Determine the pressure variation in the vertical for a fluid whose density varies linearly according to the relation  where ρ0 is a reference density at y=0, and β is a constant. In an ideal gas under...

Determine the pressure variation in the vertical for a fluid whose density varies linearly according to the relation
 where ρ0 is a reference density at y=0, and β is a constant.

In an ideal gas under isothermal conditions, the density may be related to the pressure by the expression

Where R,T are constants. Determine the pressure variation in the vertical, if p = p₀
aty = 0.