2. An air column of radius 1000 km initially at rest with respect to the
surface of the earth at 60N expands to twice its original surface area because
of horizontal divergence. What tangential velocity (in km/h) relative to the earth will
develop at the periphery of the air column.

**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)