Problem 3.66 - Problem 3.66 Given: Geometry of gate Find:...

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Problem 3.66 [Difficulty: 3] Given: Geometry of gate h D F R y F A y’ Find: Force at A to hold gate closed Solution: Basic equation dp dh ρ g = Σ M z 0 = Computing equations F R p c A = y' y c I xx Ay c + = I xx wL 3 12 = Assumptions: Static fluid; ρ = constant; p atm on other side; no friction in hinge For incompressible fluid p ρ g h = where p is gage pressure and h is measured downwards The hydrostatic force on the gate is that on a rectangle of size L and width w. Hence F R p c A = ρ g h c A = ρ g D L 2 sin 30 deg () + L w = F R 1000 kg m 3 9.81 × m s 2 1.5 3 2 sin 30 deg + × m 3 × m 3 × m Ns 2 kg m × = F R 199 kN = The location of this force is given by y' y c I xx c + = where y' and y c are measured along the plane of the gate to the free surface
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This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.

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