Question

What is the streamline equation passing through (1,1) for the following flow.

$V=3xi-3yj$

• A. $xy=0$
• B. $\frac{x}{y}=c$
• C. $xy=c$
• D. $xy=1$

Answer 1

The correct option is D $xy=1$

$u=3xandv=-3y$

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

$\int \frac{dx}{3x}=\int \frac{dy}{-3y}$

$\frac{1}{3}lnx=-\frac{1}{3}lny+lnc$

$ln\left(xy\right)=ln\left(c\right)$

xy = c

$\because$ Stream line is passing through (1,1),
c = 1

xy = 1