How to calculate the pressure applied in a compressible fluid?

If I am trying to figure the pressure needed contain a fluid like hydrogen in a cylindrical tank, how would calculating this go on? As Hydrogen is compressible to a differing amount than other compounds and has a volume, doing a force over area is un-feasible. Hence, what formula or steps are needed to compute this?

• Are you just trying to calculate pressure of a mass of hydrogen? Jan 12, 2022 at 15:15
• What is the starting state of your hydrogen in terms of temperature, pressure, and mass (or volume)? What is your desired end state for the hydrogen? As a general note, if you aren't familiar with the hazards of working with hydrogen you should familiarize yourself with them before working with the gas. Jan 12, 2022 at 19:09
• I am trying to figure out the force required for a piston to compress a certain volume X of hydrogen with two piston's, and by result, the displacement of the piston's. This is just a theoretical investigation, no device will be built. Jan 13, 2022 at 1:20

2 Answers

You need to find the compressibility factor, which is defined as $$Z = \dfrac{pV}{nRT}$$ of the hydrogen, then correlate to the "ideal gas", which has a compressibility factor of 1.

https://en.wikipedia.org/wiki/Compressibility_factor

• Thank you. That will allow me to calculate the compressibility, yet how would I use that value to compute the pressure and by proxy needed to compress a specific volume of hydrogen with a piston? Jan 12, 2022 at 2:37
• The molar volume of the ideal gas, V_ig = RT/p, and the corresponding molar volume of the real gas, V_rg = RTZ/p. Does this help?
– r13
Jan 12, 2022 at 2:54

Hydrogen will not liquify no matter how high it is compressed. Unless it is cooled down to its critical temperature which is $$- 252.8^{\circ}C$$

Hydrogen can be physically stored as either a gas or a liquid. Storage as a gas typically requires high-pressure tanks (5000–10,000 psi tank pressure). Storage of hydrogen as a liquid requires cryogenic temperatures because the boiling point of hydrogen at one-atmosphere pressure is -252.8°C.

That means theoretically if you can maintain the hydrogen below critical temperature the vessel vapor pressure is about one Atm.

Hydrogen can be stored on the surface of solids by adsorption and in the solids by absorption.

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Quote from source