The tangent drawn to the instantaneous velocity in a flow field is called:
- Atimeline
- BstreamlineCorrect
- Cpathline
- Dstreakline
Solution
Concept
A streamline is an imaginary line where the tangent at every point gives the direction of the velocity at that instant.
Formula
dx/u = dy/v = dz/w
Step-by-step solution
1. Recall the definitions of the flow lines. 2. Pathline: the actual path of one fluid particle over time. 3. Streakline: the line joining all particles that passed through one fixed point. 4. Timeline: a line formed by a set of nearby particles marked at the same instant. 5. Streamline: the tangent at any point gives the instantaneous velocity direction. 6. So the answer is (B).
Explanation
A streamline is drawn so that the velocity vector at every point is tangent to it at that instant. So no fluid crosses a streamline. In steady flow, the streamline, pathline and streakline are the same.
Why the other options are wrong
A: A timeline joins marked particles at one instant. It is not tangent to velocity. C: A pathline is the track of one particle over time. D: A streakline joins all particles that passed through one point.
Shortcut
Tangent to the velocity at an instant = streamline.
Common mistake
Mixing up streamline and pathline. They are the same only in steady flow.
Correct answer: B) streamline