Concept explainers
Converging duct flow is modeled by the steady, two-dimensional velocity field of Prob. 4-16. As vertical line segment AB moves downstream it shrinks from length
The expression for the change in the length of the line segment.
Answer to Problem 55P
The expression for the change in the length of the line segment is
Explanation of Solution
Given information:
Initially fluid particle is located at
Write the expression for the two-dimensional velocity field in the vector form.
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 y 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.
Calculation:
Substitute
Integrate the Equation (VIII).
Substitute
Substitute
Substitute
Substitute
Conclusion:
The expression for the change in the length of the line segment is
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Chapter 4 Solutions
Fluid Mechanics Fundamentals And Applications
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