
(a)
The value of function f(y) for which the laplacian of F is zero.

Answer to Problem 8.5P
The value of function f(y) for which the laplacian of F is zero.
Explanation of Solution
Given Information:
A harmonic function F(x, y, z):
F=2x2 +y3 -4xz+f(y)
Concept Used:
First, we must find the suitable f(y) which makes
Calculation:
Conclusion:
The value of function f(y) for which the laplacian of F is zero is F=2x2 -2y2 -4xz+
Here
(b)
The given function can be served as velocity potential function.

Answer to Problem 8.5P
The given function can be served as a velocity potential function as
Explanation of Solution
Given Information:
A harmonic function F(x, y,z): F=2x2 +y3 -4xz+f(y)
Concept Used:
For a function to be velocity potential the required condition is:
Calculation:
Conclusion:
The given function can be served as a velocity potential function as
But the given function may not be a realistic flow pattern.
(c)
The given function can be served as velocity potential function.

Answer to Problem 8.5P
The given function cannot be served as a stream function due to having three dimensional function.
Explanation of Solution
Given Information:
A harmonic function F(x, y, z): F=2x2 +y3 -4xz+f(y)
Concept Used:
For a function to be stream function the required condition is that the function should not be three dimensional.
Calculation:
Conclusion:
The given function is not a stream function as it is three dimensional.
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Chapter 8 Solutions
Fluid Mechanics
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