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# Consider a steady, two-dimensional flow field xy-plane

## Problem 110P Chapter 4

Fluid Mechanics | 2nd Edition

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Problem 110P Problem 110PConsider a steady, two-dimensional flow field xy-plane whose x-component of velocity is given bywhere a, b,and care constants with appropriate dimensions. Of what form does the y-component of velocity need to be in order for the flow field to be incompressible? In other words, generate an expression for v as a function of x,y, and the constants of the given equation such that the flow is incompressible.
Step-by-Step Solution:

Solution 110P

Step 1 of 4</p>

The x- component of the velocity of the two dimensional steady flow field in xy plane is given, we need to find the expression for y component of velocity such that the flow field is incompressible.

The x component of the velocity is given to be,

………...1

Where a , b and c are constants.

Step 2 of 4</p>The volumetric strain is defined as the ratio of change in volume to original volume or the unit change in volume and is related to linear strain rate for two dimension as,

………..2

Where linear strain rates along x and y direction is        and respectively.

In the given case, as the flow is incompressible, the volumetric strain rate must be zero

That is

Also

Step 3 of 4

Step 4 of 4

##### ISBN: 9780071284219

This textbook survival guide was created for the textbook: Fluid Mechanics, edition: 2. Since the solution to 110P from 4 chapter was answered, more than 260 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 110P from chapter: 4 was answered by , our top Engineering and Tech solution expert on 07/03/17, 04:51AM. The answer to “Consider a steady, two-dimensional flow field xy-plane whose x-component of velocity is given by where a, b,and care constants with appropriate dimensions. Of what form does the y-component of velocity need to be in order for the flow field to be incompressible? In other words, generate an expression for v as a function of x,y, and the constants of the given equation such that the flow is incompressible.” is broken down into a number of easy to follow steps, and 68 words. This full solution covers the following key subjects: flow, constants, incompressible, velocity, given. This expansive textbook survival guide covers 15 chapters, and 1547 solutions. Fluid Mechanics was written by and is associated to the ISBN: 9780071284219.

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Consider a steady, two-dimensional flow field xy-plane

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