Unformatted text preview: Due: In class, Friday October 12, 2007 Name For instructor or TA use only: Problem Score Points 1 15 2 15 3 15 4 25 5 30 ME 521 Fall Semester, 2007 Homework Set # 6 Professor J. M. Cimbala Total: 100 1 . (15 pts) Text problem 3.2 . Do two parts: ( a ) Find an appropriate definition for stream function ψ as asked for in the text problem. ( b ) Show that ψ is indeed constant along a streamline. Hint : First show that in the x-R plane, u x / u R = dx / dR along a streamline. 2 . (15 pts) In class, we derived the differential continuity equation using Leibniz rule for a control volume. Derive this same equation, ( ) i i u t x ρ ρ ∂ ∂ + ∂ ∂ = , by instead considering the influx and outflux of mass through the surfaces of a small fluid element of dimensions ( dx 1 , dx 2 , dx 3 ). Use Taylor series expansions to first order. 3 . (15 pts) Text problem 5.2 . Assume that the atmospheric pressure (far away from the tornado) is 101,000 N/m 2 . For simplicity, assume very low Mach numbers such that the “incompressible” form of the Bernoulli equation applies, with...
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This note was uploaded on 07/23/2008 for the course ME 521 taught by Professor Cimbala during the Fall '07 term at Penn State.
- Fall '07