Question

A two-dimensional unsteady flow has the velocity components given by u = x / (1 + t) and v = y / (1 + 2t)

Find the equation of the streamlines of this flow which pass through the point (xo, yo) at time t = 0.

Answer 1

Given data :-

• Two dimensional unsteady flow
• Component of velocity in X direction is u = x/(1+t)
• Component of velocity in Y direction is v = y/(1+2t)
• Equation of stream line or the line of constant stream function at time t = 0 and passing hrough the point (x₀ ,y₀) = ?

Solution :-

Equation of stream line vdx - udy = 0

Or slope of stream line dy/dx = slope of v/u

  

At t = 0,

  

Integrating on both sides with limits (x₀, x) and (y₀, y) we get the equation of stream line,

ln(x-x0)=ln(y-y0)