DL Worksheet - Pressure and Flow Measurement--Tevin 2 Edit

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Flow Measurement Worksheet B. Low pressure flow measurement, including manometer and pitot tube B.I Pitot tube average velocity measurement. 1. Use the pitot tube and attached differential pressure gage to measure velocity in the center of the duct. Have each person in your group take one reading with the help of another group member to monitor the pressure gage display. Take measurements as shown in Figure 2.2 of the lab procedure and record in Table 1. After calculating the average differential pressure reading, use Eq. 2.3 in lab manual to convert the pressure readings to velocity and record in Table 1. Use the tube diameter to compute the volumetric flow rate and air density to calculate the mass flow rate through the tube. Table 1: Raw pitot tube measurements and calculated average velocity for each fan speed. Fan Speed (%) ΔP 1 (in H 2 O) ΔP 2 (in H 2 O) ΔP 3 (in H 2 O) ΔP 4 (in H 2 O) ΔP avg (in H 2 O) V avg (ft/s) ? ̇ 𝒂𝒗? (ft 3 /s) ?̇ 𝒂𝒗? (lbm/s) 100% 0.135 0.140 0.142 0.146 0.141 32.9 1.49 0.0116 50% 0.028 0.027 0.028 0.026 0.027 16.5 0.745 0.0058 2. Use the vane anemometer to acquire for comparison to calculated velocity and mass flow rate from the pitot tube measurements. Use the tube diameter and air density to calculate the flow rate through the tube based on the anemometer results. Record the results in Table 2. Table 2: Anemometer results and average velocity for each fan speed. Fan Speed (%) V 1 (ft/min) V 1 (ft/min) V 1 (ft/min) V 1 (ft/min) V avg (ft/min) ? ̇ (ft 3 /s) ?̇ 𝒂𝒗? (lbm/s) 100% 1755 1763 1704 1781 1751 40.13 6.35 50% 877 836 869 844 857 20.1 3.18 3. Discuss the uncertainty for both the pitot tube and te anemometer measurement techniques. Despite each device does have associated uncertainties that have an effect on the experimental results, it is possible that measurement with the pitot tube were in a unique spot at every test point. It is also likely that the anemometer wasn’t perfectly l ined up with the tube when it was being used; which allowed air to escape and thus effect the velocity measurements.

B.II Obstruction Meter Mass Flow Measurement 1. Measure the pressure difference between upstream port and vena contracta as well as between the upstream port and downstream port for the flow nozzle, orifice and venturi. Note the reading on the manometer when there is no differential pressure applied: You will need to subtract this offset reading from all of your subsequent differential pressure observations. Make measurements at different fan speeds and record results in Table 3. Table 3: Raw pressure differential measurements for each obstruction flow device. Flow Nozzle Orifice Plate Venturi Meter Fan Speed (%) P 1 - P 2 (in H 2 O) P 1 – P 3 (in H 2 O) P 3 – P 4 (in H 2 O) P 3 – P 5 (in H 2 O) P 5 – P 6 (in H 2 O) P 5 – P atm (in H 2 O) 100% 1.43 0.88 0.66 0.30 1.52 0.44 75% 0.78 0.48 0.34 0.16 0.89 0.26 50% 0.30 0.18 0.12 0.06 0.34 0.12 2. Compare the pressure change for each flow device. Consider that the same mass flow is passing through each device and make observations about relative differences in behavior of the pressure differential at the vena contracta and the permanent pressure loss. Fan Speed ∆P Venturi ∆P Orifice ∆P Nozzle 100% 5.4913 1.7356 2.7718 75% 2.8734 0.9827 1.5482 50% 0.9827 0.1966 0.5026 3. Measure the inner diameter of the duct. D duct = 2.81 𝑖𝑛𝑐ℎ?𝑠 4. Consider that the venturi discharge coefficient is the most accurate, use this value to calculate the flow velocity in the full duct based on the measured upstream to vena contracta differential pressures (see procedure for instructions regarding C d values). Then using this ____0_______in H 2 O

velocity calculate the discharge coefficients of the nozzle and orifice. The obstruction flow meter geometry data are provided in Figure 2.2 of the lab manual. 5. Use equation editor to input the relevant equations used to convert pressure drop to velocity for the venturi and then discharge coefficient from velocity and pressure differential. Include appropriate units as well as description of variables. Input the results of these calculations in Error propagation calculations: Use equation editor to input the relevant equations used to propagate bias uncertainty of the pressure differential measurements (Dwyer Series 250-AF inclined manometer, Range of 4” H 2 O with 0.02 ” divisions. and accuracy of 1% FS) into uncertainty in velocity. Note that, just like a ruler, the overall uncertainty is the combination of the accuracy (FS uncertainty) and the precision (one-half the minimum measurable division) (i.e. ? Δ𝑃 = √ (1%𝐹𝑆) 2 + (0.01"𝐻 2 ?) 2 . Finally, propagate velocity uncertainty to overall uncertainty in discharge coefficient, C d . Input the results of these calculations in Error! Not a valid bookmark self-reference. . ? ∆? = 0.01 × (4 𝑖𝑛 𝐻 2 ? ) + 0.01 𝑖𝑛 𝐻 2 ? = 0.05 𝑖𝑛 𝐻 2 ≅ 0.2601 𝑝𝑠? Table 6. Record your response here in green font. 6. Error propagation calculations: Use equation editor to input the relevant equations used to propagate bias uncertainty of the pressure differential measurements (Dwyer Series 250-AF inclined manometer, Range of 4” H 2 O with 0.02 ” divisions. and accuracy of 1% FS) into uncertainty in velocity. Note that, just like a ruler, the overall uncertainty is the combination of the accuracy (FS uncertainty) and the precision (one-half the minimum measurable division) (i.e. ? Δ𝑃 = √ (1%𝐹𝑆) 2 + (0.01"𝐻 2 ?) 2 . Finally, propagate velocity uncertainty to overall uncertainty in discharge coefficient, C d . Input the results of these calculations in Error! Not a valid bookmark self-reference. . ? ∆? = 0.01 × (4 𝑖𝑛 𝐻 2 ? ) + 0.01 𝑖𝑛 𝐻 2 ? = 0.05 𝑖𝑛 𝐻 2 ≅ 0.2601 𝑝𝑠? ? ? = 1 2 ? 2 ∆ ? × ? ∆ ? ? ? ? = √ ( 𝜕 ? ? 𝜕 ∆ ? × ? ∆ ? ) 2 + ( 𝜕 ? ? 𝜕 ? × ? ? ) 2

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Table 4: Calculated main duct flow velocity based on C d for venturi and then C d for the nozzle and orifice including uncertainty results V= √ 2∆𝑃 𝜌𝑠 g c = Venturi Meter Flow Nozzle Orifice Plate Fan Speed (%) 𝐕 ?????𝐫𝐢 (ft/s) ? 𝐕,?????𝐫𝐢 (ft/s) 𝑪 ?,??𝒛𝒛?? ? 𝑪?,??𝒛𝒛?? 𝑪 ?,?𝒓𝒊?𝒊?? ? 𝑪?,?𝒓𝒊?𝒊?? 100% 68.3 1.43 0.863 0.0624 0.558 0.087 75% 50.7 2.08 0.848 0.103 0.52 0.186 50% 28.6 3.19 0.852 0.318 0.53 1.14 7. Generate a plot of C d as a function of Reynolds number for both the nozzle and orifice plate. The plot should include both your measurements and those from the table in the lab manual. ? ? = 1 2 ? 2 ∆ ? × ? ∆ ? ? ? ? = √ ( 𝜕 ? ? 𝜕 ∆ ? × ? ∆ ? ) 2 + ( 𝜕 ? ? 𝜕 ? × ? ? ) 2

Figure 1 Plot showing Reynolds Number Versus Discharge Coefficient Cd 8. Discuss any trends observed in the agreement between calculated C d values for the nozzle and orifice compared to the Tabulated values in the Lab Manual. As seen in figure above, the calculated flow nozzle, Cd values, seem to increase as the Reynolds number increases. This in agreement with the tabulated flow nozzle values presented in the lab manual. In comparison, the calculated orifice plate Cd values seem to decrease as the Reynolds number decreases, in the same way that the tabulated orifice plate values decrease. 9. Recall that the permanent pressure drop through fitting can be estimated using a loss coefficient K and known the flow velocity by the head loss relationship equations as ℎ 𝑓 = Δ? ρ = 𝐾 ? 2 2 Considering the permanent pressure drop measurements and the velocity in the duct calculate the loss coefficient, K, for each device. Assuming the venturi C d is likely the most accurate, use its velocity and the total pressure drop for each obstruction meter to find K for each device (i.e. use the same velocity for each device when finding K). Use equation editor to input the relevant equations used to convert pressure drop to loss coefficient. Include appropriate units as well as description of variables. Input the results of these calculations in Table 5. Record your response here in green font. 0 0.2 0.4 0.6 0.8 1 1.2 0 5000000 10000000 15000000 Discharge Coefficient Reynolds Number Flow Nozzle Orifice Plate Flow Discharge Orifice Discharge

10. Error propagation calculations: Use equation editor to input the relevant equations used to propagate bias uncertainty of the pressure differential measurements (Dwyer Series 250-AF inclined manometer, Range of 4” H 2 O with 0.01” divisions. and accuracy of 1% FS ) into uncertainty in velocity. Finally, propagate velocity uncertainty to overall uncertainty in loss coefficient, K. Input the results of these calculations in Table 5. R ? ∆? = 0.01 × (4 𝑖𝑛 𝐻 2 ? ) + 0.01 𝑖𝑛 𝐻 2 ? = 0.05 𝑖𝑛 𝐻 2 ≅ 0.2601 𝑝𝑠? Table 5: Calculated loss coefficient for each obstruction flow device including uncertainty results. Flow Nozzle Orifice Plate Venturi Meter Fan Speed (%) 𝐊 ??𝐳𝐳𝐥? ? 𝐊,??𝐳𝐳𝐥? 𝐊 ?𝐫𝐢?𝐢𝐜? ? 𝐊,?𝐫𝐢?𝐢𝐜? 𝐊 ?????𝐫𝐢 ? 𝐊,?????𝐫𝐢 100% 0.473 0.0469 0.308 0.0348 0.857 0.0488 75% 0.484 0.0863 0.311 0.0774 0.857 0.1097 50% 0.417 0.218 0.173 0.198 0.857 0.288 11. Discuss any trends observed in the calculated loss coefficients for the three devices as the fan speed changes. As water is moving through the entire duct, the most water loss appears when the fan speed is at 75%, instead of the assumed 100%. The loss coefficient decreases as it moves through the length of the pipe until it reaches the venturi meter . 12. Describe the conceptual difference between Cd and K for obstruction flow meter device. The loss coefficient measures how the pipe can affect the flow of water moving through the pipe. This can be affected by many factors, such as roughness of the pipe, shape of the pipe, and material of the pipe. Discharge coefficient measures the effect certain obstacles ? ? = 1 2 ? 2 ∆ ? × ? ∆ ? ? 𝐾 = √ ( 𝜕 𝐾 𝜕 × ? ∆ ? ) 2 + ( 𝜕 𝐾 𝜕 × ? ? ) 2

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