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

Chapter 4, Problem 110P

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QUESTION: 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.

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QUESTION: 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.

ANSWER:

Solution 110P

Step 1 of 4

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.

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