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Problem 3.82

# Problem 3.82 - Problem 3.82 Given[Difficulty 3 Curved...

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Problem 3.82 [Difficulty: 3] Given: Curved surface, in shape of quarter cylinder, with given radius R and width w; water stands to depth H. R 0.750 m = w 3.55 m = H 0.650 m = Find: Magnitude and line of action of (a) vertical force and (b) horizontal force on the curved surface Solution: We will apply the hydrostatics equations to this system. Governing Equations: dp dh ρ g = (Hydrostatic Pressure - h is positive downwards from free surface) F v A y p d = (Vertical Hydrostatic Force) F H p c A = (Horizontal Hydrostatic Force) x' F v F v x d = (Moment of vertical force) h' h c I xx h c A + = (Line of action of horizontal force) dF h H R θ Assumptions: (1) Static fluid (2) Incompressible fluid (3) Atmospheric pressure acts on free surface of the water and on the left side of the curved surface Integrating the hydrostatic pressure equation: p ρ g h = dF h’ H R F V F H y’ x’ From the geometry: h H R sin θ () = y R sin θ = x R cos θ = dA w R d θ = θ 1 asin H R

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Problem 3.82 - Problem 3.82 Given[Difficulty 3 Curved...

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