Pressure exerted by gases

[Puneeth423]

Main Question or Discussion Point

If pressure exerted by gases is same in all directions, Why does we have low pressures in higher altitudes and high pressures below.

 

[davenn]

hi there :)

because as you go up in altitude the density of the gas decreases
I can personally attest to that having been to the top of Mauna Kea in Hawaii which is at 13,796 ft and even at that height the air is much thinner and its difficult to breathe

Dave

 

[sophiecentaur]

If pressure exerted by gases is same in all directions, Why does we have low pressures in higher altitudes and high pressures below.

This pressure refers to the pressure around a small region of the gas (or any fluid). If you take a column of air in a tube, up to the 'edge' of the atmosphere, the bit at the bottom is supporting the weight of all the gas above it, so it is compressed. The pressure against the sides of the tube and the ground is the same as the pressure 'upwards'. The next section above has a bit less weight above it so the pressure is a bit less - and so on, all the way up the tube until the pressure is vanishingly small.
There is a flaw in the above simple argument and that is that, even within each small region, the weight of the molecules in that region makes a small difference to the pressure from top to bottom. But it is a fair initial explanation.
The original statement really does apply in the absence of gravity when there is no difference in Gravitational Potential over the region.

 

[Puneeth423]

So you tell that in a given room containing only gases, pressure would be more at the bottom of the room and less on top of the room? Does the same hold in a balloon containing gases?

 

[Studiot]

Posts: 14 If pressure exerted by gases is same in all directions, Why does we have low pressures in higher altitudes and high pressures below.

SophieCentaur has indicated that the statement about pressure being the same in all directions applies to 'a small region..'

This is because pressure, in this sense, is a point function and varies from point (or small region to small region) within the gas (or fluid).
So the pressure upwards = the pressure downwards = the pressure sideways
at any point in the fluid

The pressure at one point may be equal from the pressure at another (or many points) or it may be different.

So pressure may vary from point to point within a fluid or may be the same over a very large region of fluid.

There are two reasons why the pressure may vary from point to point.

The first is as SophieCentaur stated, that in a column of air the pressure at any (altitude) level is compressed (at higher pressure) by having to bear the weight of the fluid above it.

This applies to any column of any fluid standing in a gravitational field.

I have underlined standing because it leads naturally to our second reason for pressure variation.

Fluid movement.

Fluid in motion has a different (lower) pressure from static fluid. Some of the potential energy in the static fluid is used to provide the kinetic energy of motion.

So in a large body of air the pressure can be the same sideways (at the same level), on a calm day, over a huge area because the air is standing still and at any level the point pressure is the same at any point.

But on a windy day there can be zones of high pressure and zones of low pressure at the same level with air movement (wind) between them.

Does this help?

 

[Chestermiller]

If pressure exerted by gases is same in all directions, Why does we have low pressures in higher altitudes and high pressures below.

You're talking about two different concepts: uniformity and isotropy

Isotropy means that the pressure at a point in space is independent of direction.

Uniformity means that the pressure has the same value at all points in space.

In the atmosphere, the pressure is isotropic, but not uniform, and varies with altitude. This altitude variation is the result of hydrostatics (caused by the effect of gravity on the air masses comprising the column of air).

 

[sophiecentaur]

That's nice and concisely put.

 

[sophiecentaur]

So you tell that in a given room containing only gases, pressure would be more at the bottom of the room and less on top of the room? Does the same hold in a balloon containing gases?

Yes.