Concept explainers
The expression for the linear strain rate in the x direction.
Answer to Problem 53P
The expression for the linear strain rate in x direction is
Explanation of Solution
Given information:
The fluid particle is located on the centre line.
Write the expression for the two-dimensional velocity field in the
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 x 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 strain rate in x direction.
Write the expression for
Calculation:
Substitute
Integrate the Equation (X).
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The expression for strain rate in x direction is
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Chapter 4 Solutions
Fluid Mechanics: Fundamentals and Applications
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