Consider the annulus formed between a rod of radius �2 and a tube of radius �D. Find the velocity profile for the flow where the inner rod is rotated with speed Ω and simultaneously is pulled in the axial direction at a speed �F = �D, while the flow experiences an external constant pressure gradient of GH I applied in the direction of the rod axis. Do not assume that the gap is small compared to the radius. Effect of gravity can be neglected.

answer: the exterior temperature of commercial jet planes as they leave the stratosphere and return to the ground increases steadily.

explanation:

the lower most layer of atmosphere is troposphere which extends from 0 to 12 km above the surface of the earth. the temperature initially decreases as distance is increased from the earth's surface. commercial jets fly in lower part of the stratosphere. the stratosphere extends upto 50 km. the temperature in stratosphere starts rising again due to presence of ozone which traps the uv rays.

thus, when the planes leave the stratosphere and return to the ground, the exterior temperature increases steadily.

the maxium height is 34m/s