ME330_S07_HWSet3C

# ME330_S07_HWSet3C - ME 330 Fluid Mechanics Department of...

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ME 330 Fluid Mechanics Spring 2007 Department of Engineering Western Kentucky University CHAPTER 3C HW - Homework Solutions Problem #’s 3-66, 3- 68E and 3-70, Due February 9, 2007 3-66 Solution A rectangular plate hinged about a horizontal axis along its upper edge blocks a fresh water channel. The plate is restrained from opening by a fixed ridge at a point B . The force exerted to the plate by the ridge is to be determined. Assumptions Atmospheric pressure acts on both sides of the plate, and thus it can be ignored in calculations for convenience. Properties We take the density of water to be 1000 kg/m 3 throughout. Analysis The average pressure on a surface is the pressure at the centroid (midpoint) of the surface, and is determined to be () ( ) avg 32 2 2 2 1 kN 1000 kg/m 9 81 m/s 4 2 m 19 62 kN/m 1000 kg m/s CC PP g h g ( h / ) ./ . ρρ == = ⎛⎞ ⎜⎟ ⎝⎠ Then the resultant hydrostatic force on each wall becomes 2 avg 19 62 kN/m 4 m 5 m 392 kN R FP A . × = The line of action of the force passes through the pressure center, which is 2 h /3 from the free surface, m 2.667 3 m) 4 ( 2 3 2 = × = = h y P Taking the moment about point A and setting it equal to zero gives AB F y s F M P R A ridge ) ( 0 = + = Solving for F

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ME330_S07_HWSet3C - ME 330 Fluid Mechanics Department of...

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