠 This loss is due to major and minor effects. Static pressure is expressed by the equation 𝑃𝑆𝑡𝑎𝑡𝑖𝑐 = 𝜌 ∗ 𝑔 ∗ ℎ and it shows the pressure increases with the height of the fluid column. Kinetic pressure is due to the velocity of fluid flowing through the pipe expressed by the equation 𝑃𝐾𝑖𝑛𝑒𝑡𝑖𝑐 = 𝜌 ∗
𝑉2 2
If there is no loss in the piping system pressure head and velocity head compensate each other to balance the energy. In the presence of head loss major and minor loss exists and is calculated from the expression 1
𝑃1 =𝜌𝑔(ℎ1 − ℎ𝑟𝑒𝑓 )+2 𝜌𝑣12 1
𝑃2 =𝜌𝑔(ℎ2 − ℎ𝑟𝑒𝑓 )+2 𝜌𝑣22 P1 P 2 Ploss,major f
v2 L v2 P1 P 2 Ploss,min or K 2 D, 2
The values of friction factor f and minor loss factor K is different for different pipe structures. The image given below (Moody’s friction factor) shows the friction factor for different pipe roughness. From the Reynolds number and pipe roughness values the friction factor can be calculated.
Figure 3: Moody's friction chart
(Yunus, 2011)
Minor factor is different for different pipe configurations. As an example minor factor for a diffuser angle is shown below.
Figure 4: Minor loss factor for a diffuser
(Frank, 2010)
Experimental results Three experiments based on volume flow rate are conducted. The head loss is calculated and plotted in a graph. From the graph friction pressure head loss in experiment is more than the values obtained by the formulas. The graph shows as the volume flow rate increases the head loss increases, and the variation is more in experimental results compared to theoretical result. Theoretical analogy shows that the pressure head loss due to minor loss is less compared to major loss. And major loss is dominating in the theoretical approach. In this experimental result the major part of the head loss is taking place due to minor loss factors. In all three experimental results the head loss due to straight pipe is less. The slope of the graph is less at locations 2, 6 and 8 (straight pipes). The other locations show increases slope due to increased pressure drop. Velocity in the piping network only varies in reducer and enlarger. Since the diameter is same for all parts the velocity and discharge is same.
Pressure head variation 4500 4000
Pressure loss (Pa)
3500 3000
Test 3 Theoretical
2500
Test 3 Experimental
2000
Test 2 theoretical
1500
Test 2 experimental
1000
Test 1 theoretical Test1 experimental
500 0 1
2
3
4
5
6
7
8
9
location
Figure 5: Pressure head variation
Comparing the pressure drops pressure change in reducer and enlarger section is more in all cases. Since the velocity is varies in both section pressure change will compensate the loss in velocity head. It is also seen from the graph at section 3 and 4 the pressure drop is more and the slope of the graph is also more compared to other.
Static/kinetic pressure variation 300 250 200 150
Test 1 static pressire difference
Pressure differnce (Pa)
100
Test 1 kinetic pressure difference
50
Test 2 static pressure difference
0 -50
1
2
3
4
5
6
7
8
9
Test 2 kinetic pressure difference Test 3 statci pressure difference
-100
Test 3 kinetic pressure difference
-150 -200 -250
LOcation Figure 6: Static and kinetic pressure at each location
The graph above shows static and kinetic pressure at different location. Except reducer and enlarger the diameter of each pipe sections are same. In case of enlarger the velocity reduces that’s the reason the graph shows negative pressure difference at location 3. As the velocity reduces the pressure increases thereby the pressure increases at enlarger at section 3. In case of reducer at section 4 the velocity increases and pressure decreases. The kinetic pressure drop at section 4 is more than static pressure drop. Except enlarger and reducer other section has no velocity change therefore the head loss due to velocity is zero. The friction factor graph shown below describes the variation of friction factor with respect to Reynolds number. From the graph it is clear that when a flow direction changes the minor factor is increases with respect to Reynolds number. If the passage is straight without any bend variation in the friction factor /minor loss factor is less. But in the cases of bend or elbow the variation in friction factor /minor loss factor is more compared to straight pipes. Friction factor is decreases in the case of reducer at section 3 because the velocity is decreases in a reducer thereby the loss associated with velocity also reduces.
Friction factor 16 14
Pipe Elbow 1 Friection factor
12
Pipe 2
10
Reducer 3
8
Enlarger 4
6
Rounded elbow 5 Pipe 6
4
Bend 90 7 2
Pipe 8
0
Bend 90 large 9 0
1000
2000
3000
4000
5000
6000
Reynold"s number
Figure 7: Friction factor
Uncertainty analysis The only error in the reading is while measuring the volume and the chances of error is ± 1.30. The effect of this error will change the values velocity, Reynolds number, and total pressure. The input given for the analysis is given below (From Test 1)
Figure 8: Uncertainty analysis input
Executing the program in engineering equation solver shows that the 100% uncertainty is due to volume measurement only.
Result shows that the kinetic pressure may vary ±1136 for a
pressure of 16997 Pa. The total pressure varies ±1136 𝑓𝑜𝑟 18655 𝑃𝑎. Reynolds number varies 𝑚
±109.5 for a value of 3276. The velocity varies ±.005732 𝑓𝑜𝑟 0.1715 𝑠 .
Figure 9: Uncertainty result
Discussion When the velocity change takes place in a flow the pressure head will also change. The region where the pressure is high the loss in the pressure drop will be also comparatively high. Likewise the region where the velocity is high kinetic head drop will be more at those sections. Since the velocity at section where the diameter is same there is no kinetic head loss takes place. The region where the velocity changes like reducer and enlarger the kinetic head change appears. The pressure drop in a pipe is mainly due to friction and the value is directly proportional to the friction factor (f). The major pressure drop and minor pressure drop in the pipe shows the static pressure drop if the pipe diameter is not changing. The varying pipe diameter shows both kinetic and static pressure drop. No matter whatever the pipe is straight or bend energy will loss due to friction. For same diameter pipe energy loss in a bend pipe is more than the energy loss in a straight pipe provided both have same length. The effect of friction increases with velocity of flow. The variation may be drastic in bends and less variation in straight pipe. In this lab project the pressure drop is more in experimental result and the theoretical result based on the reference values are less. The change in the values are in appropriate may be because of the change in inner diameter of the pipe network due prolonged use.
References
Bansal, R, K. (2012), “A text book of fluid mechanics and hydraulic machines”, reversed ninth edition, Laxmi publications PVT LTD.
Frank, M, White. (2010), Fluid Mechanics, Fifth edition, WCB-Mc Graw Hill.
Yunus,A Cengel& Michael A Boles, 2011, Fluid mechanics, Tata McGraw-Hill Education, New Delhi.
Appendix Table 1: Test 1Measurement
Volume (ML)
Test 1 Time (S)
1
348
10.15
2
352
10.31
3
451
13.69
Average
383.6666667 11.38333333
Point 1 2 3
Measurement object Pipe elbow Reducer
4
Volume flow rate(m3/s) 3.42857E-05 3.41416E-05 3.29438E-05 3.37042E-05 Pressure in water head (mm) 169 166 165 149
Enlarger 5 6 7 8 9
151 Rounded elbow Bend 90 tight Bend 90 large
10 11
149 148 141 139 138
Sperical vale
Table 2: Test 2 measurement
Test 2 Volume (ML)
Time (S)
1
400
9.4
2
352
8.64
3
349
8.94
Average
367
8.993333333
Point 1 2 3
Measurement object Pipe elbow Reducer
4
Volume flow rate(m3/s) 4.25532E-05 4.07407E-05 3.9038E-05 4.07773E-05 Pressure in water head (mm) 185 179 176 156
Enlarger 5 6 7 8 9
160 Rounded elbow Bend 90 tight Bend 90 large
10 11
158 152 151 152 151
Sperical vale
Table 3: Test 3 measurement
Volume (ML)
Test 3 Time (S)
1
405
9.51
2
375
7.98
3
355
7.51
Average
378.3333333 8.333333333
Point 1 2
Measurement object Pipe elbow
Volume flow rate(m3/s) 4.25868E-05 4.69925E-05 4.72703E-05 0.0000454 Pressure in water head (mm) 200 193
3
191
Reducer
4
167 Enlarger
5
171 Rounded elbow
6 7 8 9
169 160 157 162
Bend 90 tight Bend 90 large
10
153 Sperical vale
11
Test 1 result table Table 4: Test 1 result
Pipe Elbo w Flo m 0.00 w 3 / 0033 rat s 89 e 0.00 Are Ar m 0226 a ea 2 865 Vel Ve 0.14 m ocit loc 9383 /s y ity 995 2853 Re Re .402 15 Wa ter 0.16 m hea 9 Pre d ssu Sta P 1657 re tic a .89 Ki 11.1 P net 5778 a ic 896 Flo w rate
Pipe
Reducer
Enlarger
Rou nded Elbo w
Pipe
Bend 90
Pipe
Bend 90 large
0.00003389
0.00 0033 89
0.00 0033 89
0.00 0033 89
0.00 0033 89
0.00 0033 89
0.00 0033 89
0.00003389
0.00 0226 865 0.14 9383 995 2853 .402 15
0.00 0226 865 0.14 9383 995 2853 .402 15
7.23 7.23 0.00 456E 456E 0226 -05 -05 865 0.46 0.46 0.14 8445 8445 9383 904 904 995 5052 5052 2853 .899 .899 .402 64 64 15
0.00 0226 865 0.14 9383 995 2853 .402 15
0.00 0226 865 0.14 9383 995 2853 .402 15
0.00 0226 865 0.14 9383 995 2853 .402 15
0.00 0226 865 0.14 9383 995 2853 .402 15
0.00 0226 865 0.14 9383 995 2853 .402 15
0.16 6
0.16 5
0.14 9
0.14 9
0.15 1
0.15 1
0.14 9
0.14 8
0.14 1
0.13 9
1628 .46 11.1 5778 896
1618 .65 11.1 5778 896
1461 .69 109. 7207 825
1461 .69 109. 7207 825
1481 .31 11.1 5778 896
1481 .31 11.1 5778 896
1461 .69 11.1 5778 896
1451 .88 11.1 5778 896
1383 .21 11.1 5778 896
1363 .59 11.1 5778 896
1492 .467 789
1492 .467 789
1472 .847 789
1463 .037 789
1394 .367 789
1374 .747 789
58.3970064 3
78.9429935 7
19.6 2
9.81
68.6 7
19.6 2
9.81
0.04 2704 313
1.22389096 5
1.65449605 2
1.75 8412 896
0.04 2704 313
6.15 4445 134
0.08 5408 626
0.87 9206 448
0.95
0.04 5
0.3
0.79
1.5
0.04 5
0.9
0.04 5
0.35
10.5 9989 952
10.3 3736 331
14.3142669
37.6942361 8
16.7 3668 345
10.3 3736 331
10.0 4201 007
10.3 3736 331
3.90 5226 137
0.00 m 1080 m 52
0.00 1053 758
0.00145915 1
0.00384243
0.00 1706 084
0.00 1053 758
0.00 1023 65
0.00 1053 758
0.00 0398 086
63.9 % 8267 239
5.10 1526 274
307.963654 9
109.429879 9
17.2 2752 637
5.10 1526 274
583. 8272 371
89.7 9694 745
151. 2018 422
63.9 % 8267 239
5.10 1526 274
307.963654 9
109.429879 9
17.2 2752 637
5.10 1526 274
583. 8272 371
89.7 9694 745
151. 2018 422
Tot P al a ΔP (lo ss) f1 or K1 Obt f2 ain or ed K2 pre Pre ssu ssu re re los s fro m Wa boo ter ks hea or d ref ere nce Pre ssu re Err los s or f or K
1669 .047 789
1639 .617 789
1629 .807 789
29.4 3
9.81
2.63 7619 343
P a
P a
1571 .410 783
1571 .410 783
Test 2 result table Table 5: Test 2 result
Pipe Elbo w
Pipe
Flo Flo m 0.00 0.000 w w 3/ 0040 0407 rate rat s 7
Reducer
Enlarger
0.0000407
0.0000407
Rou Bend nded Bend Pipe Pipe 90 Elbo 90 large w 0.00 0.00 0.00 0.00 0.000 0040 0040 0040 0040 0407 7 7 7 7
e Are a Vel ocit y Re
Pre ssu re
0.00 0.000 0.00 7.23 0226 2268 0226 456E 2 865 65 865 -05 Ve 0.17 0.179 0.17 0.56 m loc 9401 4018 9401 2577 /s ity 847 47 847 406 3426 3426. 3426 6068 Re .776 7768 .776 .250 851 51 851 674 Wa ter 0.18 0.17 0.15 m 0.179 hea 5 6 6 d Sta P 1814 1755. 1726 1530 tic a .85 99 .56 .36 Ki 16.0 16.09 16.0 158. P net 9251 2511 9251 2466 a ic 134 34 134 69 1830 1772. 1742 1688 Tot P .942 0825 .652 .606 al a 511 11 511 669 ΔP P 186. 137.3 54.0458423 (lo a 39 4 4 ss) f1 11.5 0.414 0.78535995 or 8240 5282 5 K1 601 15 f2 or 0.95 0.045 0.3 K2 Pre 15.2 14.90 P 20.6449954 ssu 8788 9238 a 5 re 577 45 Ar ea
m
Obt ain ed pre ssu re los s fro m Wa 0.00 boo ter m 0.001 1558 ks hea m 5198 398 or d ref ere nce Err Pre % 91.7 -
7.23 0.00 456E 0226 -05 865 0.56 0.17 2577 9401 406 847 6068 3426 .250 .776 674 851
0.00 0.000 0.00 0226 2268 0226 865 65 865 0.17 0.179 0.17 9401 4018 9401 847 47 847 3426 3426. 3426 .776 7768 .776 851 51 851
0.00 0226 865 0.17 9401 847 3426 .776 851
0.00 0226 865 0.17 9401 847 3426 .776 851
0.15 6
0.16
0.16
0.15 2
0.16 1
0.15 2
1530 .36 158. 2466 69 1688 .606 669
1569 .6 16.0 9251 134 1585 .692 511
1569 1549. 1491 .6 98 .12 16.0 16.09 16.0 9251 2511 9251 134 34 134 1585 1566. 1507 .692 0725 .212 511 11 511
1579 .41 16.0 9251 134 1595 .502 511
1491 .12 16.0 9251 134 1507 .212 511
102.914157 7
107. 91
107. 91
215. 82
137. 34
1.49548336 6
6.70 0.296 6.70 5603 0915 5603 478 82 478
0.65 1401 481
8.53 4404 427
0.04 5
0.35
0.79
1.5
0.158
98.1
0.045
0.9
54.3651546 9
24.1 14.90 14.4 3876 9238 8326 701 45 02
14.9 0923 845
5.63 2378 968
0.00210448 5
0.00554181
0.00 0.00 0.001 2460 1476 5198 629 377
0.00 1519 8
0.00 0574 147
161.786651
89.3016919
347.
1347
2338
-
645.
or
ssu re los s f or K
9790 821.1 452 7381 11 91.7 821.1 % 9790 7381 452 11
7
4
161.786651 7
0402 557.9 0670 319 8129 531 37
89.3016919 4
.558 846
.401 265
347. 645. 557.9 0402 0670 8129 319 531 37
1347 .558 846
2338 .401 265
Rou nded Elbo w
Bend 90
Pipe
Bend 90 large
0.00 0.00 0.000 0048 0048 0483 3 3
0.00 0048 3
0.00 0048 3
0.00 0.000 0.00 0226 2268 0226 865 65 865 0.21 0.212 0.21 2901 9019 2901 946 46 946 4066 4066. 4066 .666 6663 .666 386 86 386
0.00 0226 865 0.21 2901 946 4066 .666 386
0.00 0226 865 0.21 2901 946 4066 .666 386
Test 3 result table Table 6: Test 3 result
Pipe Elbo w Flo w rate Are a Vel ocit y Re
Pre ssu re
Flo m 0.00 w 3 / 0048 rat s 3 e 0.00 Ar m 0226 ea 2 865 Ve 0.21 m loc 2901 /s ity 946 4066 Re .666 386 Wa ter m 0.2 hea d Sta P 1962 tic a Ki 22.6 P net 6361 a ic 932 Tot P 1984 al a .663
Pipe
Reducer
Enlarger
0.000 0483
0.0000483
0.0000483
0.000 0.00 7.23 7.23 0.00 2268 0226 456E 456E 0226 65 865 -05 -05 865 0.212 0.21 0.66 0.66 0.21 9019 2901 7628 7628 2901 46 946 715 715 946 4066. 4066 7201 7201 4066 6663 .666 .388 .388 .666 86 386 392 392 386
Pipe
0.19 1
0.16 7
0.16 7
0.17 1
0.17 1
0.16
0.15 7
0.16 2
1893. 1873 33 .71 22.66 22.6 3619 6361 32 932 1915. 1896 9936 .373
1638 .27 222. 8640 509 1861 .134
1638 .27 222. 8640 509 1861 .134
1677 .51 22.6 6361 932 1700 .173
1677 1657. 1569 .51 89 .6 22.6 22.66 22.6 6361 3619 6361 932 32 932 1700 1680. 1592 .173 5536 .263
1540 .17 22.6 6361 932 1562 .833
1589 .22 22.6 6361 932 1611 .883
0.193
0.169
ΔP (lo ss) f1 or K1 Obt f2 ain or ed K2 pre Pre ssu ssu re re los s fro m Wa boo ter ks hea or d ref ere nce Pre ssu re los Err s or f or K
619
619
19
619
619
619
35.2395684 5
160.960431 6
215. 82
206.0 1
186. 39
176. 58
235. 44
0.36360646 9
1.66081075 2
9.52 0.441 8.22 2750 5093 4193 842 57 909
0.37 8436 592
10.3 8845 546
0.3
0.79
0.04 5
0.35
21.5 20.99 3043 7176 836 73
29.0750342 3
76.5642567 9
33.9 20.99 20.3 9542 7176 9725 899 73 739
20.9 9717 673
7.93 2266 764
0.00 0.002 m 2194 1403 m 744 85
0.00296381 6
0.00780471 5
0.00 0.002 0.00 3465 1403 2079 385 85 231
0.00 2140 385
0.00 0808 59
93.5 1208. % 4487 1758 067 73
21.2021563 7
110.229209 2
534. 813. 881.1 8500 7993 3190 561 232 49
740. 9702 042
2868 .130 132
110.229209 2
534. 813. 881.1 8500 7993 3190 561 232 49
740. 9702 042
2868 .130 132
P a
619
19
333. 54
274.6 8
14.7 0.588 1697 6791 857 43 0.95 P a
619
0.045
93.5 1208. % 4487 1758 067 73
051
21.2021563 7
051
Sample calculation For Test 1 result table Pipe elbow Flow rate = 0.00003389m3/s 3.14
3.14
4
4
Area = (
Velocity =
) 𝑑2 =(
𝐹𝑙𝑜𝑤 𝑟𝑎𝑡𝑒 𝐴𝑟𝑒𝑎
) . 0172 = 0.000226865 m2
0.00003389
= 0.000226865 = 0.1493 m/s
1.5
0.045
0.9
Re (Reynolds number) =
𝜌∗𝑣∗𝑑 𝜇
=
1000∗0.1493 ∗0.017 0.00089
= 2853 Water head = .29m (given)
Static pressure = 𝜌 ∗ 𝑔 ∗ ℎ = 1000* 9.81 * .169 = 1657.89Pa Kinetic pressure =
𝜌 (𝑣 2 ) 2
=
1000∗ .14932 2
= 11.15 Pa
Total pressure = Static pressure+ Kinetic pressure = 1657Pa+11.15 Pa = 1669Pa ΔP (loss) = Static pressure – Pressure at exit of the pipe elbow = 1669 – 1639.61= 29.43Pa 2∗ ΔP
2∗ 29.43
K1 = 𝜌∗𝑣2 = 1000∗.14932 = 2.63 K2 = .95 Obtained from text book (Yunus, 2011) Pressure loss =K2 *
𝜌∗𝑣 2 2
=.95*
1000∗0.14932 2
= 10.6Pa
Water head corresponding to pressure loss =
Pressure loss 1000∗9.81
=0.00108m
