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MAAE 2300Experiment 3Flow Through a Sluice Gate andHydraulic PumpDecember 1st, 2018
1.0 SummaryThe 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 thevelocity 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 section2.0 NomenclatureρairDensity of air (1.2 kg/m3)ρwaterDensity of water (1000 kg/m3)gAcceleration of gravity (9.81 m/s2) HtotTotal headwWidth of the channel (0.15875 m)PatmAtmospheric Pressure (101.325 kPa)PPressure (Pa)QVolume flow rate (m3/s)VVelocity (m/s)AArea of cross section (m2)´mMass flow rateyElevation3.0 Flow Analysis1. The volume flow rate over a 90° V-notch can be found using the equation and the height of water in thetank upstream.Q=1.38H2.5The volume flow rate can also be found using the velocity and cross-sectional area.Q=VAUsing equation 1 and 3, the equations can be combined to find velocity.V=1.38H2.5ABernoulli’s equation is used to determine the velocity of water. Both pressures can be assumed to be atmospheric pressure, therefore cancelling each other.
P1+12pwaterV12+pwaterg h1=P2+12pwaterV22+pwatergh2P1=P2=PatmTo find velocity using Bernoulli’s equation, the continuity of mass flow rate is needed.´m1= ´m2A1V1=A2V2V1=A2V2A1To find the area of cross sectionA=h∗wThe 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.V2=√2g(h1−h2)1−(A2A1)2Finding the percentage error for the theoretical and experimental flow at position 2Percent Error=Experimental−TheoreticalTheoretical×1002. 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.