Topic: Fluid Mechanics
A stream function is given by Ψ = 4x - 3y. The resultant velocity at any point is
- A. 7.81 units/s
- B. 7 units/s
- C. 3.5 units/s
- D. 5 units/s
Answer: D. 5 units/s
Explanation: The velocity components derived from the stream function are u = -(∂Ψ/∂y) = -(-3) = 3 and v = (∂Ψ/∂x) = 4. The resultant velocity V is the vector sum magnitude: V = $\sqrt{u² + v²}$ = $\sqrt{3^2 + 4^2}$ = $\sqrt{25}$ = 5 units/s.