Flow over a sphere is given by the superposition of uniform flow and 3D doublet flow. In cylindrical coordinates the flow resembles that pictured below. See Lecture Pack 3 for more information on vector operations in polar and cylindrical coordinates. Uniform flow in the z direction is o = Uz. Doublet flow is U„R®z 2(r2 + z?)3/2 where R is the radius of the sphere. 1. Calculate ur, uo, and uz as functions ofr and z for superposed uniform and doublet flow. 2. Show that r= 0, z = +R are stagnation points.

Flow over a sphere is given by the superposition of uniform flow and 3D doublet flow. In cylindrical coordinates the flow resembles that pictured below. See Lecture Pack 3 for more information on vector operations in polar and cylindrical coordinates. Uniform flow in the z direction is o = Uz. Doublet flow is U„R®z 2(r2 + z?)3/2 where R is the radius of the sphere. 1. Calculate ur, uo, and uz as functions ofr and z for superposed uniform and doublet flow. 2. Show that r= 0, z = +R are stagnation points.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

Flow over a sphere is given by the superposition of uniform flow and 3D doublet flow. In
cylindrical coordinates the flow resembles that pictured below. See Lecture Pack 3 for more
information on vector operations in polar and cylindrical coordinates. Uniform flow in the
z direction is o = Uz. Doublet flow is
U„R³z
+ z2
where R is the radius of the sphere.
1. Calculate ur, uo, and uz as functions of r and z for superposed uniform and doublet
flow.
2. Show thatr 0, z ±R are stagnation points.

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