A two- dimensional flow field is defined as \(\vec V = \vec ix - \vec jy\) the equation of the streamline passing through the point (1, 2) is 

Concept:

Streamline: It is the line along which stream function ψ remains constant.

If ψ = f (x,y)

dψ = 0

\(d\psi = \frac{{\partial \psi }}{{\partial x}}dx + \frac{{\partial \psi }}{{\partial y}}dy\)

For streamline dψ = 0

\(\begin{array}{l} vdx - udy = 0\\ \therefore \frac{{dx}}{u} = \frac{{dy}}{v} \end{array}\)

Calculation:

Given:

\(\vec V = \vec ix - \vec jy\)

So, u = x and v = -y

Streamline equation: \(\frac{{dx}}{u} = \frac{{dy}}{v}\)

\(\frac{{dx}}{x} = \frac{{dy}}{{ - y}}\)

Integrating both side

ln x = -ln y + ln c

xy = c

Given x =1 , y =2

so, c =2

so equation is xy – 2 = 0