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## Summary:

- In a rotating fluid the pressure and kinetic energy density increase as you move outward, seemingly a violation of Bernoulli’s equation?

Consider a cylindrical container filled with an ideal fluid. Let it rotate at a constant angular speed (about the symmetry axis which is oriented vertically) and let the fluid be in the steady state.

Lets just talk about a horizontal slice so that the gravitational potential is constant. The pressure must increase as we move out from the center in order to supply the centripetal acceleration.

In the frame of reference rotating with the cylinder, everything makes sense. We have a fictitious centrifugal potential which decreases as you move from the center, and the pressure increases as you move out, so Bernoulli’s equation is satisfied.

I am confused how it works in the inertial frame. We no longer have any potential. The kinetic energy density increases as we move out from the center, as does the pressure. So how can Bernoulli’s equation be satisfied if they both increase?

What am I overlooking?

Lets just talk about a horizontal slice so that the gravitational potential is constant. The pressure must increase as we move out from the center in order to supply the centripetal acceleration.

In the frame of reference rotating with the cylinder, everything makes sense. We have a fictitious centrifugal potential which decreases as you move from the center, and the pressure increases as you move out, so Bernoulli’s equation is satisfied.

I am confused how it works in the inertial frame. We no longer have any potential. The kinetic energy density increases as we move out from the center, as does the pressure. So how can Bernoulli’s equation be satisfied if they both increase?

What am I overlooking?