General Problems Consider a steady 2-D flow (Vz-0) in a pipe where the radial velocity component is ven by: (r2-1) cos 0 Determine: 1) The corresponding tangential velocity component ve, where ve -0 at r-0. 2) The corresponding stream function if it exists 3) The shear force per unit length of the pipe. Where does this force vanishes? ditione for a stagnate flow

Elements Of Electromagnetics
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General Problems
Consider a steady 2-D flow (Vz - 0) in a pipe where the radial velocity component is gven
by:
(p2 - 1) cos 0
vr
Determine:
1) The corresponding tangential velocity component ve, where ve -0 at r-0.
2) The corresponding stream function if it exists
3) The shear force per unit length of the pipe. Where does this force vanishes?
4) The conditions for.a stagnate flow.
5) Prove that the flow is rotational
6) The conditions for a potential flow. As a result find:
a) The velocity potential field
b) The pressure drop, in function of r, p and U, from an upstream point in the flow to a
point near the surface of the cylinder. U is the free stream velocity of the upstream
flow.
c) The particle acceleration. For what value(s) of r, do this acceleration vanish? Interpret
your result.
7) How do you interpret the result of part (3) and (6)? What do you conclude
Transcribed Image Text:General Problems Consider a steady 2-D flow (Vz - 0) in a pipe where the radial velocity component is gven by: (p2 - 1) cos 0 vr Determine: 1) The corresponding tangential velocity component ve, where ve -0 at r-0. 2) The corresponding stream function if it exists 3) The shear force per unit length of the pipe. Where does this force vanishes? 4) The conditions for.a stagnate flow. 5) Prove that the flow is rotational 6) The conditions for a potential flow. As a result find: a) The velocity potential field b) The pressure drop, in function of r, p and U, from an upstream point in the flow to a point near the surface of the cylinder. U is the free stream velocity of the upstream flow. c) The particle acceleration. For what value(s) of r, do this acceleration vanish? Interpret your result. 7) How do you interpret the result of part (3) and (6)? What do you conclude
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