homework3_solns - Homework 3 Fluid Mechanics CE 3502 Fall,...

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Homework 3 Fluid Mechanics CE 3502 Fall, 2008 (1) Water strikes a block as shown and is deflected 30°. The flow rate of the water is 1.50 kg/s, and the mass of the block is 1.30 kg. The coefficient of static friction between the block and the surface is 0.100 (friction force / normal force). If the force parallel to the surface exceeds the frictional force, the block will move. Find the maximum initial velocity (V) such that the block will not slip. Neglect the weight of the water. Find: maximum initial water velocity (V) such that the block will not slip. Solution: Use conservation of momentum for the stationary control volume with control surface as shown: Force / Free body diagram Momentum diagram W block F normal F friction 30° V m & V m & Conservation of momentum in the x direction: () + ρ = CS IN x CS OUT x CV x x v m v m V d v F & & For the one inlet and outlet, as shown, V IN = V OUT , so given the information in the drawing: v x,IN = V, and v x,OUT = Vcos30° There is no accumulation in the control volume, so ( ) ( ) ( ) V 2 3 1 s / kg 50 . 1 F V s / kg 50 . 1 2 3 V s / kg 50 . 1 0 F friction friction = + = Conservation of momentum in the y direction: + ρ = CS IN y CS OUT y CV y y v m v m V d v F & & v y,IN = 0, and v y,OUT = Vsin30°, and there is no accumulation in the control volume, so ( ) ( )( ) ( ) N 75 . 12 V s / kg .75 0 s / m 81 . 9 kg 30 . 1 V s / kg .75 0 F 2 / 1 V s / kg 50 . 1 0 W F 2
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This note was uploaded on 06/09/2010 for the course CIVIL 3502 taught by Professor Kimberlyhill during the Fall '08 term at University of Minnesota Crookston.

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homework3_solns - Homework 3 Fluid Mechanics CE 3502 Fall,...

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