Fluid Velocity in Rigid Body Rotation and Irrotational Flow

This Demonstration illustrates the velocity of a fluid for rigid body rotation and for irrotational flow. For rigid body rotation, the angular velocity is assumed to be constant, and the circulation is not taken into account. For irrotational flow, each contour in the vortex is assumed to have the same value of circulation, and angular velocity is not taken into account. The velocity displayed to the right of the image is the velocity of the fluid at the center of the black point.

For rigid body rotation, the velocity vectors obey the equation

,

where is the magnitude of the vector in the - plane from the center of rotation to a given point and is the angular velocity. The direction of the velocity vector is orthogonal to the vector and in the same plane.

For irrotational flow, the velocity vectors are modeled by the equation

,

where is the magnitude of the vector in the - plane from the center of rotation to a given point and is the circulation value. The direction of the velocity vector is orthogonal to the vector and in the same plane.