In the fluid aspect, capacitance is equal to the moles n of fluid multiplied by its compressibility β, and has units of (kg*mol/kPa). Since the node fluid quantity is generally proportional to volume, capacitance is proportional to volume, but it is not correct to say that it is equal to volume.

C = n · β

From the definition of compressibility with respect to specific volume υ and pressure p:

β = -1/υ · δυ/δp

Specific volume is the inverse of density, or υ = 1/ρ = V/m, so:

β = -m/V · δυ/δp

C = -n·m/V · δυ/δp

Mass is related to moles by the fluid’s molecular weight MW = m/n:

C = m ²/(MW·V) · δυ/δp

C = m ²/(MW·V) · δυ/δm · δm/δp

C = m ²/(MW·V) · δ(V/m)/δm · δm/δp

We assume volume V is constant for this definition. Volume in a node is not always constant, but when it changes, that is handled elsewhere in GUNNS so we don’t factor it in our capacitance. Thus volume cancels out of the above, so:

C = m ²/MW · δ(1/m)/δm · δm/δp

C = m ²/MW · m ^-2 · δm/δp

C = 1/MW · δm/δp

This matches our analogous definition of capacitance across all aspects in GUNNS: it is the change in quantity (moles) over change in potential. Substituting density ρ = m/V:

C = 1/MW · δ(ρV)/δp

C = V/MW · δρ/δp

This is how GUNNS computes the actual capacitance, as volume times the change in density over change in pressure, instead of working directly with the compressibility β. The δρ/δp term is purely a function of the fluid properties and works with any type of fluid state equation, so this works for liquids and real gases as well as ideal gases. The volume is a physical property of the capacitive device.

Why do we work with fluid quantity in moles instead of mass? The above relationship between capacitance and compressibility is just as true expressed in terms of mass as with moles:

C = m · β = V · δρ/δp

But GUNNS works with moles instead of mass. See Molar_Quantity_and_Flows for the reason why.

Capacitance