The variation of fluid pressure with height is described by the differential equation:
What will be an ideal response?
Substituting the ideal gas expression for density into the equation for variation of fluid pressure with height gives
If T is constant (along with M and g) then this is a separable equation that can be rearranged to give:
This can be directly integrated to give
or
The standard pressure at sea level is Po = 101325 Pa. If Denver is 1 mile = 1609 m above sea level,
M = 0.029 kg/mol, T = 10 °C = 283 K, and R then
The estimated pressure is 83430 Pa = 0.834 bar = 0.823 atm.
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