Answered: what are velocity components,potential…

Refrigeration and Air Conditioning Technology (MindTap Course List)

8th Edition

ISBN:9781305578296

Author:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson

Publisher:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson

Chapter31: Gas Heat

Section: Chapter Questions

Problem 38RQ

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Question

what are velocity components,potential function and stream function?

Uo=1m,teta=pi/6,r=1m,r0(zero)=1.25r

Expert Solution

Step 1

Stream Function $\to$ for 2D flow and 3D axial symmetric flows stream functions are defined. stream functions are used to draw the streamlines of the flow and to find velocity.

In general notations, it is represented as $ψ$

for steady flow $ψ$ = f(x,y)

In cartesian coordinates, velocity components can be calculated by

$u = - \frac{\partial ψ}{\partial γ}$

v = $\frac{\partial ψ}{\partial χ}$

Step 2

Velocity Potential Function $\to$ It may be defined as a scalar function of space and time so that its partial derivative in any of the directions gives the value of fluid velocity in that particular direction.

In general notations, it is denoted by $\emptyset$ .

for steady flow $\emptyset$ = f(x,y,z)

u = $- \frac{\partial \emptyset}{\partial x}$

v = $- \frac{\partial \emptyset}{\partial γ}$

w = $- \frac{\partial \emptyset}{\partial z}$

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