Velocity at a point in two-dimensional flow is given as V=2i+3j. The equation of stream line passing through the point is
- A3dx – 2dy = 0Correct
- B2x + 3y = 0
- C3dx + 2dy = 0
- Dxy = 6
Solution
Concept
Equation of a streamline
Formula
dx/u = dy/v
Step-by-step solution
1. V = 2i + 3j gives u = 2, v = 3. 2. dx/2 = dy/3, so 3dx = 2dy. 3. 3dx − 2dy = 0.
Explanation
A streamline is a line whose tangent at every point is the velocity direction, so dx/u = dy/v. With u = 2 and v = 3 the differential equation is 3dx − 2dy = 0.
Shortcut
Streamline: dx/u = dy/v. Cross-multiply.
Common mistake
Writing dx/v = dy/u (inverted).
Correct answer: A) 3dx – 2dy = 0