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A general equation for a steady, two-dimensional velocity

Chapter 4, Problem 59P

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QUESTION:

Problem 59P

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.

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QUESTION:

Problem 59P

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.

ANSWER:

Step 1:

        Consider a two dimensional steady state flow of fluid. The equation of velocity field is

        = = + ------(1)

        The components of velocity field are

 = -----(2)

         = -----(3)

        Where U and V  and coefficients (a,b) are constants

        To calculate the acceleration field of the flow by interpreting the velocity field

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