Problem 3.87 - Problem 3.87 [Difficulty: 4] Canoe, modeled...

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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 = L1 7 f t = d1 f t = 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 () = dR R cos θ + = The maximum value of θ : θ max acos Rd R = A free-body diagram of the canoe gives: Σ F y 0 = Mg F v = where F v is the vertical force of the water on the canoe.
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This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.

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Problem 3.87 - Problem 3.87 [Difficulty: 4] Canoe, modeled...

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