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Flow Rate measurement
Ethan Bates, Group One, 10/24/18
Team members: Erick Alvarado, Catherine Dorman, Adrian EstorgaThis experiment used a vacuum attached to a Venturi meter. The flow meter has a rapidly decreasing throat. This created a difference in pressure flow. This experiment used an auto transformer to control the power output on the vacuum. Data was taken in controlled transformer increments and random transformer increments. The upstream pressure, throat pressure, and motor output were recorded. The Bernoulli principle was used to calculate the volumetric flow rate at the different data points. The Bernoulli principle states that as the velocity of air increases, the cross-sectional area of the system must decrease. There is a direct correlation between the pressure transducer and differential pressure.
Nomenclature

Introduction
This experiment uses the Venturi meter in Figure 1. The air will be forced through the passage way using a vacuum. The velocity will increase as the cross-sectional area of the meter decreases. A Venturi meter measures mass/volumetric flow rate 2. The venturi meter is a converging conical inlet with a cylindrical throat and a diverging recovery cone.

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Figure 1. Venturi Flow Meter Schematic 1
The Bernoulli Equation is a statement of a conservation of energy. It is used to calculate the change in volumetric flow rate as the cross-sectional area of the Venturi meter decreases 3. It is assumed that there is no air loss in the meter to use the Bernoulli equation. However, in the real world, when air is flowing, into a rapidly reducing cross sectional area, it will generate a vena contracta effect 4. When analyzing the Venturi Flow Meter Schematic in Figure 1, a relationship can be mathematically written as shown in Equation 2. With Pair= 0.00238, slugs/ft3.P1-P2=12Pair(V22-V12)(1)
A2 is the cross-sectional area of the flow at the throat of the valve, and V is the flow velocity. ? is the ratio of the throat and upstream diameters. To address the effect of air loss, the Venturi coefficient (Cv) is introduced to the equation, Cv.5. This is to equal 0.8159. Equation (5) is the Bernoulli Equation, which will be used to calculate the volumetric flow rate for the experiment. Q=CvA22?PPair1-?412(2)
Experimental Setup and Procedure
The power strip and computer were turned on. The PC was logged into. The pressure transducer and process meter were turned on, using the two red switched on the analog pressure gauge board. The process meter displayed a value of 1.039 Volts. The Set up should be as shown in Figure 2.

Figure 2. Flow Rate Measurement Experimental Setup 1
The multimeter was turned on to display AC Voltage. The autotransformer was turned on and adjusted to 45%. On the computer desktop, the “Vacuum Experiment” VI was loaded. The Screen looked like Figure 3.

Figure 3. Vacuum Experiment VI Interface.

The Accelerometer is connected to the vacuum, which flows through the Venturi Flowmeter. This air pressure flows to a pressure gage and a differential pressure transducer. This is data is read by a DAQ and analyzed on a PC in LabVIEW. The data Flow Diagram is shown in Figure 4.

Figure 4. Data Flow Diagram 1There were two sets of experiments preformed. One in a randomly sampled transformer setting, and one in an incremental transformer setting. Once the experiment was started, it was continuously preformed without stopping, in order to get an accurate reading. Table 1 and 2 show what data was sampled incrementally, and which data was sampled randomly.

Table 1.Randomly Sampled Auto Transformer Settings
Randomly Sampled Autotransformer Settings (%)
50 85 80 65 45 70 75 55 60 75 80 70 60 50 55 65 85 45
Table 2.Incrementally Sampled Auto Transformer Settings
Incrementally Sampled Autotransformer Settings (%)
45 50 55 60 65 70 75 80 85 85 80 75 70 65 60 55 50 45
The Data was recorded into a text file. In that text file, the differential pressure transducer reading, the auto transformer setting, the upstream, throat pressure, and motor output. The VI was closed and all equipment was shut down.

Figure 5. Data File 1
Experimental Results and Discussion
The data collected in steady and random increments in Figures 6 and 7 show a steady increase and decrease when the transducer output voltage is adjusted accordingly. Tables 3 and 4 in the appendix show that correlation. Hysteresis error was experienced, due to the pressure being different when the transducer was shifted to the same output voltage again.

Figure 6. Transducer Calibration for Increment Data

Figure 7. Transducer Calibration for Random Data
The sensitivity for Figure 6 was 0.0813 inH2O/V and the sensitivity for Figure 7 was 0.0797 inH2O/V. The response of the pressure transducer to differential pressure is linear. As the Differential Pressure incrementally increased, the Volumetric flow rate increased roughly by a power of 2. This is to be expected due to the Bernoulli equation.

Figure 8. Flow Rate vs. Differential Pressure for Increment Data

Figure 9. Flow Rate vs. Differential Pressure for Increment Data
To calculate mass flow rate, versus the volumetric flow rate, divide the volumetric flow rate by the density. The environment will affect density due to things such as the purity of the substance, for example moisture could be in the air. The variation in the volumetric flow rate with the voltage is directly proportional. The Data in Tables 3 and 4 reflect how the voltage across the vacuum’s motor is related to the volumetric flow rate. Flow obstruction meters like the Venturi meter, are useful in measuring flow rate, but require calculations and assumptions in the Bernoulli equation. A velocity flow meter would serve as an alternative in future flow experiments, as it measures the volumetric flow in real time without calculations.
Conclusions
The Venturi flow meter accurately depicts the Bernoulli equation. The Bernoulli equation, with the integrated Venturi coefficient, states that as a cross-sectional area of a system experiencing flow decreases, the pressure and volumetric flow rate will increase. The voltage output of the vacuum was directly related to the differential pressure shift. Hysteresis error was experienced due to the shift in the values when they were recorded for a second time in the incremental and random data. While using the Venturi flow meter and calculations using the Bernoulli equation allowed for the data to me analyzed a flow rate, an easier method would’ve been to use a velocity flow meter.
References
1″Flow Rate Measurement,” Mechanical Methods and Measurements Laboratory Manual, Department of Mechanical and Aerospace Engineering, University of Texas at Arlington, Arlington, Texas, 2018.

2Widden, M., “Flow measurement: pitot tube, venturi meter and orifice meter,” Fluid Mechanics, 1996, pp. 201–239. Cited 10/31/2018.3Irimia R, Gottschling M (2016) Taxonomic revision of Rochefortia Sw. (Ehretiaceae, Boraginales). Biodiversity Data Journal 4: e7720. https://doi.org/10.3897/BDJ.4.e7720,” Bernoulli’s Equation Cited 10/31/2018.
4 Mcdonald, Kirk T. “Vena Contracta.” puhep1.Princeton.edu, 25 Feb. 2004, puhep1.princeton .edu/~ kirkmcd/ examples/ vena_contracta.pdf. Cited 10/31/2018.

5Harris, M.J Reader. Discharge Coefficients of Venturi Tubes with Standard and Non-Standard Convergent Angles. Artigo%20Venturi.pdf. Cited 10/31/2018.

Appendix
Motor Output V ?P (inH2O) Q (Ft3/min)
70.93 15.1 28.52726
119.7 35.6 43.80227
113.78 33 42.17242
92.53 22.8 35.05411
66.5 0.2 3.283119
99.56 26.1 37.50523
105.59 27.8 38.7074
78.02 16.9 30.1797
84.92 21.1 33.72196
106.25 28.6 39.26039
112.87 32.1 41.59337
92.21 26.1 37.50523
85.11 20.4 33.15787
71.52 15.2 28.62156
77.89 18 31.1464
91.78 22.8 35.05411
119.72 35.6 43.80227
66.23 0.1 2.321515
Table 3. Random Data Points
Table 4. Incremental Data Points
Motor Output V ?P (inH2O) Q (Ft3/min)
66.44 1.1 7.70
66.44 1.1 7.70
70.98 15.5 28.90
77.69 18 31.15
84.43 21.2 33.80
92.09 24.4 36.26
98.6 26.1 37.51
106.43 30.7 40.68
113.05 32.1 41.59
120.11 35.1 43.49
120.2 35.6 43.80
113.88 33 42.17
106.44 28.6 39.26
98.94 26.1 37.51
92.3 22.9 35.13
84.6 19.1 32.08
78.12 18 31.15
72.23 16.1 29.46
67.2 1.1 7.70  