Problem 3.53

# Problem 3.53 - Problem 3.53[Difficulty 4 Given...

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Problem 3.53 [Difficulty: 4] Given: Semicylindrical trough, partly filled with water to depth d. Find: (a) General expressions for F R and y' on end of trough, if open to the atmosphere. (b) Plots of results vs. d/R between 0 and 1. Solution: We will apply the hydrostatics equations to this system. Governing Equations: dp dy ρ g = (Hydrostatic Pressure - y is positive downwards) F R A p d = (Hydrostatic Force on door) y' F R A yp d = (First moment of force) dy R – d θ d y h α Assumptions: (1) Static fluid (2) Incompressible fluid Integrating the pressure equation: p ρ g h = where hyRd () = Therefore: p ρ g yRd [] = ρ g R y R 1 d R = Expressing this in terms of θ and α in the figure: p ρ g R cos θ ( ) cos α = For the walls at the end of the trough: dA w dy = 2R sin θ dy = Now since y R cos θ = it follows that dy R sin θ d θ =

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Problem 3.53 - Problem 3.53[Difficulty 4 Given...

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