Problem 3.81[Difficulty: 3]Given:Cylindrical log floating against damFind:(a) Mass per unit length of the log (b) Contact force per unit length between log and damSolution:We will apply the hydrostatics equations to this system.Governing Equations:dpdhρg⋅=(Hydrostatic Pressure - h is positive downwards fromfree surface)dF→⎯pdA→⎯⋅=(Hydrostatic Force)dFHdFhθ dFVR = D/2 Assumptions:(1) Static fluid(2) Incompressible fluid(3) Atmospheric pressure acts on free surfaces and on thefirst quadrant of the logIntegrating the hydrostatic pressure equation:pρg⋅h⋅=ρg⋅R⋅1cosθ()−⋅=Resolving the incremental force into horizontal and vertical components:dFp dA⋅=pw⋅R⋅dθ⋅=ρg⋅R⋅1cosθ−⋅w⋅R⋅dθ⋅=ρg⋅R2⋅w⋅1cosθ−⋅=dFHdF sinθ⋅=ρg⋅R2⋅w⋅1cosθ−⋅dθ⋅sinθ⋅=dFvdF cosθ⋅=ρg⋅R2⋅w⋅1cosθ−⋅dθ⋅cosθ⋅=Integrating the expression for the horizontal force will provide us with the contact force per unit length:FH03π⋅2θρg⋅R2⋅w⋅1cosθ−⋅sinθ⋅⌠⎮⎮⌡d=ρg⋅R2⋅w⋅03π⋅2θ
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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.