MAAE 2300 Experiment 3 Lab Report.docx - MAAE 2300...

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MAAE 2300 Experiment 3 Flow Through a Sluice Gate and Hydraulic Pump December 1 st , 2018
1.0 Summary The purpose of this lab is to measure the behaviour of a water flow when flowing through a hydraulic jump, and to predict the flow of water. Lab was conducted twice with two different flows to determine the velocity and total head of the fluid. The theoretical velocity for flow 1 and flow 2 at position 2 is 1.468 m/s and 1.028 m/s respectively. The experimental velocity at position 2 is 2.180 m/s for flow 1 and 1.278 m/s for flow 2. The change in total head before and after the hydraulic jump is 0.0448 m for flow 1 and 0.0847 m for flow 2. There is a lot of discrepancy and errors with the calculations and results which will be discussed in the results and discussion section 2.0 Nomenclature ρ air Density of air (1.2 kg/m 3 ) ρ water Density of water (1000 kg/m 3 ) g Acceleration of gravity (9.81 m/s 2 ) H tot Total head w Width of the channel (0.15875 m) P atm Atmospheric Pressure (101.325 kPa) P Pressure (Pa) Q Volume flow rate (m 3 /s) V Velocity (m/s) A Area of cross section (m 2 ) ´ m Mass flow rate y Elevation 3.0 Flow Analysis 1. The volume flow rate over a 90 ° V-notch can be found using the equation and the height of water in the tank upstream. Q = 1.38 H 2.5 [1] The volume flow rate can also be found using the velocity and cross-sectional area. Q = VA [2] Using equation 1 and 3, the equations can be combined to find velocity. V = 1.38 H 2.5 A [3] Bernoulli’s equation is used to determine the velocity of water. Both pressures can be assumed to be atmospheric pressure, therefore cancelling each other.
P 1 + 1 2 p water V 1 2 + p water g h 1 = P 2 + 1 2 p water V 2 2 + p water gh 2 [4] P 1 = P 2 = P atm To find velocity using Bernoulli’s equation, the continuity of mass flow rate is needed. ´ m 1 = ´ m 2 A 1 V 1 = A 2 V 2 V 1 = A 2 V 2 A 1 To find the area of cross section A = h w The equation can be rearranged and removing the pressure from the equation to solve velocity. The continuity of mass flow rate can also be plugged in. V 2 = 2 g ( h 1 h 2 ) 1 ( A 2 A 1 ) 2 [5] Finding the percentage error for the theoretical and experimental flow at position 2 Percent Error = Experimental Theoretical Theoretical × 100 [6] 2. The total head at a point in a flow as given in the lab manual. Since pressure is atmosphere pressure, it will be neglected and treated as 0. The density is water and using velocity of the position at that point.

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