Which of the following satisfies the Laplace Equation?

Question

Question

This question was previously asked in

JKSSB JE Civil 20 March 2022 Official Paper

Answer 1

Explanation:

Velocity potential (ϕ) satisfied the Laplace equation only if it represents the flow field. This can be proved in the following way:

By definition of ϕ:

u = - δϕ/δx and v = - δϕ/δy

If ϕ represents the flow field, then it must satisfy the continuity equation i.e.

δu/δx + δv/δy = 0

or

Substitute the values of u and v in the above continuity equation, we get the Laplace Equation.

\(\frac{\delta^2\phi}{\delta x^2} + \frac{\delta^2\phi}{\delta y^2} = 0\)

Note:

Stream function satisfied the Laplace equation only in the case of irrotational flow.