Consider the incompressible, irrotational, 2D flow. wherethe stream function is given by:4 = 4241) determine the Velocity field and prove the flow isPhysically Possible and irrotutional₂) Calculate and graph (do not sketch) the streamlinepattern.3) find the velocity potential for this flow and graph thelines of constant potential on the same graph asthe streamlines.

Given: φ=4zy Solution: (a) The velocity field is given as : v=∂φ∂z=∂∂z(4zy)=4yw=-∂φ∂y=-∂∂y(4zy)=-4z…

Answered: Consider the incompressible,…

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

Consider the incompressible, irrotational, 2D flow. where
the stream function is given by:
4 = 424
1) determine the Velocity field and prove the flow is
Physically Possible and irrotutional
₂) Calculate and graph (do not sketch) the streamline
pattern.
3) find the velocity potential for this flow and graph the
lines of constant potential on the same graph as
the streamlines.

Expert Solution

Step 1

Given:

$φ = 4 z y$

Solution:

(a)

The velocity field is given as :

$v = \frac{\partial φ}{\partial z} = \frac{\partial}{\partial z} (4 z y) = 4 y w = - \frac{\partial φ}{\partial y} = - \frac{\partial}{\partial y} (4 z y) = - 4 z$

Thus, velocity filed is :

$V = 4 y j - 4 z k$

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