HW1 - ASE 362K Assiment No 1 Thursday January 25th 2007 1...

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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 brush-up, 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 1-D and quasi l-D 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 /" """""""" }':3 5 1);:3Ml8 ”3 / / C f———9 WloiHn / Tar—7 1. / : x q. .. Ffi—ff—TT F1"? FT i"? W ...
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