Pressure Causes: Weight vs Molecules Motion

[ztdep]

We often say the pressure of air is caused by the air column above the surface. Obviously, it will not work for the case of air in an enclosing box. The pressure is caused by the air moleculars striking on the box surface.
But if we replace air with water. we can explain it sucessfully again with the water column weight.
So what exactly does the pressure come from? weight or molecules motion.

 

[BillTre]

Although molecules are the immediate source of the measured pressure, the overlying air column is where the force to pressurize the air is generated.

Is the box airtight? If not the pressure generated by the overlying column of water will be felt inside the box. If the pressure is less in the box, air will flow in (or out if the pressure is higher in the box) until the pressure inside and outside of the box are equalized.

This situation is analogous to a pipe of water of some height which had a bunch of turns at the bottom.
You could consider the weight of the column of water in the pipe as generating the pressure, even though it is not immediately above where you are measuring.

If the box is airtight, you can control the pressure inside of it (within bounds) by pumping air in or out. Obviously this is not due to the overlying column of air since the chamber is detached from the atmosphere. It this case only the molecules will provide an decent explanation. The pump is driving the specific pressure in the container.

 

[CWatters]

We often say the pressure of air is caused by the air column above the surface. Obviously, it will not work for the case of air in an enclosing box. The pressure is caused by the air molecules striking on the box surface.
But if we replace air with water. we can explain it successfully again with the water column weight.

Actually no. If you put water in a sealed box the pressure isn't necessarily dependent on the water column weight. The pressure can be higher or lower than that.

Consider a box with volume 1m³. If you take out all the air (vacuum) and inject 1L of water the water will evaporate/boil and the resulting water vapour will have quite a low pressure. On the other hand if you take out all the air and pump in 1.1m³ of water the pressure will be very high (because water is only slightly compressible).

Water is frequently used to pressure test gas cylinders because if the cylinder fails you don't get such a large explosion (the energy stored is lower).

 

[Chestermiller]

Pressure can exist even where there is no gravity. Therefore, a column of material cannot be regarded as the fundamental cause of pressure. Pressure is caused by momentum transport by molecules.

 

[ztdep]

Pressure can exist even where there is no gravity. Therefore, a column of material cannot be regarded as the fundamental cause of pressure. Pressure is caused by momentum transport by molecules.

you mean the momentumr transport of molecules is balanced with weight

 

[Chestermiller]

you mean the momentumr transport of molecules is balanced with weight

No. What do the words "Pressure can exist even if there is no gravity (ergo, no weight)" mean to you?

 

[Cutter Ketch]

I think the question is confusing two different questions: What is pressure, and why does the atmospheric pressure or the pressure at some depth in the ocean have a particular value. These are not the same question, and the two things mentioned are the two answers to these two different questions.

Pressure is the net force per unit area on a surface caused by collisions of the particles in a fluid. Each time a particle hits a surface it's momentum normal to the surface is reversed imparting an impulse to the surface. The average impulse is determined by the average velocity which is determined by the average thermal energy which we call temperature. The frequency of the collisions per unit area is determined by the density of particles i.e. N/V and so from this description we arrive at the ideal gas law: P = R T N/V Pressure is "caused" by thermal energy of the particles.

At equilibrium if Pressure is pushing on a wall, and the wall is not moving, something must be pushing back. The equilibrium value of Pressure is always a case of another force balancing against Pressure and V or N or T changing until the forces are balanced.

Consider the statement "Pressure can exist if there is no weight". So we have a closed container floating in space containing a gas in equilibrium. Pressure pushes the walls out. What pushes the walls in? The inward force is the elastic restoring force of the walls. This is obvious if the container is a balloon. The walls stretch out. The elastic force increases as the balloon grows. Meanwhile the volume increases and the pressure drops. At some point the two forces balance and that is the equilibrium condition. The effect is less obvious in a heavy metal container because the walls barely move, but nevertheless that is exactly what happens. The elastic constant of the walls is just really really big. Another model is a container which is a piston and cylinder. If nothing holds the cylinder in, the pressure accelerates the cylinder and blows it out of the cylinder. If we imagine a spring holding in the piston in, the piston will move compressing the spring until the spring force holding the piston in equals the Pressure force pushing the piston out.

Now imagine a vertical cylinder the height of the atmosphere holding the same number of atoms as are normally found in that column of atmosphere. Place a weightless piston at some height in the cylinder. The pressure of the gas below the piston pushes the piston up. The gas above the piston pushes the piston down. At equilibrium the two forces are equal. We also know that at equilibrium the gas above the piston is not falling (in net). That gas only has two forces acting on it: gravity pulling down, and the cylinder pushing up. Since it is not accelerating those two forces are equal and AT EQUILIBRIUM the pressure up on the piston equals the weight of gas above the piston. The question was how does this happen. If the gas below the piston has too little pressure the piston will fall and compress the volume increasing the pressure until equilibrium is reached and the forces are balanced.

So, to answer the question directly, pressure is caused by the motion of particles, and with regards to gravity the fluid will compress until the forces of pressure and gravity balance at equilibrium. Gravity doesn't create pressure, but under gravity the pressure will arrive at an equilibrium value that balances against gravity.

 

[ztdep]

Thank you very much for your answer. I suddenly feel refreshed.