Concept explainers
Assuming the velocity field given in Problem 2.6 pertains to an incompressible flow, calculate the stream function and velocity potential. Using your results, show that lines of constant
To find:
The stream function and velocity potential for the given velocity functions and to prove it’s perpendicularity.
Answer to Problem 2.11P
Equation of the velocity potential is
Equation of the stream function is
Explanation of Solution
Given:
The horizontal and vertical velocity component of velocity is given as below ( problem 2.6).
Stream function and velocity potential has to be found and prove perpendicularity of the stream function and velocity potential.
Stream function:
The equation of the stream function is given as follows:
Equation of the stream function is
Velocity potential:
The equation of the velocity potential is given as follows:
Equation of the stream function is
Proof of the perpendicularity:
Differentiate equation (2) and (3) with respect to x keeping φ and ψ constant.
Similarly,
Compare equations 7 and 9.
Hence,the stream function and velocity potential are perpendicular to each other.
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Chapter 2 Solutions
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