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# For the velocity field of Prob. 4?63, what relationship

ISBN: 9780071284219 39

## Solution for problem 60P Chapter 4

Fluid Mechanics | 2nd Edition

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Problem 60P

For the velocity field of  Prob. 4‒63, what relationship must exist between the coefficients to ensure that the flow field is incompressible?

PROBLEM: A general equation for a steady, two-dimensional velocity field that is linear in both spatial directions (x and y) is

Where U and V and the coefficients are constants. Their dimensions are assumed to be appropriately defined. Calculate the x- and y-components of the acceleration field.

Step-by-Step Solution:

Step 1:

Consider a steady flow in the two dimensional field. If the flow is incompressible the volumetric strain rate of the flow must be zero.

The given velocity field is

= = +----(1)

The components of velocity field are

= -----(2)

= -----(3)

Where  and  are constants.

The coefficients are and

Step 2:

The volumetric strain rate is defined as the rate of increase in volume of a fluid element per unit volume. The expression for volumetric strain given by the cartesian coordinate system is

=  = ++ ------(4)

Where  ,and  are the linear strain rates in the cartesian coordinates.

=

=

=

Step 3:

Assume that the flow is in two dimensional field

= = 0

Therefore the equation (4) can be written as

=  = +-----(5)

Step 4 of 5

Step 5 of 5

##### ISBN: 9780071284219

Fluid Mechanics was written by and is associated to the ISBN: 9780071284219. The answer to “For the velocity field of Prob. 4?63, what relationship must exist between the coefficients to ensure that the flow field is incompressible?PROBLEM: A general equation for a steady, two-dimensional velocity field that is linear in both spatial directions (x and y) is Where U and V and the coefficients are constants. Their dimensions are assumed to be appropriately defined. Calculate the x- and y-components of the acceleration field.” is broken down into a number of easy to follow steps, and 68 words. Since the solution to 60P from 4 chapter was answered, more than 262 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Fluid Mechanics, edition: 2. The full step-by-step solution to problem: 60P from chapter: 4 was answered by , our top Engineering and Tech solution expert on 07/03/17, 04:51AM. This full solution covers the following key subjects: Field, velocity, coefficients, equation, calculate. This expansive textbook survival guide covers 15 chapters, and 1547 solutions.

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