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For the velocity field of Prob. 4?63, calculate the linear

Chapter 4, Problem 61P

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QUESTION:

Problem 61P

For the velocity field of Prob. 463, calculate the linear strain rates in the x- and y-directions.

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.

Questions & Answers

QUESTION:

Problem 61P

For the velocity field of Prob. 463, calculate the linear strain rates in the x- and y-directions.

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.

ANSWER:

Solution to 61P

Step 1

We need to find the linear strain rates for the given velocity field:

Velocity field is given as :

Where, u and v are material velocity components, a and b are arbitrary constants, x and y are coordinates.

The linear strain rates are given by,

U and v are velocity components.

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