ME330_S07_HWSet3D - ME 330 Fluid Mechanics Department of...

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ME 330 Fluid Mechanics Spring 2007 Department of Engineering Western Kentucky University CHAPTER 3D HW - Homework Solutions Problem #’s 3-73, 3-85, and 3-88, Due February 16, 2007 3-73 Solution A retaining wall against mud slide is to be constructed by rectangular concrete blocks. The mud height at which the blocks will start sliding, and the blocks will tip over are to be determined. Assumptions Atmospheric pressure acts on both sides of the wall, and thus it can be ignored in calculations for convenience. Properties The density is given to be 1800 kg/m 3 for the mud, and 2700 kg/m 3 for concrete blocks. Analysis ( a ) The weight of the concrete wall per unit length ( L = 1 m) and the friction force between the wall and the ground are N 1271 ) N 4238 ( 3 . 0 N 4238 m/s kg 1 N 1 ) m 1 8 . 0 2 . 0 )[ m/s 81 . 9 )( kg/m 2700 ( block friction 2 3 2 3 block = = = = × × = = W F g W μ ρ V The hydrostatic force exerted by the mud to the wall is ( ) () ( ) avg 32 2 2 2 1 N 1800 kg/m 9 81 m/s 2 (1 ) 1 kg m/s 8829 N Hx C FF P Ag h h / A .h / h h ρρ == = = ⎛⎞ ⎜⎟ ⎝⎠ = Setting the hydrostatic and friction forces equal to each other gives m 0.38 = = = h h F F H 1271 8829 2 friction ( b ) The line of action of the hydrostatic force passes through the pressure center, which is 2 h /3 from the free surface. The line of action of the weight of the wall passes through the
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ME330_S07_HWSet3D - ME 330 Fluid Mechanics Department of...

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