Correct Answer - Option 3 : 9x
2 – y
3 = 8
Concept:
Streamline:
It is an imaginary line or curve drawn in space such that the tangent drawn at any point to it will give the direction of velocity.
Equation of streamline is:
\(\frac{{dx}}{u} = \frac{{dy}}{v} = \frac{{dz}}{w}\)
Calculation:
Given:
V = -y2i – 6xj, u = -y2, v = -6x
Equation of streamline is:
\(\frac{{dx}}{u} = \frac{{dy}}{v} \)
\(\frac{{dx}}{-y^2} = \frac{{dy}}{-6x} \)
6x dx = y2 dy
\(3x^2=\frac{y^3}{3}+C\)
At (1, 1)
\(3\times 1^2=\frac{1}{3}+C\)
C = 8/3
\(3x^2=\frac{y^3}{3}+\frac{8}{3}\)
∴ 9x2 - y3 = 8.