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)