Lab#3 - MAAE 2300 Fluid Mechanics Lab#3 Hydraulic Jump...

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MAAE 2300: Fluid MechanicsLab#3: Hydraulic JumpSeungyeon Hong100805514[email protected]Date Performed: Mar 10, 2011Date Submitted: Mar 17, 2011Lab group L10-9: Michael AbbottTshepo KgengwenyaneSeungyeon Hong
Table of Contents1. Summary.......................................................................................................................................................22. Nomenclature...............................................................................................................................................23. Flow Analysis.................................................................................................................................................33.1 Deriving V2,ideal.........................................................................................................................................33.2 Deriving z3=f(z2, Q)..................................................................................................................................33.3 Deriving Hpredicted......................................................................................................................................44. Experimental Setup and Procedure.............................................................................................................55. Results and Discussion.................................................................................................................................55.1 High Flow Rate........................................................................................................................................55.2 Low Flow Rate.........................................................................................................................................65.3 Discussion...............................................................................................................................................66. Conclusions...................................................................................................................................................77. References....................................................................................................................................................88. Appendix : Sample Calculations for High Flow Rate....................................................................................98.1 Deriving V2,ideal.........................................................................................................................................98.2 Deriving z3=f(z2, Q)................................................................................................................................108.3 Deriving ΔHpredicted...........................................................................................................................128.4 Volume Flow Rate Q.............................................................................................................................139. Appendix: Data Tables................................................................................................................................1410. Appendix: Original Data Sheet.................................................................................................................151
1. SummaryThis experiment was performed in order to analyze the phenomenon of “hydraulic jump” by making use of three fundamental equations: Bernoulli’s equation continuity equation, and linear momentum equation. A hydraulic flow was generated by opening a sluice gate from a reservoir of water, while the reservoir was simultaneously refilled by a pump, consequently generating a steady flow. A barrier at the end of the stream was raised, creating a sudden jump of water height and disturbance in the mid stream. The experiment was performed twice at two different flow rates. Seven measurements were taken per each flow rate: water height and total head before and after the sluice gate and after the hydraulic jump, and lastly, water level in the V-notch weir. Total head measurements were taken with a pitot tube, and height measurements with a ruler. Taking accurate measurements was difficult due to thefluctuations of water level. Few simplifying assumptions were made, such as 1D flow and no wall friction (when applying Bernoulli’s equation).2. NomenclatureA:cross sectional area[m2]F:of allthe forces[N]g:accelerationdue¿gravity=9.81ms2h:water levelVnotch[¿]H:totalhead[m]´m:massflow rate[kgs]P:static pressure[Pa]Patm:atmospheric pressure=101.3kPaQ:volume flow rate[m3s]2
3. Flow Analysis3.1 Deriving V2,idealTo answer discussion question 1, we need to derive V2,ideal. Location 1 is before the sluice gate and 2 is after the gate.We start with Bernoulli’s equationP1ρg+V122g+z1=P2ρg+V222g+z2Using continuity equation ( ´m1= ´m2)and cancelling out common constants such as ρand we getV1=V2z2z1After substituting V1V2z2z1into the Bernoulli’s equation and rearranging terms, we getV2=2(g z12)(z2+z1)……… …..eqn(1)where V2istheidealized velocity of water afterthe sluice gate .
w,
=
3
3.2 Deriving z3=f(z2, Q)In order to answer discussion question 3, we need to derive and express the water level after the hydraulic jump as a function of water level before the hydraulic jump and a volume flow rate. Location 2 is before hydraulic jump, and 3 is after the jump.We start with control volume analysis, and make use of linear momentum equation.

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