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MAAE 2300 – Fluid Mechanics ILab Experiment #3 – Hydraulic JumpAhmed Fadlalla 100998815Date: 27/03/2017
SummaryBernoulli’s Equation the Continuity equation are important concepts learned in Class. Inthis lab, these concepts were applied to understand the Hydraulic Jump. The hydraulic jumpworks by opening a sluice gate from a reservoir of water in which a hydraulic flow is created andwater flows through in an inlet at a velocity depending on how much the sluice gate is opened.The water flows through the channel and over a barrier at the end of the stream where the waterforms a jump due to the disturbance in the stream. The water then flows into a tank with a Vnotch in which water flows over pumping back to the initial reservoir.The purpose of this experiment is to analyze the hydraulic jump using basic fluidmechanics. Students must understand that the jump cannot be just analyzed using Bernoulli’sequation since the total mechanical energy is not conserved. Therefore, to solve for thedownstream flow linear momentum & continuity equations must be used. Nomenclature & Given Constants NameSymbolUnitsCross SectionalAreaAim2Acceleration due toGravityg9.81 m/s2Volumetric FlowRateQm3/sSum of all ForcesFNAtmosphericPressurePatm101325 PaWater level in VnotchhmTotal Head HmDepth of WaterlevelzmVelocity of air atoutletVOutletm/sDownstream WaterGate Velocityv2m/sVelocity AcrossHydraulic Jumpv3m/sDensity of Waterρwater1000 Kg/m3Water ChannelWidthw6.2in or 0.1575m
Flow AnalysisPart 1Volumetric Flow RateThe volumetric flow rate was calculated from the equation given in the lab manual, theequation used the height of the water level of the tank flown over a 90°V-notch to calculate thevolumetric flow. The equation is: Q = 1.38h2.5[1]The volumetric flow rate can also be calculated using the continuity equation, by using the areaat a single point of the water channel. Q = v2A2[2]v2experimental=QA2[3]Part 2Bernoulli’s EquationThe ideal downstream velocity can be calculated using Bernoulli’s equation, in which thetwo points is at the beginning of the hydraulic pump and the surface of water of the downstream.For the Bernoulli equation to work, you must assume 1-D steady state, frictionless,incompressible flow with no energy added or removed. Patm+12ρwaterv12+ρwaterg z1=P2+12ρwaterv22+ρwaterg z2[4]Since P1=P2=Patm, as both positions are exposed to atmospheric pressure. Both values for z were measured throughout the experiment. v212g+z1=v222g+z2[5]Continuity EquationSince the velocity upstream of the gate is not zero, the continuity equation must be used to solve for V1. Q1=Q2ρv1A1=ρ v2A2
ρv1w z1=ρv2w z2v1=v2z2z1[6]Now substitute equation [5] into the Bernoulli’s equation [4], we can solve for the ideal velocity after the sluice gate.

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