Problem 3.50 - Problem 3.50 Given Geometry of gate...

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Problem 3.50 [Difficulty: 3] F A H = 25 ft y R = 10 ft h A B z x y Given: Geometry of gate Find: Force F A for equilibrium Solution: Basic equation F R A p d = dp dh ρ g = Σ M z 0 = or, use computing equations F R p c A = y' y c I xx Ay c + = where y would be measured from the free surface Assumptions: static fluid; ρ = constant; p atm on other side; door is in equilibrium Instead of using either of these approaches, we note the following, using y as in the sketch Σ M z 0 = F A R A yp d = with p ρ g h = (Gage pressure, since p = p atm on other side) F A 1 R A y ρ g h d = with dA r dr d θ = and y r sin θ () = hHy = Hence F A 1 R 0 π θ 0 R r ρ g r sin θ H r sin θ r
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