# Pressure Difference in a Rotating Fluid Coloumn [closed] This question has intriqued me because two methods are generally employed to derive the shape of the surface(paraboloid) .

Both methods give equal numerical answer but differ in which of them P or Q (in figure) has greater pressure

(1) Firstly as done in the book one applies Bernoulli and finds lesser pressure at Q due to it having more velocity.

(2) One can calculate net force (gravity and centrifugal) at a point x distance away from centre and make the surface's tangent perpendicular to it , giving us a solvable differential equation.

The second method predicts more pressure at Q due to it being towards the direction of centrifugal force.

Also if one considers a point R above Q at the surface what will be its pressure.

Logic says , it is equal to pressure at P because both are at surface , but then pressure at Q is greater than at R ( it is below R) so doesnt that mean pressure at Q is greater than at P.

Please explain this situation concluding about exact pressures at P , Q and R and their corresponding reasons.

## closed as off-topic by user191954, Kyle Kanos, Jon Custer, Aaron Stevens, ZeroTheHeroApr 4 at 4:40

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – Community, Kyle Kanos, Jon Custer, Aaron Stevens, ZeroTheHero
If this question can be reworded to fit the rules in the help center, please edit the question.

• Do you read study material by RESONANCE? – user213933 Mar 23 at 13:10
• @Shreyansh No this is Aakash Study Material – user224768 Mar 23 at 13:53
• Are you in class 11? – user213933 Mar 23 at 14:20
• No I am about to finish Class XII – user224768 Mar 24 at 1:34

## 1 Answer

Bernoulli works for streamlines which in this case are circles of constant radius and constant vertical height.

This means that a line from $$P$$ to $$Q$$ is not a streamline and so the analysis in the book is flawed.

To apply Bernoulli in a useful way you must move to the rotating frame in which the fluid is at rest.
In such a rotating frame any two points are connected by a streamline and so you can use the line joining $$P$$ and $$Q$$ as a streamline and with the introduction of a fictitious force can use Bernoulli and show that the pressure at $$Q$$ is greater than the pressure at $$P$$.