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Problem 3.71 - Problem 3.71 Given[Difficulty 3 Parabolic...

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Problem 3.71 [Difficulty: 3] Given: Parabolic gate, hinged at O has a constant width. b 1.5 m = a 1.0 m 2 = D 1.2 m = H 1.4 m = Find: (a) Magnitude and moment of the vertical force on the gate due to water (b) Horizontal 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 = (Moment of vertical force) y' F H F H y d = (Moment of Horizontal Hydrostatic Force) O y y’ H x’ x F V O x F H F A 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 = (a) The magnitude and moment of the vertical component of hydrostatic force: F v A y p d = x ρ g h b d = where
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