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final draft discharge coefficients report

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Page 1 of 8 Katie Love BSEN 3310 Team 5 15 November 2017 DISCHARGE COEFFICIENTS FOR VENTURI AND ORIFICE FLOW METERS ABSTRACT Theoretical discharge coefficients for orifice and Venturi flow meters can be calculated using certain equations, but those equations have a limited use range. Our objectives were to compare experimental and theoretical discharge coefficients
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  Page 1  of 8   Katie Love   BSEN 3310   Team 5 15 November 2017   D ISCHARGE C OEFFICIENTS FOR V ENTURI AND O RIFICE F LOW M ETERS   A BSTRACT   Theoretical discharge coefficients for orifice and Venturi flow meters can be calculated using certain equations, but those equations have a limited use range. Our objectives were to compare experimental and theoretical discharge coefficients for orifice and Venturi flow meters and measure energy losses in a flow due to passage through Venturi, orifice, and rotameter flow meters. Experimental discharge coefficients were determined through use of an equation that relates slope of a trendline from a graph of flow rate versus square root of pressure drop to the discharge coefficient. These estimated discharge coefficients were compared to discharge coefficients calculated from theoretical equations that are only applicable to data with a certain β  and Reynolds number range. Flow rates from a dump valve and a rotameter were also compared in this experiment, and percent difference was determined. Percent difference was less than 22% for all flow rates, but did not follow a particular trend.  Energy losses were highest across the rotameter, followed by the orifice meter (whose losses increased with flow rate), and the Venturi meter with the lowest energy loss. The percent difference between the theoretical and experimental orifice discharge coefficients was 16.9%. The percent difference between the theoretical and experimental Venturi discharge coefficients was 52%. This was due to the error  Page 2  of 8   in calculating the experimental discharge coefficient that resulted in it being greater than 1. eywor s   Discharge coefficient, Energy loss, Orifice flow meter, Pressure drop, Rotameter, Venturi flow meter. I NTRODUCTION   There are several methods by which to measure flow rate. Flow rate can be calculated by measuring the pressure drop in a pipe due to a constriction or obstruction of flow (Cengel and Cimbala, 2014). Three flow meters were tested for this experiment: Venturi, orifice, and rotameter. Venturi and orifice flow meters are types of obstruction flow meters. Venturi meters consist of a pipe that gradually narrows to a minimum diameter and then widens again to prevent the fluid from swirling around (losing energy), such as a flow typically does on the exit side of an orifice meter. Flow meters, as fittings, have losses associated with them. The total loss for the Venturi and orifice meters can be expressed as the discharge coefficient. The discharge coefficient can be calculated using experimental or theoretical equations. Energy losses in J/kg can be calculated from pressure drop across each flow meter. Energy losses for each flow meter may be constant or increase with flow rate. Team 5 will use an Edibon Flow Meter Demonstration Module connected to an Edibon Hydraulic Bench to measure flow rate and  pressure drop across the three flow meters. Flow rates from the rotameter and the hydraulics  bench dump valve will be compared, as well as theoretical and experimental discharge coefficients for the orifice and Venturi meters. Energy losses as a function of flow rate for each meter fitting will be analyzed as well.   O BJECTIVES   The objectives for this experiment were (1) to estimate the discharge coefficients for Venturi and orifice flow meters and (2) to measure energy losses due to flow through Venturi, orifice, and rotameter flow meters.    Page 3  of 8   M ETHODS AND M ATERIALS   Team 5 used an Edibon FME18 Flow Meter Demonstration Module attached to an Edibon Hydraulic Bench for this experiment. The flow meter module had a Venturi, rotameter, and orifice flow meter. The flow meter module had manometric tubes attached to measure the  pressure difference across the flow meters. Six data readings were taken between flow rates of 200 and 1250 L/hr. Data recorded during each reading: flow rate from the rotameter, flow rate from dump valve on the bench, and the height of water in each manometric tube on the flow meter module. The data recorded during the experiment was processed using Microsoft Excel.   Pressure drop across each flow meter was calculated by using Equation 1, with Δ h being the difference in the heights read from the manometers on each side of each flow meter. To find energy loss across each flow meter, I used the equivalent expression of 1 kPa = 1 J/kg for water. Plots of flow rate versus square root of pressure drop (Pa) were made using Excel. The trendlines for each flow meter’s data set were forced through zero and the resulting slopes of the trendlines were used to calculate experimental C d  for the Venturi and orifice flow meters using Equation 2. The theoretical C d values were calculated using Equation 3 for the orifice flow meter and Equation 4 for the Venturi flow meter. Reynolds numbers for each flow rate were calculated using Equation 5. E QUATIONS   (1)   ∆ = ∆ℎ   (2)    =      √   (−[  ]  )  (3)      = 0.5959+ 0.0312 .  0.184   + . .  .  (4)      = 0.9975 6. .  .    Page 4  of 8   Equations 3 and 4 are valid for 0.25 < β < 0.75 and 10 4  < Re < 10 7   (Cengel and Cimbala, 2014)   (5)    =     Where ρ  is density of water, g is the gravitational constant, C d  is the discharge coefficient, A o  is the area of the orifice, A 1 is the area of the pipe leading to the orifice, A 2  is the area of the orifice, and  =     , V is flow velocity, d is diameter of pipe, and µ is viscosity of water (taken to be 0.00089 Pa *s).   R  ESULTS AND D ISCUSSION   The flow rates from the dump valve on the Edibon Hydraulics Bench and the flow rates recorded from the rotameter have a percent difference that varies, but does not follow any  particular distribution. The percent difference between the flow rates is less than 22%, with the lowest at 2.78% (Table 1). Percent error for rotameters is normally ±5 % (Cengel and Cimbala, 2014). The larger percent differences may come from errors in timing the dump valve readings, or in reading the flow rate from the rotameter.   Table 1. Flow rates obtained from the rotameter and the dump system on the hydraulics bench. Percent differences between the two readings for each flow rate are included. Rotameter(m 3 /s) Bench (m 3 /s) % difference 5.556E-05 6.670E-05 16.71 9.722E-05 1.000E-04 2.778 1.389E-04 1.667E-04 16.68 2.083E-04 2.667E-04 21.88 2.778E-04 3.167E-04 12.28 3.472E-04 3.833E-04 9.412
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