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

Step 1: Recall where Bernoulli's equation comes from.
Bernoulli's equation is Euler's equation of motion integrated along a streamline for steady, incompressible, inviscid flow.
That integration only uses the streamline direction, so it always holds between two points on the same streamline, rotational or not.

Step 2: Check what happens off the streamline.
To connect two points that do not lie on the same streamline, the flow must be irrotational, so the Bernoulli constant is the same for every streamline in the field.
If the flow is rotational, each streamline can carry a different constant, so jumping between arbitrary points gives a wrong result.

Final Answer:
Bernoulli's equation fails only for arbitrary points in rotational flow, so option (A) is correct. \[ \text{Valid: same streamline in any flow, or any two points only in irrotational flow} \]