# Confused about pressure

alkaspeltzar
Summary: Trying to understand pressure and it's relation to force

Okay here is my dumb thought. A force is defined as an influence on an object, causing change in motion correct?

Then how can pressure be a force on an area? Maybe I'm stuck on the word "on". But the way I'm reading the force is on an area, force is always on a body or such, area isn't a body? So I'm confused.

Or maybe I'm reading into it? Is pressure just the force of a body given within an area? My gut tells me pressure is a force exherted by a liquid or gas within or given region . Someone help, please and thank you if you can straighten me out.

## Answers and Replies

Mentor
I think that pressure is probably more fundamental than force. So you can think of it the other way around. A force is just the sum of all the pressure over an area:

$$F=\int_A P\; dA$$

alkaspeltzar
What do you mean by "over ". What I'm stuck on is they say force acts on a body. Then they pressure is force on an area? They mean force exherted per/ within/ over an area right? You can't literally have a force pushing an area right?

Mentor
What do you mean by "over ".
I mean that the summation (integration) is done by adding up all of the little areas to get the big area.

alkaspeltzar
Dale, that's not really my question. My question is does force act on a body, per definition and if so, why do we describe pressure as force on an area? Force can't be physically on an area

Mentor
Dale, that's not really my question
I know. I am trying to get you to look at it in a different way that may avoid your question entirely. Start with pressure as the fundamental thing and then explain force in terms of pressure. It seems easier and more understandable to me.

alkaspeltzar
Can you answer my question or am I over reading it?

Science Advisor
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Suppose a container has something in it under pressure, every part of the inner surface of the container is under a force from the contents. If you measure an area of the inner surface of the container, the total force on that area is the answer you are looking for. Pressure exerts a force per unit area of the container inner surface. It is reasonable to say that the pressure is everywhere in the contents, but the force from the contents is being applied to other parts of the contents itself, which is pushing back with equal force.

alkaspeltzar
You say force on that area.. area isn't a body...that's why I don't get it

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You say force on that area.. area isn't a body...that's why I don't get it
The size of part of a body can be measured by its area. In this context, when they talk about an area, they mean any part of the body with a certain surface area exposed to the pressure.

alkaspeltzar
alkaspeltzar
Okay, So then was I right when I thought about pressure as force exerted on a body per/within area. Basically pressure is the expression of force on a body given a certain area or size.

We aren't saying for example if we have 10 psi, that we are trying to move 1 sq inch with 10 lbs, but rather for the size of 1sq inch, a 10 lbs force is applied

Mentor
A force does not have to cause movement of a body. If there are multiple forces acting on a body, the body can be in static equilibrium and doesn't have to be moving at all.

With regard pressure in liquids and gases, the pressure doesn't just act on solid surfaces. If we subdivide the gas or liquid (conceptually) into smaller parcels, pressure is the force per unit area exerted by a given parcel at its common interface with its adjacent neighbors, and the force per unit area exerted by these adjacent neighbors on it.

alkaspeltzar
alkaspeltzar
Answer this I guess. Let say the pressure is 10 psi. Does that mean there is an exherted force of 10 lbs throughout an area of 1 sq inch?

What I wanted to make sure is that saying 10 psi doesn't mean we have 10 lbs trying to move a square inch ...right? That makes no sense?

Mentor
Answer this I guess. Let say the pressure is 10 psi. Does that mean there is an exherted force of 10 lbs throughout an area of 1 sq inch?

What I wanted to make sure is that saying 10 psi doesn't mean we have 10 lbs trying to move a square inch ...right? That makes no sense?
If the system is in equilibrium, there is no movement.

Pressure is used to describe a "distributed force," as opposed to a "point force." 10 psi means that we have a distributed force of 10 lbs acting uniformly over an area of 1 sq in.

alkaspeltzar
Okay, I think that makes sense...it's a distributed force. So we are saying that 10 psi is 10lbs force (acting on or balance whatever thing we don't care) spread throughout a square inch.

Is that the right way to thinking of it? We not saying we want to move with 10lbs a square inch, but that for 10 psi we have 10 lbs distributed across an area 1 inch square

FactChecker
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Pressure is actually the cumulative force of billions of tiny molecular impacts on an area of a surface (or on other molecules). So it is best thought of as a force uniformly distributed on the surface. At room temperature, the average speed of an air molecule at sea level pressure is over 1,100 mph!

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Mentor
Okay, I think that makes sense...it's a distributed force. So we are saying that 10 psi is 10lbs force (acting on or balance whatever thing we don't care) spread throughout a square inch.

Is that the right way to thinking of it? We not saying we want to move with 10lbs a square inch, but that for 10 psi we have 10 lbs distributed across an area 1 inch square
Yes, that's perfect.

alkaspeltzar
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If the liquid/gas under pressure is in motion, the pressure can vary greatly on different parts of a surface. That is the subject of aerodynamics or fluid dynamics.

Mentor
for 10 psi we have 10 lbs distributed across an area 1 inch square
Yes, that is right

alkaspeltzar
alkaspeltzar
Thank you. For some reason I was thinking 10 psi meant we we're trying to force 1 sq inch with a 10 lbs force ...but then I was like an area isn't something a force does work on.

I need to remember pressure is like force, just saying it's distributed. 10 psi means we have a 10 lb force being spread out over each sq inch

Chestermiller
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Pressure is a rate: 10lbs per square inch. If you have a surface area of 0.5 square inch holding back the pressure, then there is 5 lbs of force on that area. 10 psi pushing on a piston with area ##x## square inches is exerting a force of ##10*x## lbs on the piston.

Science Advisor
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What I'm stuck on is they say force acts on a body.

Most likely, the body is modeled as a particle, so the force is applied at a point.

Then they pressure is force on an area?

Now the force is distributed over (some part of) the surface of an object that's not a particle. The area they refer to is, of course, the area of that surface.

alkaspeltzar
alkaspeltzar
This makes good sense too. Pressure is the force on some part of a body, in which the area defines the size/ how much. This then is force PER area.