hw6_Sol - The University of Michigan Department of...

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Unformatted text preview: The University of Michigan Department of Mechanical Engineering ME 320 - Section 1 Homework #6 - Due Friday October 24, 2008 by 10:00am Problem 1: Problems 5.41 and 5.51 of the text. Problem 2: (a) Problem 5.40 of the text. (b) The results of a wind tunnel test to determine the drag on a body are summarized below. The upstream (section 1) velocity is uniform at 100 ft/s. The static pressures are given by p1 = p2 = 14.7 psia. The downstream velocity distribution, which is symmetrical about the centerline is given by u = 100 - 30 1 - u = 100 |y| 3 | y | 3ft | y |> 3ft where u is the velocity in ft/s and y is the distance on either side of the centerline in feet. Assume that the body shape does not change in the direction normal to the paper. Calculate the drag force (reaction force in x direction) exerted on the air by the body per unit length normal to the plane of the sketch. Problem 3: (a) Problems 5.56 and 5.58 of the text. (b) A cart which can roll freely in the x-direction deflects water from a parallel jet (in the x-direction) into its tank with a vane inclined at an angle . The jet issues steadily at a speed V with density and has cross-sectional area A. The cart is initially at rest with a mass mo . (a) Formulate a differential expression governing the mass, m(t), of the cart plus the fluid in the cart as a function of time. (b) Solve this equation and find m(t). Problem 4: (a) Problems 5.50 and 5.60 of the text. (b) A jet of water strikes a disk of mass M from below. The jet leaves the nozzle at speed Vo and area Ao . Obtain a differential equation for the disk height above the jet exit plane, h(t), assuming the disk is released from an initial height of H. What is the equilibrium position of the disk, ho ? Sketch h(t) and explain why your sketch is as you show it. r, V,A jet m(t) q x Problem 5: A plastic toy rocket is propelled by a jet of water forced out of the nozzle by compressed air. As a first approximation, assume that the water speed in the rocket chamber is given by V = Vo - kt. The chamber and exit areas are Ac and Ae , respectively. The area ratio is approximately Ae /Ac = 0.10. Assume the initial mass of the rocket is Mo and neglect the mass of the air. Find (a) the velocity of the water at the nozzle exit, (b) the mass of the rocket, M (t), and (c) the acceleration of the rocket as a function of time. ...
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