Question

Which of the following statement(s) is/are true for streamlines in a steady incompressible flow?

• A. Two streamlines cannot intersect each other.
• B. Flow rate increases between two diverging streamlines.
• C. Flow rate decreases between two diverging streamlines.
• D. Stream function has a constant value along a streamline.

Hint:

In steady, incompressible flow, streamlines do not intersect, and the stream function is constant along each streamline.

Answer 1

The Correct Option is A, D

Streamlines represent the path followed by fluid particles in steady flow. For incompressible flow, the velocity at every point is tangent to the streamline.
Step 1: Analyzing the options.
- (A) is correct: Two streamlines cannot intersect each other because if they did, it would imply two different velocity directions at the same point, which is not possible in a steady flow.
- (B) is incorrect: Flow rate decreases between diverging streamlines because the area between the streamlines increases, causing a decrease in velocity for incompressible flow.
- (C) is incorrect: The flow rate decreases between diverging streamlines, as mentioned above.
- (D) is correct: The stream function is constant along a streamline. This means the stream function value at any point on a streamline is the same for all points along that streamline.
Step 2: Conclusion.
Thus, the correct answers are (A) and (D).