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hw3_alternate_solutions - Chapter 3 Solution 70 Two parts...

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Chapter 3, Solution 70. Two parts of a water trough of semi-circular cross-section are held together by cables placed along the length of the trough. The tension T in each cable when the trough is full is to be determined. Assumptions 1 The atmospheric pressure acts on both sides of the trough wall, and thus it can be ignored in calculations for convenience. 2 The weight of the trough is negligible. Properties We take the density of water to be 1000 kg/m 3 throughout. Analysis To expose the cable tension, we consider half of the trough whose cross-section is quarter-circle. The hydrostatic forces acting on the vertical and horizontal plane surfaces as well as the weight of the liquid block are: Horizontal force on vertical surface: N 3679 m/s kg 1 N 1 m) 3 m m)(0.5 2 / 5 . 0 )( m/s 81 . 9 )( kg/m 1000 ( ) 2 / ( 2 2 3 = × = = = = = A R g A gh A P F F C ave x H ρ ρ The vertical force on the horizontal surface is zero, since it coincides with the free surface of water. The weight of fluid block per 3-m length is N 5779 m/s kg 1
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