Question

Bernoulli's equation CANNOT be applied between:

• A. any two arbitrary points in the flow field for steady incompressible rotational flow
• B. any two arbitrary points in the flow field for steady incompressible irrotational flow
• C. any two points along a streamline for steady incompressible flow
• D. any two points along a streamline for steady incompressible rotational flow

Hint:

Think about whether the Bernoulli constant stays the same across different streamlines.

Answer 1

The Correct Option is A

This question checks how far Bernoulli's equation can be stretched: along one streamline only, or across the whole flow field.

1. Any two arbitrary points in the flow field for steady incompressible rotational flow: this fails. In rotational flow the Bernoulli constant changes from one streamline to the next, so two random points that sit on different streamlines are not guaranteed to share the same constant.
2. Any two arbitrary points in the flow field for steady incompressible irrotational flow: this works. Irrotational flow has zero vorticity everywhere, so the Bernoulli constant is the same for every streamline, and the equation connects any two points in the field.
3. Any two points along a streamline for steady incompressible flow: this works. Along a single streamline, Euler's equation integrates directly into Bernoulli's equation for any steady, incompressible flow, rotational or not.
4. Any two points along a streamline for steady incompressible rotational flow: this works for the same reason as the previous case, the streamline restriction removes the need for irrotationality.

Only the first statement describes a case where Bernoulli's equation genuinely fails, so option (A) is correct.