Problem 3.74[Difficulty: 2]Given:Open tank as shown. Width of curved surfaceb10ft⋅=Find:(a) Magnitude of the vertical force component on the curved surface(b) Line of action of the vertical component of the forceSolution:We will apply the hydrostatics equations to this system.Governing Equations:dpdhγ=(Hydrostatic Pressure - h is positive downwards)L x’ x FRyy FvAyp⌠⎮⎮⌡d−=(Vertical Hydrostatic Force)x' Fv⋅Fvx⌠⎮⎮⌡d=(Moment of vertical force)Assumptions:(1) Static fluid(2) Incompressible fluid(3) Atmospheric pressure acts at free surface of waterand on outside of wallIntegrating the hydrostatic pressure equation:pγh⋅=We can define along the surfacehLR2x2−()12−=We also define the incremental area on the curved surface as:dAybdx⋅=Substituting these into the force equation we get:FvAyp⌠⎮⎮⌡d−=0RxγLR2x2−12−⎡⎢⎣⎤⎥⎦⋅b⋅⌠⎮⎮⎮⌡d−=γ−b⋅0Rx2x2−−⌠⎮⌡d⋅=γ−b⋅R⋅π4⋅−⎛⎝⎞⎠⋅=Fv62.4lbfft3⋅10×ft⋅4×ft⋅10 ft⋅4ft⋅π4×−⎛⎝⎞⎠×⎡⎢⎣
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