Concept explainers
Using the results of Prob. 4—57 and the fundamental definition of linear strain rate (the rate of increase in length per unit length), develop an expression for the linear strain rate in the y-direction
The expression for the linear strain rate in y direction.
Answer to Problem 58P
The expression for the linear strain rate in y direction is
Explanation of Solution
Given information:
The general strain in y direction is
Write the expression for the two-dimensional velocity field in the vector form.
Here, the horizontal speed is
Write the expression for the velocity component along x direction.
Here, the variable is
Write the expression for the velocity component along x direction.
Here, the variable is
Write the expression for the velocity in y direction in differential form.
Write the expression for the initial length.
Here, the initial location of A is
Write the expression for the final length.
Here, the final location of A is
Write the expression for the change in lengths.
Write the expression for the linear strain rate in y direction.
Write the expression for the
Calculation:
Substitute
Integrate the Equation (X).
Substitute
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Substitute
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Substitute
Conclusion:
The expression for the linear strain rate in y direction is
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Chapter 4 Solutions
Fluid Mechanics: Fundamentals and Applications
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