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Problem 4.72 - Problem 4.72 Given Gate held in place by...

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Problem 4.72 [Difficulty: 4] Given: Gate held in place by water jet Find: Required jet speed for various water depths Solution: Basic equation: Momentum flux in x direction for the wall Note: We use this equation ONLY for the jet impacting the wall. For the hydrostatic force and location we use computing equations F R p c A = y' y c I xx A y c + = Assumptions: 1) Steady flow 2) Incompressible flow 3) Uniform flow Hence R x V ρ V A jet ( ) = ρ V 2 π D 2 4 = This force is the force generated by the wall on the jet; the force of the jet hitting the wall is then F jet R x = ρ V 2 π D 2 4 = where D is the jet diameter For the hydrostatic force F R p c A = ρ g h 2 h w = 1 2 ρ g w h 2 = y' y c I xx A y c + = h 2 w h 3 12 w h h 2 + = 2 3 h = where h is the water depth and w is the gate width For the gate, we can take moments about the hinge to obtain F jet h jet F R h y' ( ) + F jet
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