Question

If the Laplace equation is satisfied by the velocity potential, then the fluid flows.

(a) True

(b) False

The question was asked in homework.

My question is from The Velocity Potential Equation in portion Velocity Potential Equation of Aerodynamics

Answer 1

Right choice is (a) True

For explanation: For the fluid to flow, it is essential for the velocity potential ϕ to satisfy the Laplace equation. If the condition is not met, the fluid does not flow and has zero velocity.

Thus, the condition for the fluid to flow is:

\(\frac {∂^2 ϕ}{∂x} + \frac {∂^2 ϕ}{∂y} + \frac {∂^2 ϕ}{∂z}\) = 0

Or

∇^2ϕ = 0