# I Compressibility of liquid vs solid actual numbers

1. Feb 16, 2017

### fahraynk

I was trying to find the compressibility of water and compressibility of air to compare.
For compressibility of water I found 46.4e-6
For compressibility of a gas... I am having a tough time finding anything. compressibility factor I can find, which is 1 for Hydrogen... but how does that relate to compressibility?

Also... if a liquid is much more viscous than water... water is .001[Pa*sec] so say if the viscosity = 2 then would it likely be more or less compressible than water?

Last edited: Feb 16, 2017
2. Feb 16, 2017

### Staff: Mentor

That is the compresibility, which for an ideal gas is exactly 1, and real gases have k ≈ 1.

I will let more knowledgeable people answer, but I would be surprised if there was a link between compressibility and viscosity.

3. Feb 16, 2017

### Staff: Mentor

Hi DrClaude,
From the value he give for liquid water, I don't think he was referring to the compressibility factor z. I think he was referring to the reciprocal of the bulk modulus. For an ideal gas, the compressibility is equal to 1/p. For liquid water, it looks like the value he gave has units of 1/kPa.

I agree with your assessment.

4. Feb 16, 2017

### Staff: Mentor

Thanks for the clarification.

5. Feb 16, 2017

### fahraynk

From Fundamentals of aerodynamics John D Anderson :
Compressibility Φ :
$$\phi = \frac{1}{\rho}\frac{d\rho}{dP}$$
$$dP=\rho\phi d\rho$$

He derives this by manipulating this equation : $$\phi=\frac{1}{v}\frac{dv}{dP}$$ where v is specific volume = 1/ρ

Also I got the compressibility of water from this source : http://hydrogen.physik.uni-wuppertal.de/hyperphysics/hyperphysics/hbase/tables/compress.html

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6. Feb 16, 2017

### Staff: Mentor

If you apply this to an ideal gas, you get a compressibility of 1/P.

7. Feb 16, 2017

### fahraynk

So, am I right to say that 1/(46.4e-6), water is 21551 times less compressible than an ideal gas? (at a pressure of 1atm)

8. Feb 16, 2017

### Staff: Mentor

No. The comparison depends on the pressure. In the case of liquid water, the compressibility is very insensitive to pressure. In the case of an ideal gas, the compressibility is sensitive to the pressure. So you have to specify at which pressure you are making the comparison.

9. Feb 16, 2017

### fahraynk

1 atm.
The compressibility on this site if I am reading it correctly (I might not be) says 46.4e-6 at 1atm http://hydrogen.physik.uni-wuppertal.de/hyperphysics/hyperphysics/hbase/tables/compress.html
The compressibility of ideal gas, 1/P... is that pressure in atmospheres? Because then the compressibility at 1atm = 1, and 1/46.4e-6 = 21551

10. Feb 16, 2017

### Staff: Mentor

If the compressibility of the liquid water is 46.4E-4/atm (i.e., the pressure unit used for the pressure change is atm.), then I agree with this comparison.

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