Unformatted text preview: ASE 362K, Assiment No 1 Thursday, January 25th, 2007 1) Reading Anderson, Chapter 1, sections 1.1 through 1.3. If your thermodynamics
could stand a brushup, read section 1.4 also. 2) In class today we basically “wrote down” the mass conservation, momentum and
energy equations, and discussed the physical meaning of each of the terms. I am making
the assumption that you have seen (and used) these equations in the past and that I am
simply doing an “action replay” to jog your memories back into gear. Now let’s test that
assumption. First, draw a suitable control volume, look at what goes in and out of the
control volume, what happens inside the control volume and on its surfaces, and derive
the three conservation equations in integral form for a 3—D, unsteady, inviscid ﬂow. In
other words, derive the equations given on slide 31 (mass conservation), slide 36
(momentum equation) and slide 42 (energy equation) of my Powerpoint introduction
which is now posted on Blackboard. Second, starting with the equations you have just
derived, obtain algebraic equations for steady, adiabatic 1D and quasi lD ﬂow. Finally, obtain the differential forms of the mass conservation, momentum and energy equations,
namely d(pu) = 0, dP = pudu and dh = udu. 3) The problems below require use of one or more of the conservation equations. Your
job is to decide which is/are needed for a given problem, and then solve it. (i) A pressure vessel lm3 in volume contains air at an initial pressure of 6
atmospheres (6.07 x 105 Nm'z) and at an initial temperature of 298K. Air is
discharged isothermally from the tank at the rate of 0.1m3/s. Assuming that the
discharged air has the same density as that of the air in the tank, ﬁnd an
expression for the time rate of change of density of the air in the tank. After 5
seconds, What is the rate of pressure decrease in the tank? Assume a perfect gas. (ii) Water ﬂows steadily past a porous ﬂat plate (below). Constant suction is applied
along the porous section. The velocity proﬁle at cd is given by ﬁwamt Calculate the mass ﬂow across section be. C V r"
J /"
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x q. .. Fﬁ—ff—TT F1"? FT i"? W ...
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 Spring '07
 DOLLING,D

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