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LAB 3: Uncertainties in fluid flow rate Measurement 1 Lab 3: UNCERTAINTIES IN FLUID FLOW RATE MEASUREMENT Dhairya Soni, 101129894 Carleton University-Fluid Mechanics (MAAE 2300) [email protected] Group L03-B
LAB 3: Uncertainties in fluid flow rate Measurement 2 SUMMARY Fluid 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 choice of 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 flow rate, 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. NOMENCLATURE P atm = Atmospheric Pressure (Pa): 101325 Pa ρ Air = Density of Air (kg/m3): 1.225 kg/m3 ρ Water = Density of Water (kg/m3): 1000 kg/m3 C d = discharge coefficient Re = Reynold’s number q = flow rate V = flow velocity A = Cross-sectional area g = acceleration of gravity 9.81 m/s 2 r rms = root mean square ω = angular velocity u i,q = Bias error/instrument error q j - ´ q = mean value subtracted from value at point i u m,q = Standard deviation u total,q = total uncertainty q act = actual flow rate
LAB 3: Uncertainties in fluid flow rate Measurement 3 FLOW ANALYSIS For the Venturi Meter: Figure 1: Venturi Meter diagram Velocity 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 A2 Simplifying and combining equations 1 and 2 we obtain: qactual = Cd (π / 4) D2 2 [ 2 (p1 - p2) ]1/2 / [ ρ (1 - d4) ]1/2 Cd 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 Measurement 4 Figure 2: Orifice Meter diagram Similar 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.

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