Spring 08 HW 8

# Spring 08 HW 8 - CEE 3304 Spring 2008 CEE 3304 Spring 2008...

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Unformatted text preview: CEE 3304 Spring 2008 CEE 3304, Spring 2008, HW#8 by: Amr A. El-Sayed 1 HW #8 Momentum Equation Problem 6.6 Given: Horizontal round jet strikes a plate. Water at 70 o F, ρ = 1.94 slug/ft 3 , Q = 2 cfs. Horizontal component of force to hold plate stationary: R x = 200 lb. Find : Speed of water jet: v Momentum Equations: X-direction: ( ) ( ) ( ) j in x out x x V Q QV QV F − = − = ∑ ρ ρ ρ j x QV R ρ − = − . 2 94 . 1 200 × = = Q R V x j ρ Vj = 51.5464 fps R x CEE 3304 Spring 2008 CEE 3304, Spring 2008, HW#8 by: Amr A. El-Sayed 2 Problem 6.8 Given : An engineer is designing a toy to create a jet of water. Force F 1 is the force needed to move the piston. Force F 2 is the force to hold the handle stationary. Cylinder diameter is D = 80 mm. Nozzle diameter is d = 15 mm. Piston speed is V(piston) = 300 mm/s. Find : (a) Which force (F 1 versus F 2 ) is larger? Explain your answer using concepts of the momentum principle. (b) Calculate F 1 . (c) Calculate F 2 . Assumptions: 1) Neglect friction between the piston and the wall. 2) Assume the Bernoulli equation applies (neglect viscous effects; neglect unsteady flow effects). Properties: Table A.5 (water at 20 ◦ C): ρ = 998 kg/m 3 . F V V 1 1 2 F 2 V 1 = velocity of the piston = 300 mm/s = 0.3 m/s Continuity equation: 2 2 1 1 V A V A = Î 2 2 2 1 2 1 4 4 V d V D π π = CEE 3304 Spring 2008 CEE 3304, Spring 2008, HW#8 by: Amr A. El-Sayed 3 s m V d D V / 533 . 8 30 . 15 80 2 2 1 2 2 2 1 2 = × = = 533 . 8 4 015 . 2 2 2 × × = = π V A Q = 0.001508 m 3 /s Finding the larger force (F 1 versus F 2 ): Since the fluid is accelerating to the right, the net force must act to the right. Thus, F 1 is larger than F 2 . This can also be seen by applying the momentum ....
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Spring 08 HW 8 - CEE 3304 Spring 2008 CEE 3304 Spring 2008...

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