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I'm working on an extracurricular project and I'm trying to determine what volume of propellant tank I need to 12.14 kg of hydrazine propellant stored at 22 bar. I researched and found this pressure was typical for storage and wondered if it changed the volume of the propellant compared to if I were to do a basic density to volume conversion.

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  • $\begingroup$ I don't have a reference for this, but it may help you decide if the effect is significant enough for you to pursue: for simulations of the shuttle OMS fuel tank (it was MMH) the fuel density change over the range of 0 to 20 bar was around a tenth of a percent at constant temperature. $\endgroup$ Dec 26, 2020 at 16:23
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    $\begingroup$ Further to the other comments/answers you may find that the temperature range for storage has a larger effect on the density than its compressibility. Typical storage temperature ranges start at its freezing point, plus a sensible margin, and run up to various figures according to circumstances. e.g 9degC to 40degC in a tank through to a max of 90degC tolerated in pipe inlets to thrusters, though I suspect the latter is asking for trouble from bubble generation $\endgroup$
    – Puffin
    Dec 27, 2020 at 0:38

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The volume change is negligible for most purposes.

Ordinary liquids (water, organic solvents, hydrazine) are relatively incompressible in the sense that their change in density is negligible for easily accessible pressures. 22 bar is only 4 times what I pump my bike tires up to with a manual pump, so it's not that extreme.

This 1977 US Air Force document gives the compressibility of hydrazine as

$$\beta = 2.51 \times 10^{-5}~\mathrm{atm}^{-1} = 2.48 \times 10^{-5}~\mathrm{bar}^{-1}.$$

The compressibility is $$\beta = -\frac{1}{V} \frac{\partial V}{\partial p},$$ where $V$ is the volume and $p$ is the pressure. I assume that the US Air Force report is giving the isothermal compressibility, which means that the partial derivative is taken for constant temperature. In any case, for sufficiently small changes in pressure:

$$\frac{\Delta V}{V} \approx - \beta \Delta p$$.

You want to calculate the change in volume for hydrazine at standard temperature going from atmospheric pressure to 22 bar, $\Delta p$ is equal to $(22 - 1.01325) = 20.98675~\mathrm{bar}$. So the volume of hydrazine would change by $\frac{\Delta V}{V} \approx -5 \times 10^{-4}$.

The density of hydrazine at standard conditions is $1.021~\mathrm{g/cm^3}$, so you have 12.15 L of hydrazine. The volume would decrease by 0.006 L = 6 mL upon applying 22 bar of pressure, which is probably less than the uncertainty in your other measurements.

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    $\begingroup$ Water at 4000 bar is compressed to about half the volume as I remember from a water cutting machine demonstration. $\endgroup$
    – Uwe
    Dec 26, 2020 at 17:31

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