Concept explainers
Combine your results from Prob. 4—100 to form the two-dimensional strain rate tensor in the xy-plane,
The two-dimensional strain rate tensor
Answer to Problem 101P
The two-dimensional strain rate tensor
Explanation of Solution
The given figure represents Poiseuille flow between two plates.
Figure-(1)
Write the expression for two-dimensional strain rate tensor along
Here, the strain rate tensor is
Write the expression for the velocity component along
Here, the velocity along
Write the expression for the velocity component is
Write the expression for linear strain rate along the
Substitute
Write the expression for linear strain rate along the
Substitute 0 for v in the Equation (V).
Write the expression for shear strain rate in
Write the expression for shear strain rate in
...... (VII)
Differentiate Equation (II) with respect to
Differentiate Equation (III) with respect to
Calculation:
Substitute
Substitute
Substitute
Therefore, the two-dimensional strain rate tensor
Conclusion:
The two-dimensional strain rate tensor
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Chapter 4 Solutions
Fluid Mechanics: Fundamentals and Applications
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