Pressure and density of compressible fluids.

[Nathanael]

If a fluid is compressible, will the density be directly proportional to the pressure?

(I'm sure there's a limit where an increase in pressure stops producing a change in density, but I'm talking about for more "normal" (smaller) amounts of pressure.)

 

[paisiello2]

Are you assuming constant temperature as well?

 

[Nathanael]

Are you assuming constant temperature as well?

Temperature would effect the energy, right?

And pressure is essentially the density of energy, (Newton-Meters per Cubic Meter)

So wouldn't a change in temperature only effect the pressure? And so it doesn't really need to be considered when considering the relationship between pressure and density, right?

Or no?

 

[Chestermiller]

If a fluid is compressible, will the density be directly proportional to the pressure?

(I'm sure there's a limit where an increase in pressure stops producing a change in density, but I'm talking about for more "normal" (smaller) amounts of pressure.)

The word "proportional" has a certain exactness to it, and nothing is exact. The most one can say is that the density increases with increasing pressure. Over limited regions of pressure, the density change is approximately proportional to the pressure change.

Chet

 

[paisiello2]

Well, if temperature affects pressure and pressure in turn affects density then the conclusion is that temperature would also affect density.

Or no?

 

[Chestermiller]

Well, if temperature affects pressure and pressure in turn affects density then the conclusion is that temperature would also affect density.

Or no?

I think Nathanael, in his original post, was referring to the effect of pressure on density at constant temperature. At least that was my interpretation.

Nathanael, is that what you meant?

Chet

 

[Nathanael]

Well, if temperature affects pressure and pressure in turn affects density then the conclusion is that temperature would also affect density.

Or no?

Sorry, I wasn't thinking about my last post. I was under the unexamined impression that a change in pressure caused by temperature would affect the density (simply because it affects pressure) but now that I'm thinking about it, I realize that a change in pressure caused by temperature will have no effect on density (right?).

I think Nathanael, in his original post, was referring to the effect of pressure on density at constant temperature. At least that was my interpretation.

Nathanael, is that what you meant?

Chet

In a sense I was talking about constant temperature, (in the sense that temperature was not a part of my picture) but honestly I didn't think about temperature.

(I never learned or thought of temperature affecting pressure, even though it's a common-sense kind of idea.)

The most one can say is that the density increases with increasing pressure.

My original question was just asking is if the increase in density was (approximately) linear, or if it curved upward, or curved downward, (or what I really mean is does it "bend" downward) or what?

Over limited regions of pressure, the density change is approximately proportional to the pressure change.

That answers the question. Thanks.

 

[boneh3ad]

Temperature absolutely and directly affects the pressure and density. For example, many gases behave as ideal gases at most ordinary conditions and so very closely follow the ideal gas law, which can be expressed as

$$p = \rho R T$$

where ##p## is pressure, ##\rho## is density, ##R## is the specific gas constant, and ##T## is temperature.

 

[boneh3ad]

Liquids are generally nearly incompressible so usually this isn't a concern. You can likely find a similar equation of state for liquids like water but I don't know it off the top of my head and it won't be terribly useful.

Real gases generally follow a similar pattern to ideal gases but with various corrections and variations on things like exponents depending in the gas in question and the phenomenon causing it to behave non-ideally.