Fluid Rotating in a Cylinder

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

The diagram shows a cross section and a top view of a closed cylinder. Half of it is filled with a fluid. Modify the angular velocity and gravity to observe how the parabola of the surface changes. At high velocity and low gravity most of the bottom is dry and the rotating surface approximates a cylinder.

Contributed by: Michael Schreiber (March 2011)
Open content licensed under CC BY-NC-SA



The cross section at high speeds has a smaller area than the cross section at rest. Their volumes, however, are equal if they are distinguished by a critical radius of or 0.707.

A cross section of the surface is a parabola or two segments of it. This parabola is shown in the left image by a red line plotting: . The volume of the shifted paraboloid can be obtained by: .

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.