Here we use pressure (across variable) of each independent fluid capacitor (A-type element) and volume flow rate (through variable) of each independent fluid inerter (T-type element) as system (state) variables.
Note that a fluid capacitor stores potential energy (a “fluid spring”) unlike the mechanical A-type element (inertia), which stores kinetic energy. For a liquid control volume V of bulk modulus b we have the fluid capacitance
For an isothermal (constant temperature, slow-process) gas of volume V and pressure P we have the fluid Capacitance
For an adiabatic (zero heat transfer, fast-process) gas we have the capacitance
which is the ratio of specific heats at constant pressure and constant volume?
For an incompressible fluid contained in a flexible vessel of area A and stiffness k, we have the capacitance
This is a T-type element. But, it stores kinetic energy, unlike the mechanical T-type element (spring), which stores potential energy. For a flow with unif form velocity distribution across an area A and over a length segment Dx we have the fluid inheritance
For a nonuniform velocity distribution, we have
In the approximate, linear case we have
The more general, nonlinear case is given by