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# A steady, incompressible, two-dimensional velocity field

ISBN: 9780071284219 39

## Solution for problem 18P Chapter 4

Fluid Mechanics | 2nd Edition

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Problem 18P

A steady, incompressible, two-dimensional velocity field is given by the following components in the xy-plane:

Calculate the acceleration field (find expressions for acceleration components a x and a y), and calculate the acceleration at the point(x, y) = (-1, 2).

Step-by-Step Solution:

Step 1:

The two dimensional velocity field for a steady, incompressible flow in the xy plane

= ----(1)

= -----(2)

Step 2:

To calculate the acceleration field components and

Calculating x component

=  +  +  + ----(3)

Since t and w are not given in the velocity field, they get cancelled

= 0 ; = 0

Step 3:

=

=

=

=

Step 4:

Substituting derived values

=  +

= +

= ----(4)

Step 5 of 7

Step 6 of 7

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