The expression for velocity component
Answer to Problem 94P
The expression for velocity component
Explanation of Solution
Given information:
The flow is steady, laminar, two-dimensional and incompressible. The flow is rotationally symmetric means nothing is function of coordinate
The inner cylinder is fixed and angular speed of outer cylinder is
Write the expression for continuity equation.
Here, velocity components are
Write the expression for the
Here, density is
Calculation:
Substitute
Since both sides of Equation (IV) are equal, therefore continuity equation is verified.
Substitute
Change from partial derivative to total derivative in Equation (V).
Integrate Equation (VI) with respect to
Here arbitrary constant is
Again, Integrate Equation (VII) with respect to
Here, arbitrary constant is
Substitute
Substitute
Substitute
Substitute
Conclusion:
The expression for velocity component
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