# HW2 - MAE 150A, Winter 2009 J. D. Eldredge Homework 2 (5...

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MAE 150A, Winter 2009 J. D. Eldredge Homework 2 (5 problems + 1 OPTIONAL), due Friday, January 23 1. Problem 4.23, Wilcox (4.24 in 2nd edition). 2. A vortex has a velocity distribution given by u = u θ e θ , where u θ = Γ 2 πr ± 1 - e - r 2 2 ² and Γ and σ are constant. (a) Find the vorticity ﬁeld corresponding to this velocity (see Wilcox § D.2 for vorticity in cylin- drical coordinates). (b) Accurately plot both u θ and ω versus r (taking Γ = 1 and σ = 1 for simplicity). Using Matlab or some other mathematical software is recommended. (c) Estimate the value of r (to two decimal places) at which u θ is maximum (again, σ = 1). 3. A spherical air bubble in an incompressible ﬂuid has a radius R ( t ) that changes with time. Using the integral form of conservation of mass, ﬁnd the radial velocity u r ( r ) in the ﬂuid outside the bubble, in terms of R and dR/dt . (Hint: consider a spherical control volume with an inner wall just outside the bubble, and an outer wall at distance

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## This note was uploaded on 10/09/2009 for the course MAE 150A taught by Professor Eldridge during the Spring '09 term at UCLA.

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HW2 - MAE 150A, Winter 2009 J. D. Eldredge Homework 2 (5...

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