Worksheet - Pressure Losses in Flow

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Feb 20, 2024

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Pressure Losses in Flow Worksheet This worksheet supports Section 3 in the general Lab Manual. I. Head Losses in Pipe and Fittings 1. Determine the transducer voltage bias average value from the data file. Include the 95% CI for this value. 2. Record the following data: Value Precision L small pipe 39 7/16 1/32 L large pipe 39 3/8 1/32 L rough pipe 39 3/8 1/32 Each team member should make an independent measurement of the diameter for each of the three pipes. Record the readings and compute the 95% confidence intervals. Also note the manufacturer’s stated accuracy (bias) for the calipers. Reading 1 Reading 2 Reading 3 Reading 4 95% CI Mfgr Accuracy D small pipe .427 .425 .424 .429 .42625 +/– .004 0.001 D Large pipe .670 .672 .674 .674 .6725 +/–. 003 0.001 D rough pipe .625 .628 .627 .627 .62675 +/– .002 0.001 3. Complete the first four columns of Table 1 below. Use recorded data and determine the average, standard deviation of the voltage signals for each measurement, and 95% CI for each measurement. 1. Third from top diameter length of pipe 2. Largest length of smooth pipe 3. Length of roughened pipe 4. 90 degree elbow (brass fitting after valve section) 5. 90 degree long radius (tubing in top right) ME 460 1 Pressure Losses in Flow V o = 2.6241323+/– 2.899*10^-5
From the data file, find the average value, standard deviation and CI for each fill in Table. ME 460 2 Pressure Losses in Flow
Table 1: Flow rate and pressure transducer voltage measurement results for various fittings and pipe configurations. Pipe/Fitting Flow Rate (GPM) Avg Voltage (Volts) St Dev (Volts) 95% CI (Volts) Pressure Loss (PSID) 3 rd Tube from Top 9 6.2056 .0184 0.0038 6.7709 8 5.5664 .012381 0.0029 6.4012 7 4.902511 .009200 0.0032 5.9152 6 4.39717 .012705 0.0127 5.4469 5 3.922362 .01275 0.0034 4.8970 Largest Smooth Pipe 12 3.111849 0.01151 0.0026 3.5704 10 3.000707 0.05242 0.0098 3.3327 8 2.852248 0.0186008 0.0038 2.9861 6 2.708298 0.01128335 0.0029 2.6139 4 2.60758 0.01128543 0.0030 2.3290 Rough Pipe 11 5.1072575 0.03308824 0.0090 6.0786 9 4.2729534 0.03160118 0.0093 5.3148 7 3.5579196 0.03638409 0.0088 4.3753 5 3.1157204 0.03777299 0.0101 3.5784 3 2.7149301 0.04565835 0.0123 2.6319 90 deg elbow 11 3.2988303 0.01289019 0.0034 3.9343 90 deg long radius 11 2.6938629 0.01049060 0.0027 2.5743 ME 460 3 Pressure Losses in Flow
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4. Pressure loss calculation: Use equation editor to input the relevant equation used to convert voltage signal into pressure loss. Convert voltages in the table above and complete the table with the pressure differential for each case. Ideal PSI= [ R ( I 4 mA ) ( psid Range R 16 mA ) ] −[ ( V V 0 ) ( psid Range ∆Vmax ) ] 5. Calculate the maximum measurement precision error (95% CI) for measured pressure differential in the table above. Report your value below in green font. Compare this value to the manufacturer’s bias for the pressure transducer. Do you need to consider the precision error in uncertainty propagation? Discuss. P MAX =6.7709+.0127(max CI)=6.7836 The pressure transducer has an accuracy of .25%. This accuracy percentage would result in a range of +- .01692725. The 95% confidence interval found shows is well within the range described by the manufacturer. 6. Use the equation editor to document in green font the equations used to calculate 1) friction factor f D , and 2) loss coefficient, K , from the measured parameters ( L, D, GPM, PSI ). Include units to demonstrate that f D and K are indeed unitless. K = h f ( 2 g c ) V 2 ¿ ¿ s 2 ¿ 2 s 2 f D = h f ( D )( 2 g c ) L V 2 ¿ ¿ ¿ s 2 ¿ ¿ 2 s 2 Use your equations to compute the nominal values for f D and K and insert them in the columns of Table 2. 7. Error propagation calculations: Use equation editor to input the relevant equations used to propagate uncertainty in length, diameter, flow rate, and pressure drop into the calculated values for f D and K . Note: For the pressure transducer (Omega PX2300-25DI the manufacturer states the accuracy is 0.25% FS. For the flow meter (Omega FL-75D Rotameter), the stated accuracy is 3% FS. ME 460 4 Pressure Losses in Flow
U Δ P = ¿ Measure∆ P 2 + .25 2 Measurement = 10/8 * (V_V0) U D = ¿ .0005 U L = ¿ .03125 U GPM = ¿ Measured Flow rate 2 + .03 2 U f D = ¿ ¿¿ U K = ¿ ¿¿ Input the results of these calculations in Table 2. ME 460 5 Pressure Losses in Flow
Table 2 - Friction Factor and Loss Coefficient Results Pipe Flow Rate (GPM) Friction Factor, f D Uncertainty, U f 3 rd Tube from Top 9 0.0262 0.0005 8 0.0314 0.0006 7 0.0379 0.0008 6 0.0475 0.0010 5 0.0615 0.0012 Largest Smooth Pipe 12 0.0626 0.0018 10 0.0842 0.0024 8 0.1179 0.0034 6 0.1834 0.0052 4 0.3677 0.0105 Rough Pipe 11 0.1099 0.0032 9 0.1435 0.0042 7 0.1953 0.0058 5 0.3130 0.0092 3 0.6395 0.0188 0.0262 0.0005 Fitting Loss Coefficient, K Uncertainty, U K 90 deg elbow 11 2.406544 0.292145 90 deg long radius 11 1.459633 0.179879 ME 460 6 Pressure Losses in Flow
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Prepare plots showing the variation of f D with Reynolds number. Show measured values as data points (with no lines) and include a dashed line with corresponding theoretical values from the Swamee-Jain relation. What value did you determine for the absolute roughness of the roughened pipe? = .0012 feet Discuss your results and uncertainties. This Lab provided a very easy to understand demonstration of the principles of head loss. However it appears that some of the data shown in the Reynolds number vs friction factor graph is a little off, as shown by two of the curves not following the line as expected. Aside from this instance, the results are as expected with changes accruing as expected from change in flow rate, diameter, and roughness. The largest source of error expected would be from reading the flow rate, followed by possible rounding errors when making calculations. ME 460 7 Pressure Losses in Flow