ME 304 Mechanical Measurements Worksheet

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ME 304 Session # 4, Exp. #7 Venturi and Orifice Flow Meters Performed by: Team A John Brown Mary Power Mark Smith Report Evaluation: Submitted by: Mark Smith Date: 1/13/2011 Comments: Technical Content: (%) Writing (%) Combined Score: Background and Theory This laboratory investigates two types of flow meters that are commonly used in industry: Venturi flow meter and orifice flow meter. The two flow meters represent so called obstruction type flow meters, which measure flow rate indirectly by measuring the pressure loss across a calibrated obstruction. In this way, a more difficult (and more expensive) flow measurement is replaced with an easier (and less expensive) pressure measurement. This is especially true for flow in pipes of large diameter. The objective of this experiment is to measure the pressure drop P across the two flow meters at various flow rates Q and to determine the calibration curves Q(P). Principally, any calibrated obstruction could be used as a flow meter by measuring the pressure drop pm across the obstruction. The most common obstructions used for this purpose are Venturi nozzle, flow nozzle and orifice [1]. The flow rate through these devices can be determined from [2]: Q= CA2 2p m 1 − ( A2 / A1 ) 2  (Eq. 1) where A1 is the cross-sectional area before obstruction, A2 is the area at the smallest diameter, and C is an empirical discharge coefficient. 2 Experimental Setup and Procedure Schematic of the experimental setup used is presented in Figure 1. In the experiment, centrifugal pump 5 drew water from water tank 6 and pumped it along the path indicated with arrows. Valves 10, 11, 12, 16 and 44 remained fully open. Flow rate Q was adjusted to the desired value using valve 52 and flow meter 5a, and pressure drop across the orifice flow meter 7 and the Venturi flow meter 8 was measured with differential pressure gages (not shown). The measurements were collected at eight values of flow rate, ranging from 2 GPM to 12 GPM. 5a Figure 1 Schematic of the experimental setup used. 3 Experimental Results All experimental results are presented in Table A- 1 in the Appendix and the averaged values for each flow rate are listed in Table 1. All values in Table 1 were converted to SI units and are presented in Table 2. Table 1 Averaged Measured Values Q (GPM) 2 4 6 7 8 9 10 12 ΔPV (mbar) 1.0 7.4 18.1 22.9 31.0 39.2 48.3 57.9 Table 2 Averaged Measured Values in SI units ΔPO (mbar) 0.4 2.6 6.2 6.6 10.3 12.7 17.3 21.5 ΔPV (Pa) Q (m3/s) ΔPO (Pa) 0.000126 100 40 0.000252 740 260 0.000379 1810 620 0.000442 2290 660 0.000505 3100 1030 0.000568 3920 1270 0.000631 4830 1730 0.000757 5790 2150 The data of Table 2 was used to create Figure 2, which graphs two calibration curves: one for the Venturi flow meter Q(PV) and the other for the orifice flow meter Q(PO). 0.0008 0.0007 0.0005 3 Q (m /s) 0.0006 0.0004 Venturi 0.0003 Orifice 0.0002 0.0001 0 0 1000 2000 3000 4000 5000 6000 P V , P O (Pa) Figure 2 Calibration curves for the tested Venturi and orifice flow meters. The two solid lines in Figure 2 represent least square fits of the form Q = a P . 4 Discussion Examining the data of Figure 2 one can see that the measured flow rate is proportional to square root of the pressure drop in each device for both flow meters, which is consistent with Eq. (1). It can also been observed that the proportionality constant a for the orifice tested is about 100% higher than the corresponding constant for the Venturi flow meter. It means that at a given flow rate, the pressure difference in the orifice flow meter is about twice the corresponding pressure drop in the Venturi flow meter. This larger pressure drop may be beneficial for measuring low flow rates. The square root fits are not perfect and the measured data shows scatter from the trend lines, which is within 5% of the measurement value. The deviation does not show any obvious trend, suggesting random (rather than systematic) error present in measurements. Indeed, significant variation in both flow rate and pressure measurements was observed due to fluctuations in the flow. The random error could be reduced by taking more than three repeats at each flow rate setting. Conclusion Calibration curves were determined for two obstruction flow meters. It was shown that the flow rate through these devices is proportional to the square root of the measured pressure drop. The calibration allows for the flow rate to be measured indirectly by much easier measurement of the pressure drop. References [1] J.P. Holman, Experimental Methods for Engineers, 7th Edition, McGraw Hill, New York, 2001 [2] F. M. White, Fluid Mechanics, 5th edition, , McGraw Hill, 2003 5 Appendix Table A- 1 presents all experimental results taken during the laboratory. Table A- 1 All Experimental Results Taken Flow rate (gpm) P Venturi (mbar) P orifice (mbar) 2 4 6 7 8 9 10 12 Sample Calculations 6 Data Collected During ME-304 Lab Experiment: Date: Team: 1 Angled Plate Weight Flow rate position (GPM) (mm) 6 33,0 5,5 28,0 5 23,0 4,5 17,0 4 12,0 3,5 7,0 3 3,0 2,5 1,0 2 0,0 1,5 0,0 Flat Plate Weight Flow rate position (GPM) (mm) 6 49,0 5,5 39,0 5 33,0 4,5 28,0 4 19,0 3,5 12,0 3 9,0 2,5 8,0 2 7,0 1,5 5,0 Uncertainty Estimate Parameter Unit Uncertainty M (g) 1 g y l 2 (m/s ) (mm) (mm) 0 0,5 0,5 Conical Plate Weight Flow rate position (GPM) (mm) 6 63 5,5 57 5 43 4,5 36 4 28 3,5 21 3 16 2,5 11 2 6,0 1,5 3 Hemispherical Cup Weight Flow rate position (GPM) (mm) 6 81,0 5,5 73,0 5 56 4,5 44 4 35 3,5 24 3 17 2,5 13 2 7 1,5 4 Data Collected During ME-304 Lab Experiment: Date: Team: 1 gal/min 1m g M l d h ρ 1 = = = = = = = = 6,31E-05 1000 9,81 0,6 0,15 0,01 0,035 998 Angled Plate Flow rate Force F (Experimental) Mass flow rate Jet exit water velocity u (m3/s) 3,79E-04 3,47E-04 3,16E-04 2,84E-04 2,52E-04 2,21E-04 1,89E-04 1,58E-04 1,26E-04 9,47E-05 (N) 1,29 1,10 0,90 0,67 0,47 0,27 0,12 0,04 0,00 0,00 (kg/s) 0,38 0,35 0,31 0,28 0,25 0,22 0,19 0,16 0,13 0,09 (m/s) 4,82 4,42 4,02 3,62 3,21 2,81 2,41 2,01 1,61 1,21 Water velocity at vane u o (m/s) 4,75 4,34 3,93 3,52 3,10 2,69 2,26 1,83 1,38 0,87 Momentum at vane entrance L o (kg-m/s^2) 1,79 1,50 1,24 1,00 0,78 0,59 0,43 0,29 0,17 0,08 Force F (Theoretical) (N) 0,90 0,75 0,62 0,50 0,39 0,30 0,21 0,14 0,09 0,04 m3/s mm m/s^2 kg m m m kg/m^3 Flat Plate Percent Difference Flow rate Force F (Experimental) Mass flow rate Jet exit water velocity u [%] 44% 46% 46% 34% 20% -7% -45% -73% -100% -100% (m3/s) 3,79E-04 3,47E-04 3,16E-04 2,84E-04 2,52E-04 2,21E-04 1,89E-04 1,58E-04 1,26E-04 9,47E-05 (N) 1,92 1,53 1,29 1,10 0,75 0,47 0,35 0,31 0,27 0,20 (kg/s) 0,38 0,35 0,31 0,28 0,25 0,22 0,19 0,16 0,13 0,09 (m/s) 4,82 4,42 4,02 3,62 3,21 2,81 2,41 2,01 1,61 1,21 Water velocity at vane u o (m/s) 4,75 4,34 3,93 3,52 3,10 2,69 2,26 1,83 1,38 0,87 Theoretical Calculations 4,00 y = 2x Angled Plate 3,50 Flat Plate 3,00 y = 1.5x Hemispherical Cup 2,50 Force F (N) Conical Plate Linear (Angled Plate) 2,00 Linear (Flat Plate) y=x 1,50 Linear (Conical Plate) 1,00 Linear (Hemispherical Cup) y = 0,5x 0,50 0,00 0,00 0,50 1,00 1,50 2,00 0,00 0,00 0,50 1,00 Momentum in x-Direction 1,50 (kg-m/s2) 2,00 Conical Plate Momentum at vane entrance L o (kg-m/s^2) 1,79 1,50 1,24 1,00 0,78 0,59 0,43 0,29 0,17 0,08 Force F (Theoretical) Percent Difference Flow rate Force F (Experimental) Mass flow rate Jet exit water velocity u (N) 1,79 1,50 1,24 1,00 0,78 0,59 0,43 0,29 0,17 0,08 [%] 7% 2% 5% 10% -5% -20% -17% 9% 58% 137% (m3/s) 3,79E-04 3,47E-04 3,16E-04 2,84E-04 2,52E-04 2,21E-04 1,89E-04 1,58E-04 1,26E-04 9,47E-05 (N) 2,47 2,24 1,69 1,41 1,10 0,82 0,63 0,43 0,24 0,12 (kg/s) 0,38 0,35 0,31 0,28 0,25 0,22 0,19 0,16 0,13 0,09 (m/s) 4,82 4,42 4,02 3,62 3,21 2,81 2,41 2,01 1,61 1,21 Angled Plate Flat Plate Conical Plate Hemispherical Cup Linear (Angled Plate) Linear (Flat Plate) Linear (Conical Plate) Linear (Hemispherical Cup) onical Plate He Water velocity at vane u o (m/s) 4,75 4,34 3,93 3,52 3,10 2,69 2,26 1,83 1,38 0,87 Momentum at vane entrance L o (kg-m/s^2) 1,79 1,50 1,24 1,00 0,78 0,59 0,43 0,29 0,17 0,08 Force F (Theoretical) Percent Difference Flow rate Force F (Experimental) (N) 2,69 2,25 1,86 1,50 1,17 0,89 0,64 0,43 0,26 0,12 [%] -8% -1% -9% -6% -6% -7% -2% 0% -9% -5% (m3/s) 3,79E-04 3,47E-04 3,16E-04 2,84E-04 2,52E-04 2,21E-04 1,89E-04 1,58E-04 1,26E-04 9,47E-05 (N) 3,18 2,86 2,20 1,73 1,37 0,94 0,67 0,51 0,27 0,16 Hemispherical Cup Mass flow rate Jet exit water velocity u Water velocity at vane u o Momentum at vane entrance L o Force F (Theoretical) Percent Difference (kg/s) 0,38 0,35 0,31 0,28 0,25 0,22 0,19 0,16 0,13 0,09 (m/s) 4,82 4,42 4,02 3,62 3,21 2,81 2,41 2,01 1,61 1,21 (m/s) 4,75 4,34 3,93 3,52 3,10 2,69 2,26 1,83 1,38 0,87 (kg-m/s^2) 1,79 1,50 1,24 1,00 0,78 0,59 0,43 0,29 0,17 0,08 (N) 3,59 3,01 2,48 1,99 1,56 1,18 0,86 0,58 0,35 0,17 [%] -11% -5% -11% -13% -12% -20% -22% -11% -21% -5% Experimental Results 3,50 y = 1,8381x - 0,0591 3,00 y = 1,4055x + 0,0071 2,50 Angled Plate Flat Plate y = 1,0298x + 0,0088 Force F (N) 2,00 Conical Plate Hemispherical Cup 1,50 Linear (Angled Plate) Linear (Flat Plate) 1,00 y = 0,8214x - 0,1606 Linear (Hemispherical Cup) 0,50 0,00 0,00 -0,50 Linear (Conical Plate) 0,20 0,40 0,60 0,80 1,00 1,20 Momentum in x-Direction (kg-m/s2) 1,40 1,60 1,80 2,00 Data Collected During ME-304 Lab Experiment: Date: Team: 1 1/17/2020 D Angled Plate Flow rate Weight position Force F (Experimental) Force Uncetainty Force F (Theoretical) Percent Difference (GPM) 6 5,5 5 4,5 4 3,5 3 2,5 2 1,5 (mm) 33,0 28,0 23,0 17,0 12,0 7,0 3,0 1,0 0,0 0,0 (N) 1,29 (N) 0,02 (N) 0,90 [%] 44% Uncertainty Estimate Parameter Unit Uncertainty aw/x M (g) 1 0,002 0 varies -0,003 g y l 2 (m/s ) (mm) (mm) 0 0,5 0,5 Flat Plate Flow rate Weight position Force F (Experimental) Force Uncetainty Force F (Theoretical) Percent Difference (GPM) 6 5,5 5 4,5 4 3,5 3 2,5 2 1,5 (mm) 49,0 39,0 33,0 28,0 19,0 12,0 9,0 8,0 7,0 5,0 (N) 1,92 (N) 0,02 (N) 1,79 [%] 7% Flow rate (GPM) 6 5,5 Conical Plate Hemisph Weight position Force F (Experimental) Force Uncetainty Force F (Theoretical) Percent Difference Flow rate Weight position (mm) 65,5 33 (N) 2,47 (N) 0,02 (N) 2,69 [%] -8% (GPM) 6 (mm) 80,0 Hemispherical Cup Force F (Experimental) Force Uncetainty (N) 3,18 (N) 0,02 Percent Force F Differenc (Theoretical) e (N) [%] 3,59 -11% ME304 Mechanical Measurements II Experiment 1: Impact of a Liquid Jet Objective To investigate the impact force from a water jet striking vanes of various shapes at various flow rates. Theoretical Background When a vane obstructs a liquid jet, it reduces its linear momentum. Per Newton’s second law, the rate of change of this momentum is equal to the force exerted on the fluid by the vane. Consider a vane, which is symmetrical about the xaxis, as shown in Figure1. A jet of fluid flowing at the  (kg/s) along the x -axis with the mass flow rate of m velocity u0 (m/s) strikes the vane, is deflected and leaves the vane with the velocity u1 (m/s) directed at an angle  to the x-axis. Changes in elevation from the striking the vane to leaving it are neglected. x  F The rate of x-momentum entering the system is:  u0 L0 = m (kg m/s2 ) while the rate of x-momentum leaving the system is:  u1 cos  L1 = m u0 Figure 1 (kg m/s2 ) The force on the vane in the x-direction is equal to the rate of change of the x-momentum:  (u0 - u1 cos  ) F= m (N) Assuming that the jet velocity does not change so that u0 = u1, one can write:  u0 (1 – cos  ) F= m (N) The values of angle and the predicted values of the force for the four vanes used in this experiment are listed in Table 1. Table 1: Theoretical values of force F for four vanes used in this lab. Shape Angled Plate Flat Plate Conical Plate Cup Experiment description  60o 90o 120o 180o F  u0 0.5 m  u0 m  u0 1.5 m  u0 2 m u1 Water is pumped from a water tank through a regulating valve and a flow meter, then discharged vertically upwards through a nozzle and striking a vane being tested. The vane is supported by a balance system, which allows for the vertical force acting on the vane to be measured indirectly by measuring the position of the balance weight. Thus the dependence of the impact force on the water flow rate through the jet can be established. Experimental Goal Experimentally determine the impact force F as a function of the rate of linear momentum at the  u0 for four vanes (hemispherical cup, conical plate, angled plate and flat vane entrance L0 = m plate) and compare the findings with the simple theoretical model presented on the first page. Useful Equations y l 1. Force of the water jet: F = Mg 2. Mass flow rate: m =  V V u= 2 d / 4 3. Water velocity at jet exit: 4. Water velocity at vane: u0 = u 2 − 2 gh 5. Rate of momentum at vane entrance:  u0 L0 = m Where M g y l  d V h = mass of the balance weight = gravitational acceleration = balance weight position = distance from the vane axis to the lever pivot (0.15 m) = water density = nozzle diameter = volumetric flow rate = Height of vane above tip of nozzle Presentation of Results Based on the direct measurements recorded, calculate the force F and the rate of momentum in  u0 at the vane entrance. the vertical direction L0 = m Compare the experimental curves with the simple theoretical model presented on Page 1. Discuss possible reasons for the discrepancy between the experimental and theoretical curves. Consider both the sources of experimental error and the applicability of the theoretical model. References (1) J.P. Holman, Experimental Methods for Engineers, 7th Edition, McGraw Hill, New York, 2001 (2) Instructions of “Impact of a jet” by TQ Intelligent Solutions for Education and Training
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Experiment 1

Impact of a Liquid Jet
Discussion
The force and the rate of change in momentum are the foundation of the
discussion of the experiment. The experimental results show that Force F (N) is directly
proportional to change in momentum in the x-Direction (kg-m/s2). From, newton’s
second law, the rate of change of momentum is equal to the force exerted on the fluid by
the vane. We can see that t...


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