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)