# Can it be practically evaluated?

Classical Mechanics Level 5

Mayank and Akul are vexed at the practical unimportance of the following problem:

A narrow horizontal cylindrical tube is filled with a gas. The tube rotates in a horizontal plane with an angular velocity $$w$$ about a perpendicular axis through one of its ends A. The length of the tube is $$l$$ and cross sectional area is $$S$$. Total mass of contained gas is $$M$$. When the tube was at rest initially, it had a pressure $${ p }_{ o }$$ and a temperature $$T$$.

Assuming that the temperature remained constant, find the Pressure in the tube as a function of distance x from the end A.

If $$\large p=\dfrac { { { p }_{ o }l{ e }^{ k{ w }^{ 2 }{ x }^{ 2 } } } }{ \int _{ 0 }^{ l }{ { e }^{ k{ w }^{ 2 }{ x }^{ 2 } } \, dx } }$$

Find $$\dfrac { { p }_{ o }klS }{ M }$$

Mayank and Akul

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