A fluid flow is represented by the velocity field = axî

Home » Fluid Mechanics and Hydraulic Machinery » Fluid Mechanics and Hydraulic Machinery Miscellaneous » Question

A fluid flow is represented by the velocity field = ax_î + ay_ĵ, where a is a constant. The equation of stream line passing through a point (1, 2) is

1. x – 2y = 0
2. 2x + y = 0
3. 2x – y = 0
4. x + 2y = 0

Correct Option: C

Given: u_x = ax and u_y = ay
Equation of steam line is,

du	=	dy
u_x	=	u_y

⇒	du	=	dy
	ux		uy

Integrating both sides, we have
log(ax) = log(ay) + log c
or ax = c'ay
or x = cy
Since the steam line is passed through point (1, 2), therefore
1 = 2c

⇒ c =	1
	2

∴ x =	y
	2

Hence equation of steam line is
2x – y = 0.