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Problem 3.87 - Problem 3.87[Difficulty 4 Canoe modeled as a...

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Problem 3.87 [Difficulty: 4] Given: Canoe, modeled as a right semicircular cylindrical shell, floats in water of depth d. The shell has outer radius R and leng R 1.2 ft = L 17 ft = d 1 ft = Find: (a) General expression for the maximum total mass that can be floated, as a function of depth, (b) evaluate for the given conditions (c) plot for range of water depth between 0 and R. Solution: We will apply the hydrostatics equations to this system. Governing Equations: dp dy ρ g = (Hydrostatic Pressure - y is positive downwards from free surface) F v A y p d = (Vertical Hydrostatic Force) Assumptions: (1) Static fluid (2) Incompressible fluid (3) Atmospheric pressure acts on free surface of the liquid. dF y θ d θ max y is a function of θ for a given depth d: y d R R cos θ ( ) ( ) = d R R cos θ ( ) + = The maximum value of θ : θ max acos R d ( ) R = A free-body diagram of the canoe gives: Σ F y 0 = M g F v = where F v is the vertical force of the water on the canoe.
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