Concept explainers
The rate of rotation of a fluid element and the shear strain rate of the element located at y.
Explanation of Solution
Draw the schematic representation of velocity distribution as in Figure (1).
Calculation:
Consider the steady flow of an ideal fluid. According to the velocity profile in Figure 1,
Here, h is the depth of water below the top plate and U is the constant velocity of the top plate.
The velocity, v, perpendicular to the direction of flow is zero.
Write the expression for the rate of rotation of a fluid element.
Here,
Substitute
The negative value of the rate of rotation represents an anticlockwise rotation.
Write the mathematical expression for the rate of shear strain.
Therefore, the rate of rotation of a fluid element is
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Chapter 7 Solutions
Fluid Mechanics (2nd Edition)
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