Question

A fluid flow is represented by the velocity field $\overrightarrow{V}$$=ax\hat{i}+ay\hat{j}$, where a is a constant. The equation of stream line passing through a point (1,2) is

• A. x-2y=0
• B. 2x+y=0
• C. 2x-y=0
• D. x+2y=0

Answer 1

The correct option is C 2x-y=0

Given:
$\overrightarrow{V}$$=ax\hat{i}+ay\hat{j}$

i.e., u = ax and v = ay
Equation of stream line is given by

$\frac{dx}{u}=\frac{dy}{v}$

$\therefore \frac{dx}{ax}=\frac{dy}{ay}$

$or\frac{dx}{x}=\frac{dy}{y}$

Integrating both sides,we get
Inx = Iny+Inc
(where c is constant of integration)
$\therefore$ x = cy
Since the stream line passed through point (1,2),
therefore
1 = 2c
c = 1/2
Hence equation of stream line is

$x=\frac{1}{2}y$

or 2x-y = 0