1. An air column at rest with respect to the surface of the
earth at the equator has a radius of 100 km. This air column moves to the
North Pole. Determine (a) what relative circulation, if any, the air
column will develop, and (b) what the tangential velocity would develop at the
periphery of the air column upon its arrival at the North Pole. Assume no
real torques and that the area of the air column does not change.

**Fundamental
Relation Needed: Conservation of
Absolute Circulation**

(1)

**Basic Definitions Needed**

Definition of circulation

(2)

Relation of tangential velocity to angular
velocity

(3)

(4)

where A is the cross-sectional area
of air column.

(5)