Problem 3.73

# Problem 3.73 - Problem 3.73[Difficulty 2 Given Liquid...

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Problem 3.73 [Difficulty: 2] Given: Liquid concrete is poured into the form shown R2 f t = w1 5 f t = SG c 2.5 = (Table A.1, App. A) Find: Magnitude and line of action of the vertical force on the form Solution: We will apply the hydrostatics equations to this system. Governing Equations: dp dh ρ g = (Hydrostatic Pressure - h is positive downwards) F v A y p d = (Vertical Hydrostatic Force) x' F v F v x d = (Moment of vertical force) Assumptions: (1) Static fluid (2) Incompressible fluid (3) Atmospheric pressure acts at free surface of concrete and on outside of gate Integrating the hydrostatic pressure equation: p ρ g h = F v A y p d = A ρ g h sin θ () d = where dA w R d θ = and hRy = R R sin θ = Therefore, F v 0 π 2 θ ρ g R R sin θ w R sin θ d = ρ g w R 2 0 π 2 θ sin θ ( ) sin θ 2 d = Evaluating the integral: F v ρ g w R 2

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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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Problem 3.73 - Problem 3.73[Difficulty 2 Given Liquid...

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