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MAAE 2300 B Lab 3 Report: Flow through a Sluice Gate and Hydraulic Jump Yicheng Li 101083322 2018-12-02
Lab 3 report: Flow through a Sluice Gate and Hydraulic Jump Yicheng Li 101083322 [email protected] 1.0 Summary The objective of this lab is to analyze the phenomenon of hydraulic pump by the application of three engineering principles: Bernoulli’s equation continuity equation, and linear momentum equation. Once the sluice gate is opened, a hydraulic flow is produced by the reservoir of water. The reservoir of water is constantly refilled by the pump, results in a steady flow. The hydraulic jump in the mid stream is caused by a barrier at the end of the stream. Two flow rates are applied to the experiment the objective of this experiment is achieved. The behaviour of a water flow passing through a hydraulic jump was examined and its characteristics after the hydraulic jump were predicted. 2.0 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 : total head [ m ] ´ m : massflow rate [ kg s ] P : static pressure [ Pa ] P atm : atmospheric pressure = 101.3 kPa Q : volume flow rate [ m 3 s ] 1
Lab 3 report: Flow through a Sluice Gate and Hydraulic Jump Yicheng Li 101083322 [email protected] V : velocity of fluid [ m s ] w : channelwidth = 0.16 m z : waterlevel [ m ] ρ : density [ kg m 3 ] 3.0 Flow analysis Using Bernoulli’s equation to define stream line between two points: P 1 + 1 2 ρv 1 2 + ρg z 1 = P 2 + 1 2 ρv 2 2 + ρg z 2 [ 1 ] Since P 1 = P 2 = P atm and density of the fluid (water) remains the same through out the experiment, these terms can be canceled out from equation : 1 2 v 1 2 + g z 1 = 1 2 v 2 2 + g z 2 [ 2 ] To express v 1 in terms of v 2 , continuity equation is applied: ´ m 1 = ´ m 2 → ρ 1 v 1 A 1 = ρ 2 v 2 A 2 [ 3 ] v 1 = v 2 A 2 A 1 [ 4 ] As A = wz , and the channel width remains the same, thus: v 1 = v 2 z 2 z 1 [ 5 ] Substitute  to  to obtain: 1 2 v 2 2 z 2 2 z 1 2 + g z 1 = 1 2 v 2 2 + g z 2 [ 6 ] 2
Lab 3 report: Flow through a Sluice Gate and Hydraulic Jump Yicheng Li 101083322 [email protected] z 2 z 1 ¿ ¿ ¿ ¿ ¿ 2 g ( z 2 z 1 ) ¿ v 2 = ¿ The actual v 2 can be obtained by applying the flow rate in the channel using the V-notch weir at the downstream end of the flume: Q = 2.5
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