Problem 3.81 - Problem 3.81 [Difficulty: 3] Given:...

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Problem 3.81 [Difficulty: 3] Given: Cylindrical log floating against dam Find: (a) Mass per unit length of the log (b) Contact force per unit length between log and dam 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) dF →⎯ pdA = (Hydrostatic Force) dF H dF h θ dF V R = D /2 Assumptions: (1) Static fluid (2) Incompressible fluid (3) Atmospheric pressure acts on free surfaces and on the first quadrant of the log Integrating the hydrostatic pressure equation: p ρ g h = ρ g R 1 cos θ () = Resolving the incremental force into horizontal and vertical components: dF p dA = pw R d θ = ρ g R 1 cos θ w R d θ = ρ g R 2 w 1 cos θ = dF H dF sin θ = ρ g R 2 w 1 cos θ d θ sin θ = dF v dF cos θ = ρ g R 2 w 1 cos θ d θ cos θ = Integrating the expression for the horizontal force will provide us with the contact force per unit length: F H 0 3 π 2 θ ρ g R 2 w 1 cos θ sin θ d = ρ g R 2 w 0 3 π 2 θ
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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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