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

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MAAE 2300: Fluid Mechanics Lab#3: Hydraulic Jump Seungyeon Hong 100805514 [email protected] Date Performed: Mar 10, 2011 Date Submitted: Mar 17, 2011 Lab group L10-9: Michael Abbott Tshepo Kgengwenyane Seungyeon Hong
Table of Contents 1. Summary ....................................................................................................................................................... 2 2. Nomenclature ............................................................................................................................................... 2 3. Flow Analysis ................................................................................................................................................. 3 3.1 Deriving V 2,ideal ......................................................................................................................................... 3 3.2 Deriving z 3 =f(z 2 , Q) .................................................................................................................................. 3 3.3 Deriving H predicted ...................................................................................................................................... 4 4. Experimental Setup and Procedure ............................................................................................................. 5 5. Results and Discussion ................................................................................................................................. 5 5.1 High Flow Rate ........................................................................................................................................ 5 5.2 Low Flow Rate ......................................................................................................................................... 6 5.3 Discussion ............................................................................................................................................... 6 6. Conclusions ................................................................................................................................................... 7 7. References .................................................................................................................................................... 8 8. Appendix : Sample Calculations for High Flow Rate .................................................................................... 9 8.1 Deriving V 2,ideal ......................................................................................................................................... 9 8.2 Deriving z 3 =f(z 2 , Q) ................................................................................................................................ 10 8.3 Deriving Δ H predicted ........................................................................................................................... 12 8.4 Volume Flow Rate Q ............................................................................................................................. 13 9. Appendix: Data Tables ................................................................................................................................ 14 10. Appendix: Original Data Sheet ................................................................................................................. 15 1
1. Summary This 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 the fluctuations of water level. Few simplifying assumptions were made, such as 1D flow and no wall friction (when applying Bernoulli’s equation). 2. Nomenclature A : cross sectional area [ m 2 ] F : of allthe forces [ N ] g : accelerationdue ¿ gravity = 9.81 m s 2 h : water level V notch [ ¿ ] H : totalhead [ m ] ´ m : massflow rate [ kg s ] P : static pressure [ Pa ] P atm : atmospheric pressure = 101.3 kPa Q : volume flow rate [ m 3 s ] 2
V : velocity of fluid [ m s ] w : channelwidth = 0.16 m z : waterlevel [ m ] ρ : fluid density [ kg m 3 ] 3. Flow Analysis 3.1 Deriving V 2,ideal w , =
3
3.2 Deriving z 3 =f(z 2 , 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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