Problem 3.56[Difficulty: 3]RyRxFRFnGiven:Geometry of lock systemFind:Force on gate; reactions at hingeSolution:Basic equationFRAp⌠⎮⎮⌡d=dpdhρg⋅=or, use computing equationFRpcA⋅=Assumptions:static fluid; ρ= constant; patmon other sideThe force on each gate is the same as that on a rectangle of sizehD=10 m⋅=andwW2 cos 15 deg⋅()⋅=FRAp⌠⎮⎮⌡d=Aρg⋅y⋅⌠⎮⎮⌡d=butdAw dy⋅=HenceFR0hyρg⋅y⋅w⋅⌠⎮⌡d=ρg⋅w⋅h2⋅2=AlternativelyFRpcA⋅=andFRpcA⋅=ρg⋅yc⋅A⋅=ρg⋅h2⋅h⋅w⋅=ρg⋅w⋅h2⋅2=Using given dataFR121000⋅kgm3⋅9.81×ms2⋅34 m⋅2 cos 15 deg⋅⋅×10 m⋅2×Ns2⋅kg m⋅×=FR8.63 MN⋅
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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.