Question

The equation of streamline passing through (1, 1) for the velocity function V = -y²i – 6xj is
1. 10x² – 2y³ = 8
2. 9x³ – y³ = 8
3. 9x² – y³ = 8
4. 9x² – y² = 8

Answer 1

Correct Answer - Option 3 : 9x² – y³ = 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.