Problem 3.72

# Problem 3.72 - Problem 3.72 Given[Difficulty 3 Parabolic...

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Problem 3.72 [Difficulty: 3] Given: Parabolic gate, hinged at O has a constant width. b2 m = c 0.25 m 1 = D2 m = H3 m = Find: (a) Magnitude and line of action of the vertical force on the gate due to water (b) Horizontal force applied at A required to maintain equilibrium (c) Vertical force applied at A required to maintain equilibrium Solution: We will apply the hydrostatics equations to this system. Governing Equations: dp dh ρ g = (Hydrostatic Pressure - h is positive downwards) Σ M z 0 = (Rotational equilibrium) F v A y p d = (Vertical Hydrostatic Force) x' F v F v x d = (Location of line of action) F H p c A = (Horizontal Hydrostatic Force) h' h c I xx Ah c + = (Location of line of action) O y h’ B x’ x F V O x F H y Assumptions: (1) Static fluid (2) Incompressible fluid (3) Atmospheric pressure acts at free surface of water and on outside of gate Integrating the hydrostatic pressure equation: p ρ g h =

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Problem 3.72 - Problem 3.72 Given[Difficulty 3 Parabolic...

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