Concept explainers
A steady, incompressible, two-dimensional (in the xy-plane) velocity field is given by
The acceleration at the point
Answer to Problem 23P
The acceleration of the flow is
Explanation of Solution
Given information:
Write the expression for the velocity field.
Here, the variables are
Write the expression for the velocity component along x direction.
Here, the variables are
Write the expression for the velocity component in y direction.
Here, the variables are
Write the expression for the acceleration of a flow along horizontal axis at point
Here, the velocity component in x direction is
Write the expression for the acceleration of a flow along vertical axis at point
Here, the velocity component in x direction is
Write the expression for the magnitude of the acceleration.
Here, the magnitude of the acceleration is
Write the expression for the vector notation of the acceleration.
Calculation:
Differentiate Equation (II) with respect to
Differentiate Equation (II) with respect to
Differentiate Equation (II) with respect to
Differentiate Equation (III) with respect to
Differentiate Equation (III) with respect to
Differentiate Equation (III) with respect to
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The acceleration of the flow is
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