Lab1 MAAE 2300, Rima El Boustani, 101267764, L05-4

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Dec 6, 2023

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Flow Through a Venturi Rima El Boustani, 101267764 2023-10-10 TA: Ali Shahrouzian Group members: Corbeau, Raven Li, Melody Mughal, Zaib Nejem, Tasneem Rahman, Samaarah Group L05-4

Table of Contents Summary ....................................................................................................................................................... 3 Nomenclature ............................................................................................................................................... 3 Set Up and Procedure ................................................................................................................................... 4 Flow Analysis ................................................................................................................................................. 6 Results: Data for Lab 1 ................................................................................................................................. 8 Discussion ...................................................................................................................................................... 9 Conclusion ................................................................................................................................................... 12 References .................................................................................................................................................. 12 Appendix 1 .................................................................................................................................................. 12 Appendix 2 .................................................................................................................................................. 13

Summary To sum up, the aims of this laboratory session focus on gaining a deeper understanding of manometer utilization, implementing Bernoulli's equation in actual flow scenarios, and comprehending the physical implications of static, dynamic, and stagnation pressure concepts. Throughout the experiment, inaccuracies were found. These inaccuracies had an impact on the calculations, preventing us from reaching a perfect value for the Venturi Coefficient. Nomenclature

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Set Up and Procedure The Experimental Setup and Procedure for the experiment were done according to the lab manual. Figure 1: Manometer (U-tube)

Figure 2: Venturi Setup

Flow Analysis The Hydrostatic Equation is used to obtain the pressure of a fluid that is in static motion. It takes the pressure at 2 different points, using their height and neglecting the distance between them. (1.0) Absolute pressure can be obtained by adding the atmospheric pressure and gauge pressure. (1.1) To obtain the velocity of the of the inlet, we use Bernoulli’s equation. This equation relates 2 different points of the stream, one at the start of the inlet, and the other one that is much further away from the apparatus. Two assumptions are made, the 2 points have the same height and the velocity of the stream at the point much further away from the inlet is 0. (1.2) The 2 pressure points can be replaced by the hydrostatic equation to then determine the velocity of the inlet: (1.3) We can calculate the actual volumetric flow rate once both area and velocity are obtained. (2.0) The Ideal Volumetric flow rate can be calculated using the Area of the throat and the velocity of the throat. By substituting Bernoulli’s equation, we get the velocity of the throat: (3.0) (3.1)

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After calculating the actual and ideal volumetric flow rate of the venturi meter, we can obtain the venturi coefficient as the ratio of the 2. (4.0) Static pressure is the pressure at rest and is in the first part of Bernoulli’s equation, it is calculated using the formula below. (5.0) Dynamic pressure is when the liquid is in motion. (5.1) Stagnation pressure is the total pressure of the liquid. (5.2) We can obtain the flow velocity using Q actual and the Area of the point that can be found by calculating the diameter using a few mathematics equations. (6.0) Theoretical static pressure can be then calculated using Bernoulli’s equation including v x calculated above. (6.1) The continuity equation is then used to calculate the velocity at different taps with different areas. (7.0)

Results: Data for Lab 1 VENTURI METER Apparatus No. 3 Taper begins just after tap #3 Tap No. Distance from current Tap to Throat Tap (Center to Center) (in) Flow Rate 1: Manometer Fluid Height (mm) Flow Rate 2: Manometer Fluid Height (mm) 1(inlet) 5.3125 139 124 2 4.3125 145 128 3 3.3125 159 136 4 2.75 176 148 5 2.3125 210 167 6 1.8125 250 191 7 1.3125 360 259 8 0.8125 386 279 9(throat) 0 551 378 10 -0.8125 394 330 11 -1.3125 325 226 12 -1.8125 278 198 13 -2.3125 256 187 14 -2.8125 232 176 15 -3.3125 219 166 16 -4.3125 207 160 Atm Ref N/A 89 82

Inlet to Throat Taper Length: 85 mm density-Air 1.23(kg/m3) Throat to Outlet Taper Length: 85 mm Density-Water 1000(kg/m3) Throat Diameter: 0.707 in Atmospheric Pressure 101325 (Pa) Inlet Diameter: 1.045 in S.G.: 1.00 Discussion More Sample Calculations can be found in Appendix 2. 1. Q actual (Flow 1) = A inlet V inlet = 0.01563 m ^3 /s Q actual (Flow 2) = A inlet V inlet = 0.01432 m ^3 /s 2. Q ideal (flow 1) = A throat V throat = 0.02175 m ^3 /s Q ideal (flow 2) = A throat V throat = 0.01740 m ^3 /s 3. Cv (Flow1) = Q actual /Q ideal = 0.7186 Cv (Flow 2) = Q actual /Q ideal = 0.8230 4. P stag1 = P static +P dynamic = 101325.5 pa P stag2 = P static +P dynamic = 101324.7 pa P static1 = P atm – ρg(Z throat -Z ref ) = 96792.8 pa P static2 = P atm – ρg(Z throa t-Z ref ) = 98421.2 pa P dynamic1 = 1/2 ρ air V throat^2 = 4532.7 pa P dynamic2 = 1/2 ρ air V throat^2 = 2903.5 pa

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5. Graph 1: Flow 1 Static Pressure at the 16 Tap levels Graph 2: Flow 2 Static Pressure at the 16 Tap levels

6. The actual flow rate is less than the ideal flow rate since friction and viscous forces are not included in the ideal flow rate calculation. Not including these factors makes the value for the ideal rate higher and neglecting them is not realistic. So, in reality, friction and viscous forces affect and reduce from the flow rate. The venturi coefficient is not that high, and the results are reasonable. 7. For both flow 1 and flow 2, Theoretical static pressure is higher than the experimental static pressure because of frictional losses and other factors that are not included in Bernoulli’s equation. Static pressure is the lowest at the throat of the venturi, this is because the velocity is the highest at that point. The static pressure varies with velocity. When velocity increases, static pressure decreases. 8. Figure 3: Velocity Profiles Along the Venturi The velocity of Downstream profile is equal to the upstream profile due to the continuity equation (7.0) which states that if the area of the profiles is the same then the velocity will be too. Equation (7.0) was also used to calculate the velocity of the throat (it can be found in Appendix 2).

9. Sources of error within the lab can be; leaking from the rubbery plastic tubes that are connected to the Manometer, tubes not being fully airtight to the Venturi, and moisture content in the tubes which can cause evaporation. These sources can decrease the flow rate of the liquid. Conclusion In conclusion, Bernoulli’s equation is not perfect and does not include real life factors like friction. But, it is good enough and the theoretical values of static pressure is close to that of experimental. It is also proved that static pressure decreases as velocity increases in the Venturi. References 1. Carleton University: Department of Mechanical & Aerospace Engineering. “MAAE 2300 Fluid Mechanics I LABORATORY EXERCISES”, 2020. Appendix 1

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