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# HW5 - upward to inﬁnity and had width L as shown below...

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MAE 150A, Winter 2009 J. D. Eldredge Homework 5 (4 problems + 2 OPTIONAL), due Friday, February 20 1. Problem 12.4, Wilcox 2. Problem 13.21, Wilcox. 3. Problem 13.23, Wilcox. 4. Two thin layers of viscous fluids flow down an inclined wall at angle β , as shown below. The lower fluid has density ρ 1 and dynamic viscosity μ 1 , and its layer has thickness δ 1 . The upper fluid has density ρ 2 and viscosity μ 2 , and its thickness is δ 2 . The upper layer is exposed to air, which exerts negligible shear stress on the fluid. Derive an expression for the velocity in the lower layer (you don’t need to solve for the velocity in the upper layer). β x y g ρ 1 , μ 1 δ 1 δ 2 ρ 2 , μ 2 Air p 5. (OPTIONAL 1) In the Rayleigh problem, consider a closed ‘box’ that extends from the wall
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Unformatted text preview: upward to inﬁnity and had width L as shown below. Show that the circulation about this box does not change with time. What is the signiﬁcance of this in terms of the vorticity creation? What would be diﬀerent (in terms of vorticity creation) if the velocity of the wall was changing in time? L U ∞ 6. (OPTIONAL 2) Explain, with words and equations, why potential ﬂow theory cannot be used to describe a rotating cylinder whose rate of rotation is changing in time. In particular, try to connect this problem with the Rayleigh problem....
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