Lab Report.pdf - 1 Summary The purpose of this report is to...

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Fluid Mechanics MAAE2300 Experiment 1 Flow Through a Venturi Meter Jeremy Levasseur 101030732 [email protected] 2018 March 1 Group Number 6 Group Members Matthew Betts 101031952 Harrison Rothwell 101043356 1
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Contents 1 Summary 3 2 Nomenclature 3 3 Flow Analysis 4 3.1 Actual Volumetric Flow Rate . . . . . . . . . . . . . . . . . . . . . 4 3.2 Ideal Volumetric Flow Rate . . . . . . . . . . . . . . . . . . . . . . 5 3.3 Venturi Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.4 Stagnation Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.5 Static Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.6 Dynamic Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.7 Gage Pressure Of Syringe . . . . . . . . . . . . . . . . . . . . . . . 7 4 Experimental Setup and Procedure 7 5 Results and Discussion 8 6 Conclusion 11 7 References 12 8 Appendices 12 8.1 Appendice A - Signed Data Sheet . . . . . . . . . . . . . . . . . . . 12 8.2 Appendice B - Sample Calculations . . . . . . . . . . . . . . . . . . 14 8.3 Appendice C - Data Tables . . . . . . . . . . . . . . . . . . . . . . . 15 2
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1 Summary The purpose of this report is to test the accuracy of Bernoulli’s equation by analyz- ing a venturi meter using a manometer bank. The ‘actual’ and ‘ideal’ volumetric flows for the venturi meter were calculated using Bernoulli’s equation and the Con- tinuum equation. The venturi coefficient, which is the ratio of these two volumetric flow values, was found to be 0.97983 for a low flow rate of air and 0.91783 for a high flow rate of air. The static pressure at various points along the venturi meter were calculated using the manometer bank and then they were compared against pre- dicted values obtained through Bernoulli’s equation. It was found that Bernoulli’s equation is a good estimator for the static pressure along the venturi meter. The small differences in values is due to the assumptions that are required to apply the equation. Air is assumed to be an inviscid fluid that flows steadily through the ven- turi meter, however these assumptions are a large factor in the difference between the theoretical and measured values. 2 Nomenclature Table 1: Symbols Name Symbol Units Specific Weight of Water γ water N/m 3 Specific Weight of Mercury γ mercury N/m 3 Density of Water ρ water kg/m 3 Density of Air ρ air kg/m 3 Acceleration due10cm to Gravity g m/s 2 Atmospheric Pressure P atm Pa Static Pressure P stat Pa Dynamic Pressure P dyn Pa Stagnation Pressure P stag Pa Actual Volumetric Flow Rate Q actual m 3 /s Ideal Volumetric Flow Rate Q ideal m 3 /s Velocity V m/s 2 Intake Radius r intake m Throat Radius r throat m Intake Area A intake m 2 Throat Area A throat m 2 Height of Water in Manometer h m Venturi Coefficient C v - 3
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Table 2: Constants[1] Name Value Gravity 9.81 m/s 2 Speicfic Weight Of Water 9790 N/m 3 Density Of Water 997.96 kg/m 3 Density Of Air 1.2028 kg/m 3 Atmospheric Pressure 101325 Pa 3 Flow Analysis 3.1 Actual Volumetric Flow Rate The equation for Volumetric Flow is: Q = V * A (3.1) where V is the velocity of the fluid and A is the cross sectional area that the fluid is passing through. To find the “Actual” Volumetric Flow, the velocity of the air at the bell mouth must first be calculated by employing Bernoulli’s Equation, which is P 1 + 1 2 ρ air V 2 1 + ρ air gz 1 = P 2 + 1 2 ρ air V 2 2 + ρ air gz 2 (3.2) where point 1 is just inside the bell mouth and point 2 is far away from the apparatus. It is assumed that V 2
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