Answered: what are velocity components,potential…

Precision Machining Technology (MindTap Course List)

2nd Edition

ISBN:9781285444543

Author:Peter J. Hoffman, Eric S. Hopewell, Brian Janes

Publisher:Peter J. Hoffman, Eric S. Hopewell, Brian Janes

Chapter2: Measurement, Materials, And Safety

Section2.6: Metal Composition And Classification

Problem 14RQ: What is (are) the major alloying element(s) of 6061 aluminum?

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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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