# 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.

• Do you read study material by RESONANCE? – user213933 Mar 23 '19 at 13:10
• @Shreyansh No this is Aakash Study Material – user224768 Mar 23 '19 at 13:53
• Are you in class 11? – user213933 Mar 23 '19 at 14:20
• No I am about to finish Class XII – user224768 Mar 24 '19 at 1:34

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