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Problem 3.47

# Problem 3.47 - Problem 3.47 Given[Difficulty 2 Door of...

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Problem 3.47 [Difficulty: 2] Given: Door of constant width, located in plane vertical wall of water tank is hinged along upper edge. D p s L h y x F pdA Hinge b 1 m = D 1 m = L 1.5 m = Atmospheric pressure acts on outer surface of door; force F is applied at lower edge to keep door closed. Find: (a) Force F, if (b) Force F, if p s p atm = p sg 0.5 atm = Plot F/Fo over tange of ps/patm (Fo is force determined in (a)). Solution: We will apply the hydrostatics equations to this system. Governing Equations: dp dh ρ g = (Hydrostatic Pressure - h is positive downwards) F R A p d = (Hydrostatic Force on door) Σ M z 0 = (Rotational Equilibrium) Assumptions: (1) Static fluid (2) Constant density (3) Door is in equilibrium Taking moments about the hinge: F L A y p d + 0 = dA b dy = Solving for the force: F 1 L 0 L y b y p d = 1 ( ) We will obtain a general expression for F and then simplify for parts (a) and (b).

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Problem 3.47 - Problem 3.47 Given[Difficulty 2 Door of...

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