# Is pressure a rate?

My question is pressure a rate? Rate is defined as a some measure per another measure or quantity. Doesn't pressure fit that definition? yet everything I read says no...pressure is not a rate? Same with density

Is it because pressure is really a distributed force per area, and it is not a value dependent upon another. Like mph(speed) is change in distance per time. Can someone please explain this aching thought in my head?

Sorry if this is incorrect forum, just looking for help.

Thankyou

Rate is the change in any quantity with respect to time, and time only.

Okay, I agree with that and that's what I always thought.

But then there are definition and examples of rates like " $per pound " so how does that work? Okay, I agree with that and that's what I always thought. But then there are definition and examples of rates like "$ per pound " so how does that work?
Words in everyday language can be used very loosely and have found various applications, as is the case over here. In physics, however, word meanings are very specific and non-interchangeable.

Gold Member
Rate is the change in any quantity with respect to time, and time only.

Well that's not true. A rate, as one definition in the dictionary puts it, is:

4a :a quantity, amount, or degree of something measured per unit of something else <her typing rate was 80 words per minute>

In that sense, a pressure would be a rate. It's the rate at which force on a surface under pressure changes per unit of area considered. It's a rather unconventional definition of rate, but it would still technically be a rate.

More importantly, why does it matter? It's just semantics and doesn't really affect the physical interpretation at all.

Rate is the change in any quantity with respect to time, and time only.

lapse rate
literacy rate
those are at least somewhat "sciencey"

not to mention:
tax rate
exchange rate
interest rate

etc.
etc.

But I would really hesitate to call pressure a rate...

oops looks like boneh3ad beat me to it...

Actually... What ur all saying makes sense. From a practical physics or science background, rates always include time. Therefore pressure is not. Its not something changing or defined by a particular unit of time.
But the term does get thrown round loosely, and therefore we see things like percentages called rates or things like exchange rates.

I will not worry about it. Pressure is pressure, its force applied over area, as in psi. Rates are quantities depending on time, like speed and flow rate. That's good enough.

PS. English fudges word meaning all the time

Gold Member
Actually... What ur all saying makes sense. From a practical physics or science background, rates always include time. Therefore pressure is not. Its not something changing or defined by a particular unit of time.
But the term does get thrown round loosely, and therefore we see things like percentages called rates or things like exchange rates.

Actually that's not what I am saying at all. There are many practically important rates in mathematics and physics that do not involve time: rate of change of a quantity as a function of space, angular frequency versus wavenumber, pressure versus density, and many others.

Pressure just isn't very useful as a rate because it doesn't really pop up anywhere useful in that fashion. It's still a rate, though, in the sense that you can integrate it over a surface exposed to variable pressure (such as a vertical wall in a water tank) in order to get the total force on that surface. You don't really ever see it done in the opposite direction, though, as pressure is the more fundamental property.

Okay..I guess now I am just confused. You say its a rate but then not useful as a rate. So is it or is it not?

To me it doesn't seem like one as it doesn't fit the description as compared to speed or acceleration or something that is one unit based on another, like time.

Looking online...there are many definitions of rate. Some deal with money, many in sciences deal with time/frequency. For application i think I over confused that and started over analyzing pressure as one based on how we express it. I know what it is, I guess I am not going to concern myself with its strict definition. Thanks

If you "froze" time would pressure still exist? I know you can measure pressure at any given time, but if you froze time would pressure still be exerted?

CWatters
Homework Helper
Gold Member
Pressure just isn't very useful as a rate because it doesn't really pop up anywhere useful in that fashion.

Am I missing something? We routinely calculate forces by multiplying pressure by area. Isn't that an example of using pressure as a rate?

If not what about pressure vs depth as in "0.1 bar per meter of water" ?

In GR the energy-momentum tensor's (1,1), (2,2), (3,3) diagonal components are momentum flux or flow and are equivalent to pressure aren't they?