Effect of altitude on gas pressure

Does gas pressure increase with increase in altitude? Yes, it does! Believe me. :)

Effect of Altitude on gas pressure is an interesting topic and I used to discuss this with my colleagues in my earlier city gas company and people working in planning, design, projects and O&M departments would be interested in this.

Let’s see this through Fluid Mechanics basics.

We know that, Atmospheric pressure is about 1013 mbar at sea level. = (A)
It becomes less as altitude increases. The reason is simple: Weight of the column of air is reduced.

Now, pressure at the depth of this column is = h (height of column) x d (density) x 9.81 kg/m3. (Let us call this as ‘Equation-X’). Now with this equation as foundation, let’s start our investigation.

Take a rise in altitude of 100m. At 100m above seal level the atmospheric pressure will be less by an amount equivalent to the pressure caused by a column of air 100m high.Hence, assuming air density as 1.248 kg/m3, pressure exerted by this column = 100m x 1.248 kg/m3 x 9.81 = 1224 N/m2 or 12.24 mbar = (B)

So, atmospheric pressure 100m above sea level is = (A) – (B) = 1013 – 12.24 = 1000.76 mbar

This was for air, but what happens to the gas? Here the things get interesting,

Assuming specific gravity of gas as 0.5 (for calculation sake), considering Equation-X above, pressure of 100m of gas will be = 100m x 1.248 kg/m3 x 0.5 x 9.81 = 612.14 N/m2 or 6.12 mbar

Thus , the gas pressure reduces by 6.12 mbar when the atmospheric pressure reduces 12.24 mbar.

The consequence of this is an apparent increase in gas pressure of 6.12 mbar for every 100m increase in altitude.

Based on above logic, following is the general formula which states the relation between difference in pressure and altitude.

Pressure difference = 0.12 x h x (1-S) mbar
(Where, h = height in metre, S = Specific Gravity of gas)

So from the formula above it is obvious that if the gas is heavier than air, then the difference will be decrease in pressure NOT increase. :)

Hope you find this helpful.

Let there be Light Gas! :)