Problem 3.66[Difficulty: 3]Given:Geometry of gateh D FRy FAy’ Find:Force at A to hold gate closedSolution:Basic equationdpdhρg⋅=ΣMz0=Computing equationsFRpcA⋅=y'ycIxxAyc⋅+=IxxwL3⋅12=Assumptions:Static fluid; ρ= constant; patmon other side; no friction in hingeFor incompressible fluidpρg⋅h⋅=where p is gage pressure and h is measured downwardsThe hydrostatic force on the gate is that on a rectangle of size L and width w.HenceFRpcA⋅=ρg⋅hc⋅A⋅=ρg⋅DL2sin 30 deg⋅()⋅+⎛⎝⎞⎠⋅L⋅w⋅=FR1000kgm3⋅9.81×ms2⋅1.532sin 30 deg⋅+⎛⎝⎞⎠×m⋅3×m⋅3×m⋅Ns2⋅kg m⋅×=FR199 kN⋅=The location of this force is given by y'ycIxxc⋅+=where y' and ycare measured along the plane of the gate to the free surface
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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.