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let r be distance from axis of rotation. the acceleration is (W^2)r,directed radially outward. This acceleration exerts a force on the gas away from the axis, at each point in the tube. let P(r) be pressure(r is distance fron axis), and let ρ(r) be density.
dP(r)=ρW2rdr, from this equation it is clear that pressure increases as the distance from the axis increases.
PV=nRT, density ρ is directly proportional to n/V =P/RT, T is uniform and constant. and P increases as r increases, therefore ρ(r) also increases as r increases
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