# Calculating Density/Specific Volume

1. Feb 7, 2005

### minger

This is my first time here and I'd just like to say HI first of all.

Anyways, I have flowing water at a known temperature and pressure. Call it pure water. What is the best way to get the density or specific volume from this? I am at very high pressures (800 psig) so I do not want to approximate it as a saturated liquid, however, I can't find any tables or anything like that. Any help is appreciated.

2. Feb 7, 2005

3. Feb 7, 2005

### minger

Yes yes, but the one in my textbook doesn't have pressures as high as I would like. If this is the only way to get it, is there someplace that I can get a larger chart, or possibly just an enlargement of the chart above the critical point?

4. Feb 7, 2005

### Astronuc

Staff Emeritus
The critical point conditions for water are:

Critical Temperature: 705 °F
Critical Pressure: 3203.6 psia
Critical specific volume: 0.0505 ft3/lbm

But only the pressure (800 psig) is mentioned, and this pressure is well below the critical point pressure. Depending on the temperature, one will compressed liquid, saturated (2 phase) liquid-vapor, or superheated steam. Each domain has a different T-v relationship.

5. Feb 8, 2005

### minger

Is there somewhere I can find T-v relationships, a chart maybe? I know how to get all the properties for a saturated liquid, a saturated mixture, and superheated gas. But, as said before, is there someplace (online hopefully) that I can get a "bigger" P-v diagram for water. Or, based on what Astronuc just said, somewhere that I can find a T-v diagram (which I would assume has lines of constant pressure).

Thanks a lot for the help so far.

6. Feb 9, 2005

### Gokul43201

Staff Emeritus
Water is sufficiently incompressible that ONLY 800 psig will hardly affect its density. To quantify 'hardly' better, my estimate would put the density change at less than one-third of 1%. So, if your accuracy requirements are looser than about 1 part in 1000, I'd recommend you use $\rho(800) = \rho _0 * (1.0025 +/- 0.001)$

Last edited: Feb 9, 2005
7. Feb 14, 2005

### minger

I ended up finding Compressed Liquid Tables in a Thermodynamics book. Interpolating specific volume between 200°F and 250°F in 500 psi and then again in 1000 psi (then of course interpolating between those and taking inverse for density), I ended up with a specific gravity of 0.956. That's almost 5% density change, much greater than 0.3%. I also needed somewhat good precision anyways because my answer was a somewhat strong function of density and we were borderline as it was. Thanks anyways for the help, even though it was like week, haha.

8. Feb 14, 2005

### Gokul43201

Staff Emeritus
From pg 20 here - http://widget.ecn.purdue.edu/~me200/Spring2005/Div. 3/ME 200 - Chapter 2(L7-L9).pdf

The specific volumes at 500 and 1000 psi (at 50F) are respectively 0.015998 and 0.015972 cu.ft./lb. Linearly interpolating for 800 psi gives 0.0159877. Converting this into a density gives d = 1.001908 gm/cc or an increase of about 0.2% (which is within my previous estimate).

I didn't know you wanted the density at high temperatures.

Last edited by a moderator: Apr 21, 2017
9. Feb 15, 2005

### minger

Don't you think the density will change with relation to temperature too? Here are my compressed liquid tables:
500 psia - 200°F v=0.016608 ft³/lbm
500 psia - 250°F v=0.016972 ft³/lbm
1000 psia - 200°F v=0.016580 ft³/lbm
1000 psia - 250°F v=0.016941 ft³/lbm
Now, dont even interpolate. Just look at the first one 0.016608^-1 = 60.2119 lbm/ft³. The reference density for water is what, 62.4? Dividing there gives you a specific gravity of 0.964. 3%, and my temperatures and pressures are even higher.

edit: I needed the exact density because lowering the density and specific gravity lowers required orifice that I needed, and I was right on the bubble, and every fraction of an inch helps while I was trying to get down to the next lower orifice size.

Last edited: Feb 15, 2005
10. Feb 15, 2005

### Gokul43201

Staff Emeritus
Of course it will. In this case, temperature plays the dominant role in affecting density (the 4% drop in density is from increasing temperature, not hardly from the pressure). If you look up the density of water at 200F and 1 atm pressure, you will find that it's about 0.96 g/cc.

However, in your previous posts you had forgotten to mention that you were looking for the density at high (~200 to 250 F) temperatures, so I assumed the temperature to be roughly that of cold tapwater.

11. Feb 15, 2005

### minger

Ooooohh, OK, I think we had some misunderstanding there, I apologize. However, even if it was at room temperature, I would want to have the density as exact as I could. I was really really close to not being able to use what I wanted ;)

12. Feb 15, 2005

### Gokul43201

Staff Emeritus
In that case I would pay more attention to the temperature (than to the pressure), as that is the dominant effect. It completely negates your being careful about the pressure if you are not extremely careful withnthe temperature.