9867

Pressure of a Rotating Fluid

This Demonstration shows how the pressure in a fluid is affected by rotation at constant angular velocity. The graph on the left shows the isobaric surfaces (surfaces of constant pressure) that result from the rotation. The graph on the right shows pressure contours taken from cross sections in the , plane of the graph on the left. The cross section is represented by a blue plane in the 3D graph; a darker color indicates higher hydrostatic pressure. The pressure profile does not depend on the direction of the angular velocity. This physical situation is closely analogous to Newton's classic rotating-bucket experiment.

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The pressure in the fluid is modeled by the equation:
,
where is the pressure in the fluid, is the density of the fluid, is the radial distance from the center, is the angular velocity, and is the specific weight of the fluid. The constant is defined to be the hydrostatic pressure of the fluid at the bottom of the column, given an angular velocity of zero. In this Demonstration, the constant is the specific weight of the fluid multiplied by the height (10 m).
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