LAB 3: Uncertainties in fluid flow rate Measurement2SUMMARYFluid flow rate measurement is a vastly utilized technique in Aerospace and Mechanical engineering. Depending on factors such as degree of accuracy and type of application, the choiceof flow meter devices varies as shown in this experiment. Each device provides a different level of accuracy. The aim in this experiment is to measure and evaluate fluid flow rate measurements uncertainties in a water closed-loop experimental setup. The five devices used are: The Venturi Meter; Orifice Meter; Rotameter; Turbine Flow Meter; and an Ultrasonic Meter. Uncertainty analysis of these are performed considering uncertainty associated with measurement of the flowrate, as well as uncertainty associated with the flow meter instrument. In addition to the uncertainty analysis, we learn how to establish error propagations in measurements and error propagation methods which are essential techniques to be applied in any experimental and computational work.NOMENCLATUREPatm= Atmospheric Pressure (Pa): 101325 PaρAir= Density of Air (kg/m3): 1.225 kg/m3ρWater= Density of Water (kg/m3): 1000 kg/m3Cd= discharge coefficientRe = Reynold’s numberq = flow rate V = flow velocityA = Cross-sectional areag = acceleration of gravity 9.81 m/s2rrms= root mean square ω = angular velocityui,q= Bias error/instrument errorqj-´q= mean value subtracted from value at point ium,q= Standard deviationutotal,q= total uncertainty qact= actual flow rate
LAB 3: Uncertainties in fluid flow rate Measurement3FLOW ANALYSISFor the Venturi Meter:Figure 1: Venturi Meter diagramVelocity and pressure at the throat section and inlet section are in relation via the Bernoulli Equation:P1 + 1/2 ρ V1 = P2 + 1/2 ρ V2 = Const.Since uniform velocity profiles are assumed and ρ being the density of the fluid, q being the flow rate and A1 and A2 are cross-sectional areas of section 1 and 2 respectively we get:q = V1 A1 = V2 A2Simplifying and combining equations 1 and 2 we obtain:qactual = Cd (π / 4) D2 2 [ 2 (p1 - p2) ]1/2 / [ ρ (1 - d4) ]1/2Cd is the discharge coefficient valued at 0.95, D2 is the diameter at the throat section, D1 is the diameter at section 1, and d = D2 / D1 is the diameter ratio. P1-P2 becomes the change in pressure.For the orifice meter:
LAB 3: Uncertainties in fluid flow rate Measurement4Figure 2: Orifice Meter diagramSimilar equation used for the Venturi Meter are used for the Orifice meter as well. As an analogy, V1 and P1 are the velocity and pressure as shown in section 1 of the venturi meter. V2 and P2 are the velocity and pressure as shown in section 2 of the venturi meter.