Problem 3.74 - Problem 3.74[Difficulty 2 Given Open tank as...

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Problem 3.74 [Difficulty: 2] Given: Open tank as shown. Width of curved surface b 10 ft = Find: (a) Magnitude of the vertical force component on the curved surface (b) Line of action of the vertical component of the force Solution: We will apply the hydrostatics equations to this system. Governing Equations: dp dh γ = (Hydrostatic Pressure - h is positive downwards) L x’ x F Ry y 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 water and on outside of wall Integrating the hydrostatic pressure equation: p γ h = We can define along the surface h L R 2 x 2 ( ) 1 2 = We also define the incremental area on the curved surface as: dA y b dx = Substituting these into the force equation we get: F v A y p d = 0 R x γ L R 2 x 2 ( ) 1 2 b d = γ b 0 R x L R 2
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