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1. Show that the problem may be formulated in terms of the velocity potential (r, 0) satisfying r dr with the boundary conditions O - Ur cos0 = 0 dr Ir=R

1. Show that the problem may be formulated in terms of the velocity potential (r, 0) satisfying r dr with the boundary conditions O - Ur cos0 = 0 dr Ir=R

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 13E: Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii...
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Consider the problem of an irrotational and incompressible flow past a circular cylinder with radius R we treated in class. 1. Show that the problem may be formulated in terms of the velocity potential 6(r, 0) satisfying r dr with the boundary conditions O - Ur cos 0 = 0 dr r=R 2. Solve this equation by separation of variables, i.e. assuming that the potential (r, 0) can be written as o(r, 0) = f(r)g(0) and solving for f and g.
Transcribed Image Text:Consider the problem of an irrotational and incompressible flow past a circular cylinder with radius R we treated in class. 1. Show that the problem may be formulated in terms of the velocity potential 6(r, 0) satisfying r dr with the boundary conditions O - Ur cos 0 = 0 dr r=R 2. Solve this equation by separation of variables, i.e. assuming that the potential (r, 0) can be written as o(r, 0) = f(r)g(0) and solving for f and g.
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