Question

If the stream function $\psi =3x^2-y^3$, what is the magnitude of velocity at point (2,2)?

• A. 9
• B. 13
• C. 15
• D. 17

Answer 1

The correct option is D 17

Stream function,$\psi =3x^2-y^3$

$\therefore \frac{\partial \psi }{\partial x}=6xand\frac{\partial \psi }{\partial y}=-3y^2$

$Butu=-\frac{\partial \psi }{\partial y}$

$=-(-3y^2)=3\times 2^2=12$

$v=\frac{\partial \psi }{\partial x}=6x=6\times 2=12$

$\therefore$ Resultant velocity $=\sqrt{u^2+v^2}$

$=\sqrt{{\left(12\right)}^2+{\left(12\right)}^2}=\sqrt{288}$
= 16.97 = 7