Question

The stream function in a two dimensional flow field is given by $\psi =x^2-y^2$ . The magnitude of the velocity at point (1,1) is

• A. 2
• B. 2$\sqrt{2}$
• C. 4
• D. 8

Answer 1

The correct option is B 2$\sqrt{2}$

Given data:
Stream function,
$\psi =x^2-y^2$
The velocity component u and v in the direction of x and y are given by
$u=-\frac{\partial \psi }{\partial y}=-\frac{\partial }{\partial y}(x^2-y^2)=2y$
$orv=\frac{\partial \psi }{\partial x}=\frac{\partial }{\partial x}(x^2-y^2)=2x$
$Thevelocityatpoint(1,1)$
$\overrightarrow{V}=u\hat{i}+V\hat{j}=2y\hat{i}+2x\hat{j}$
$=2\times 1\hat{i}+2\times 1\hat{j}=2\hat{i}+2\hat{j}$
The magnitude of the velocity,
$V=\sqrt{{\left(2\right)}^2+{\left(2\right)}^2}=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}$