University The of Michigan
Department of Mechanical Engineering
ME 320 - Sections 1 & 2
Homework #6 - Due Friday October 28, 2010 by 5:00pm
Problem 1: Problems 5.48, 5.66 and 5.70 of the text.
Problem 2:
(a) Problem 5.60 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 5.42 of the text.
(b) A cart which can roll freely in the x-direction deects 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 dierential expression governing the mass, m(t), of the cart plus uid the in
the cart as a function of time. (b) Solve this equation and nd m(t).
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x
Problem 4:
(a) Problems 5.51 and 5.52 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 dierential 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.
Problem 5:
(a) Problems 5.56 and 5.67 of the text.
(b) A plastic toy rocket is propelled by a jet of water forced out of the nozzle by compressed
air. As a rst 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.