Hydraulic JumpObjectivesTheoryExperimental MethodsQuestionsObjectives In this laboratory you will investigate an open-channel flow (flow down a channel with a freesurface, e.g., not confined by a rigid surface as would be the case in pipe flow) using conservationequations (mass, linear momentum and energy). You will be introduced to the hydraulicphenomenon known as the hydraulic jump (see Figure ) – the sudden transition from a higherenergy state to a lower energy state while conserving momentum (analogous to a shock wave incompressible gas flows). This is your chance to get a tangible sense of these conservationequations and concepts such as the energy grade line and hydraulic grade line. You will also get achance to think about the energy equation and when the assumptions of the Bernoulli equation arevalid and when they are violated1. TheoryFlow through a sluice gate can be reasonably modeled using the Bernoulli equation. Thepotential energy of the water behind the sluice gate is converted into kinetic energy as the waterpasses under the gate. Thus the velocity of the water can be calculated directly from the height ofthe water behind the sluice gate. Hydraulic jumps occur in open channel flow when the flowtransitions from supercritical to subcritical flow. A description of the phenomena can be found inMunson, et al. page 653. The upstream (y1) and downstream (y2) depths are related by equation .()221111 1 82yFry= - + +where the upstream Froude number (Fr1) is defined as111VFrgy=1 Adapted from Lab #3 Conservation Equations and the Hydraulic Jump, CEE 331 Fall 2001,Professor Cowen, Cornell University)Hydraulic JumpFigure . Constant-head flume with supercritical flow exiting the sluice gate at the left-hand side ofpicture, a hydraulic jump at the beginning of the test section, and subcritical going over the weir at theoutlet.The velocity in the channel can be determined by applying the Bernoulli equation in the regionwhere velocity is increasing between the reservoir and immediatelydownstream of the sluice gate. The velocity can also be measuredwith a stagnation tube connected to a pressure sensor. Thestagnation tube will be filled with water prior to connecting to thepressure sensor and the pressure sensor output will be zeroed withthe stagnation tube held vertically (in the same orientation used fortaking measurements.) Thus the pressure sensor will measure thepressure at point 3 (Figure ). From the Bernoulli equation acrossstreamlines we can obtain the following relationship. 1 21 2p pz zg g+ = +Since 1pg=0 we have21 2pz zg= -From the Bernoulli equation along streamlines we have223 32 22 32 2p Vp Vz zg gg g+ + = + +where 3pg will be measured using a pressure transducer. Since 232Vg is zero and 2 3z z= we canobtain2321 32pVz zgg= - + Thus the stagnation pressure head includes both the static head based on the submergence of thestagnation tube tip as well as the velocity head.Experimental MethodsA small flume will be set up with a stable hydraulic jump. Your goal is to measure the flumedimensions and fluid velocity upstream and downstream from the hydraulic jump.Make the following measurementsusing the bottom of the channel as yourelevation datum. In addition to thesemeasurements you should play with thestagnation tube and the hydraulic jumpso you can answer the questions for thelab report.QuestionsBefore doing lab:Height of water in the reservoir (cm)Stagnation pressure head at theopening of the sluice gate (cm)Stagnation pressure head just upstreamof the hydraulic jump (cm)Depth of submergence of thestagnation tube for previousmeasurement (cm)Depth of water just upstream of thehydraulic jump (cm)Depth of water downstream of thehydraulic jump (cm)321zPressure sensorStagnation tube33221zzPressure sensorStagnation tubeFigure . Stagnation tube and pressuresensor used to measure velocity inopen channel flow.1) Roughly plot the EGL to see what kind of energy changes you expect to happen.2) Think about a way to calculate the fluid velocity right outside the sluice gate without havingto use a Pitot or stagnation tube. Also, since we won’t be taking measurements in the regionafter the hydraulic jump, figure out a way to find the velocity there.After the lab:1) Calculate the velocities and Froude numbers in the super and sub critical regions.2) Create a more exact EGL plot using your test data. Was it similar to what you expected? Ifnot, what are the reasons for this?3) Why was the weir important in generating the hydraulic jump?4) Explain which equations you can or can’t use to analyze the different sections of the set-up.Why?5) Describe the properties of the sub and super critical regions. If you had no instruments, whatcould you do to differentiate between sub and super critical flows.6) What happens if you measure the stagnation pressure at the very bottom of thechannel? Explain based on the properties of real