FLUIDS_LAB_REPORT_5_1

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Dec 6, 2023

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Lab Experiment #5: Energy losses in pipes CE 336: Fluids Mechanic Laboratory Instructor: Andres Acosta, MS, PE Submitted by: Steven Ramirez Eddie Rangel Selena Nguyen Shakir Shihabudeen Justin Nguyen Date of performing lab experiment: 10/12/2022 Date of submitting lab report:11/09/2022

1 Introduction In this lab experiment a C6-MKII-10 Armfield apparatus was used to measure the major losses when fluid flows through the pipes. The apparatus was powered by the hydraulic bench to allow the fluid flow into the pipes at different flow rates. The apparatus had 5 pipes with various diameters. The 5th pipe had the same diameter as pipe 4, however pipe 5 had a special coating inside to make its inside rough. This was conducted for all 5 pipes. The data that was collected was the pressure drops from 2 different points at the pipe and the volumetric flow rate.The experiment was conducted by allowing the fluid flow into each pipe and a manometer was used to measure pressure at 2 points in the pipe. The 2 points of pressure drop were subtracted to get the measured head loss. The flow rate was decreased 10 times to have 10 different measurements for each pipe. Using the data, we can calculate the Re,friction factor, and the calculated head loss. Purpose of Study The purpose of this experiment is to demonstrate major losses when fluid flows through pipes. We also see how different pipe sizes can affect energy losses in pipes for both laminar and turbulent flows. Theory Reynolds number was developed by Osbonrne Reynolds to demonstrate that in pipe there are two types of flow which are Laminar flow and Turbulent flow. Reynolds number is defined as: ℜ= VD v = ρVD μ Where V is the flow velocity through the pipe, D is the diameter of the pipe, v is the kinematic

2 viscosity of the fluid, μ is the dynamic viscosity of the fluid, and ρ is the density of the fluid. For ℜ < 3000, flow is defined as laminar, ℜ > 5000 flow is defined as turbulent flow, and for 3000 < ℜ < 5000, flow is transitional and it cannot be defined accurately. The experiments show that frictional head losses in pipes are not dependent on pressure of the fluid flows. Also the head loss is proportional to the length of the pipe and is inversely to the diameter of the pipe. The pipe roughness is related to the head loss when dealing with turbulent flow. Henry Darcy and Julius Weisbach found the equations for frictional head loss based on the relationships found through several experiments: h = f L D V 2 2 g Where h is the frictional head loss, f is the Darcy-Weisbach friction factor, L is the length of the pipe, D is the diameter of the pipe, V is the flow velocity. For the laminar flow: f = 64 ℜ The friction factor can be calculate by using the Swamee-Jain equation: f = 0.25 [ log ( ε D 3.7 + 5.74 ℜ 0.9 )] 2 Where ε D is the relative roughness of the pipe material. ε is the roughness height of the pipe material and D is the diameter of the pipe.

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3 For turbulent flow, the friction factor can also be determined by the Moody chart which was developed by Lewis Moody. The chart shows four zones of pipe flow: ● Laminar flow zone ● Transitional zone ● Transitional turbulent flow ● Turbulent zone Equipment A C6-MKII-10 Armfield apparatus which consists of the following: ● 4 smooth pipes with different diameters ● 1 rough pipe ● A hand held pressure measure device that can be attached with the attachments to measure the head loss in pipes which are separated by 1 meter. ● A 500 ml cylinder and a stopwatch to measure the flow rate of the 5 mm diameter pipe. Experimental Setup & Procedures: This experiment consists of two exercises: measure the head loss of the flow through smooth pipes and the head loss of the flow through roughened pipe. The first part of the experiment starts with opening the valve of the roughened 17 mm which is located at the bottom of the apparatus, shutting the valve of the hydraulic bench all the way.

4 Next, turn the hydraulic bench pump. Adjust the valve of the hydraulic bench to establish a slow and steady flow through the pipe, make sure to close the valve of all the different diameter pipes. Now, measure the head loss of the flow through the roughened pipe by using the pressure measure device, connect the device to the two tapings in the pipe separated by one meter. After absorbing the pressure values from the two tapings, the head loss can be obtained by the difference from the pressure values. The flow rate can be obtained by reading the screen of the hydraulic bench. Next, decrease the flow rate by 0.02 l/s in the hydraulic bench by slowly adjusting the valve and record the head loss by measuring pressure for the two tapings on the pipe. Repeat these steps and observe the head loss for ten different flow rates. The second part of the experiment consists of working on the remaining 4 smooth pipes with different diameters. After establishing the data for the roughened 17 mm pipe, close the valve of this pipe completely and open the 17 mm smooth pipe which is located right upper the roughened pipe. Repeat the pressure drop records for ten different flow rates for this pipe. The flow rate can still be obtained by reading the screen of the hydraulic bench. Do the same things for the 11 mm and 8 mm diameter pipes to obtain the head loss for ten different flow rates, the flow rate values can still be collected by reading the screen of the hydraulic bench. The flow rate for the 5 mm pipe can be obtained by using the 500 ml cylinder and the stopwatch. Open the valve completely for this pipe and measure the time to collect 500 ml of water, from time and volume values, the flow rate can be calculated. After obtaining the flow rate, use the pressure measure to collect the pressure of the two tapings of the pipe and from that the head loss can be calculated. Repeat the steps for ten different flow

5 rates to obtain the head losses. Calculations: D = 8 mm = .008 m .008 ¿ 2 ¿ π ¿ A = π D 2 4 = ¿ ε D = 0 ( smooth pipe ) Q = ∀ t = 500 mm 3 ∗ 10 − 3 7.93 s = .000063 m 3 s V = Q A = .000063 m 3 s 0.00005027 m 2 = 1.253 m s ℜ= VD ν = 1.253 m s ∗ .008 m 10 − 6 = 10026.761 log ( ε / D 3.7 + 5.74 R e 0.9 ) ¿ 2 ¿ log ( 0 3.7 + 5.74 10026.761 0.9 ) ¿ 2 ¿ ¿ ¿ f = 0.25 ¿ 1.253 m s ¿ 2 ( ¿¿ 2 ( 9.81 ))= 0.310 m H 2 0 ¿ h = f L D V 2 2 g =( 0.0309 )( 1 m .008 m ) ¿ Questions/Discussion Data Table 1: Pipe loss data for D=5mm Table 1 Relative 0 Diameter(m) 0.005 Area 0.0000196

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6 roughness 3 Volume Time Flow Rate Velocity Reynolds Number Calculated Friction Factor Calculated head loss Measured head loss V (liters) t (secs) Q (m^3/s) V (m/s) Re f h_c (mH2O) h_m (m H2O) 500 7.93 0.000063 3.209 16042.818 0.0273 2.865 3.094 500 8.24 0.000061 3.107 15533.522 0.0275 2.709 3.094 500 8.47 0.000059 3.005 15024.227 0.0278 2.556 3.094 500 8.65 0.000057 2.903 14514.931 0.0280 2.408 3.023 500 8.84 0.000056 2.852 14260.283 0.0282 2.335 2.531 500 10.28 0.000048 2.445 12223.100 0.0293 1.787 1.969 500 16.92 0.000029 1.477 7384.789 0.0337 0.750 0.633 500 19.43 0.000025 1.273 6366.198 0.0352 0.582 0.352 500 27.62 0.000018 0.917 4583.662 0.0389 0.333 0.070 500 117.2 4.30E-06 0.219 1094.986 0.0640 0.031 0.000 Table 2: Pipe loss data for D=8mm Table 2 Relative roughness 0 Diameter(m) 0.008 Area 0.0000502 7 Volume Time Flow Rate Velocity Reynolds Number Calculated Friction Factor Calculated head loss Measured head loss V (liters) t (secs) Q (m^3/s) V (m/s) Re f h_c (mH2O) h_m (m H2O) - - 0.000205 4.078 32626.763 0.0229 2.428 2.250 - - 0.0002 3.979 31830.989 0.0230 2.324 2.180 - - 0.000195 3.879 31035.214 0.0232 2.223 2.039 - - 0.00019 3.780 30239.439 0.0233 2.124 1.898 - - 0.000185 3.680 29443.664 0.0235 2.026 1.758 - - 0.00018 3.581 28647.890 0.0236 1.931 1.617 - - 0.000175 3.482 27852.115 0.0238 1.837 1.547 - - 0.00017 3.382 27056.340 0.0240 1.746 1.406 - - 0.000165 3.283 26260.566 0.0241 1.657 1.266 - - 1.60E-04 3.183 25464.791 0.0243 1.570 1.055

7 Table 3: Pipe Loss Calculations for D=11m Table 3 Relative roughness 0 Diameter(m) 0.011 Area 0.0000950 3 Volume Time Flow Rate Velocity Reynolds Number Calculated Friction Factor Calculated head loss Measured head loss V (liters) t (secs) Q (m^3/s) V (m/s) Re f h_c (mH2O) h_m (m H2O) - - 0.000324 3.409 37502.692 0.0222 1.194 1.308 - - 0.000304 3.199 35187.711 0.0225 1.067 1.104 - - 0.000284 2.988 32872.730 0.0229 0.946 1.146 - - 0.000264 2.778 30557.749 0.0233 0.832 0.998 - - 0.000244 2.568 28242.768 0.0237 0.724 0.773 - - 0.000224 2.357 25927.787 0.0242 0.623 0.738 - - 0.000204 2.147 23612.806 0.0248 0.529 0.633 - - 0.000184 1.936 21297.825 0.0254 0.441 0.422 - - 0.000164 1.726 18982.844 0.0262 0.361 0.316 - - 0.000144 1.515 16667.863 0.0270 0.288 0.337 Table 4: Pipe Loss Calculations for D=17mm Table 4 Relative roughness 0 Diameter(m) 0.017 Area 0.0002269 8 Volume Time Flow Rate Velocity Reynolds Number Calculated Friction Factor Calculated head loss Measured head loss V (liters) t (secs) Q (m^3/s) V (m/s) Re f h_c (mH2O) h_m (m H2O) - - 0.000430 1.894 32205.471 0.0230 0.247 0.141 - - 0.000410 1.806 30707.542 0.0232 0.227 0.211 - - 0.000390 1.718 29209.613 0.0235 0.208 0.211 - - 0.000370 1.630 27711.684 0.0238 0.190 0.211 - - 0.000350 1.542 26213.755 0.0241 0.172 0.070 - - 0.000330 1.454 24715.826 0.0245 0.155 0.141 - - 0.000310 1.366 23217.898 0.0249 0.139 0.070 - - 0.000290 1.278 21719.969 0.0253 0.124 0.070

8 - - 0.000270 1.190 20222.040 0.0257 0.109 0.176 - - 0.000259 1.141 19398.179 0.0260 0.102 0.088 Table 5: Pipe Loss for D=17mm (rough) Table 5 Relative roughness 0.0375 Diameter(m) 0.017 Area 0.0002269 8 Volume Time Flow Rate Velocity Reynolds Number Calculated Friction Factor Calculated head loss Measured head loss V (liters) t (secs) Q (m^3/s) V (m/s) Re f h_c (mH2O) h_m (m H2O) - - 0.000391 1.723 29284.510 0.0643 0.572 0.879 - - 0.000371 1.635 27786.581 0.0644 0.516 0.879 - - 0.000351 1.546 26288.652 0.0645 0.462 0.717 - - 0.000331 1.458 24790.723 0.0646 0.412 0.809 - - 0.000311 1.370 23292.794 0.0647 0.364 0.647 - - 0.000291 1.282 21794.865 0.0648 0.319 0.492 - - 0.000271 1.194 20296.936 0.0649 0.277 0.387 - - 0.000251 1.106 18799.007 0.0650 0.238 0.422 - - 0.000231 1.018 17301.079 0.0652 0.202 0.141 - - 0.000211 0.930 15803.150 0.0654 0.169 0.105 Figure 1: Measured Head Loss vs. Velocity for D=5mm Laminar Flow Transational Flow Turbulent Flow

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9 Figure 2: Measured Head Loss vs. Velocity for D=8mm Figure 3: Measured Head Loss vs. Velocity for D=11mm

10 Figure 4: Measured Head Loss vs. Velocity for D=17mm Figure 5: Measured Head Loss vs. Velocity for D=17mm(rough) Figure 6: Log h m vs. log V for D=5mm log h_m log v 0.4905 0.5063 0.4905 0.4923 0.4905 0.4778 0.4805 0.4628 0.4033 0.4552 0.2942 0.3882 -0.1988 0.1694

11 -0.4540 0.1049 -1.1530 -0.0378 0.0000 -0.6596 Slope (n) 0.8268177026 Figure 7: Log h m vs. log V for D=8mm log h_m log v 0.3521 0.6105 0.3384 0.5998 0.3094 0.5888 0.2784 0.5775 0.2449 0.5659 0.2087 0.5540 0.1894 0.5418 0.1480 0.5292 0.1023 0.5162 0.0000 0.5029 Slope (n) 3.026094972

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12 Figure 8: Log h m vs. log V for D=11mm log h_m log v 0.117 0.533 0.043 0.505 0.059 0.475 -0.001 0.444 -0.112 0.410 -0.132 0.372 -0.199 0.332 -0.375 0.287 -0.500 0.237 0.000 0.180 Slope (n) 1.124306416

13 Figure 9: Log h m vs. log V for D=17mm log h_m log v -0.8520 0.2775 -0.6759 0.2568 -0.6759 0.2351 -0.6759 0.2122 -1.1530 0.1881 -0.8520 0.1625 -1.1530 0.1354 -1.1530 0.1064 -0.7551 0.0754 0.0000 0.0573 Slope (n) -0.9022904503 Figure 10: Log h m vs. log V for D=17mm (rough) log h_m log v -0.0561 0.2362 -0.0561 0.2134 -0.1444 0.1893 -0.0923 0.1638 -0.1892 0.1368 -0.3079 0.1079 -0.4126 0.0770 -0.3749 0.0437 -0.8520 0.0076

14 0.0000 -0.0317 Slope (n) 1.42192944 Figure 11: h m vs Re for all pipe diameters

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15 Questions 1. What is the n value when you plot log h m versus log V for each size of pipes (h m ∞V n ) for all pipe sizes? What value of n you expected? a. The n values for the various pipe sizes after plotting are as follows. The pipe with the diameter of 5mm had an n value of 0.827 . The following pipe with a diameter of 8mm had a value of 3.026 . Next, the diameter of 17mm had a value of -0.902 . Lastly, the pipe with the same diameter of the previous (17mm) but a non smooth (rough) interior had a n value of 1.422 . The values from each of the pipes align with what we expected. 1. Comparing between the head loss values computed using Darcy Weisbach’s equation and the corresponding measured values for various pipe sizes we see that the measured values have an average error of 22% compared to the calculated values. 2. Darcy Weisbach’s equation can also be utilized to obtain friction losses if fluid velocity and pipe dimensions are known as well as the head loss by manipulating the equation. 3. The Reynold’s number was significantly higher initially in every step as the flow rate was at its highest and as that decreased so did the number. 4. As the Reynold’s number decreased in each trial the measured head loss did as well. The pipe with the highest value of head loss was the 8mm diameter pipe. 5. Rough pipes will always have greater head loss than their smooth counterparts. Two trials within the experiment tested pipes of the same 17mm diameter, but one considered smooth and the other considered rough. The rough pipe experienced twice as much head

16 loss with the same flow rate into both. Conclusion This lab successfully demonstrated the characteristics of major head losses when fluid flows through pipes of various diameters and roughnesses experiencing laminar and turbulent flow. We observed that frictional head losses in pipes are not dependent on pressure of the fluid flows and the head loss is proportional to the length of the pipe and is inversely to the diameter of the pipe. Each pipe within the experiment had varying diameters and the values for head loss both calculated and measured reflect how as the diameter decreased the head loss values generally increased. It was apparent that turbulent flow is considered more so in rough pipes than in smooth pipes. With various ways to obtain head loss through equations and charts when compared to the measured values throughout the lab there is an average error margin of 22%. However, the ultimate purpose of the experiment was to observe and report the trends between head loss, pipe geometry, and friction factors. These trends were made very apparent while analyzing the data obtained and agree with our understanding of major losses in pipes.