A liquid accumulator, also called a lumped capacitance, models a liquid- filled container in a system (Wylie, et al, 1993Wylie, E.B., V.L. Streeter & L. Suo, Fluid Transients in Systems, Prentice Hall, Englewood Hills, New Jersey, 1993., pp. 124-125). The interaction with the pipe system occurs as the container stretches and contracts in response to transient pressures. The liquid accumulator is similar to a branch, and thus the same equations are involved.

where SC and SB are given by Equations 2 and 3 from Branch Waterhammer Theory. The relationship between accumulator pressure and volume is assumed to be linear,

where K’ is the effective bulk modulus of elasticity of the container, which describes the elastic effects of both the fluid and container, and has units of pressure. The change in volume can be related to flow rate as follows:

Therefore,

Substituting and eliminating flow rate

Liquid Accumulator Vapor Cavitation Theory

When the calculated pressure at a Liquid Accumulator junction drops below vapor pressure, a vapor cavity forms at the junction.

The vapor volume calculation is as follows:

where ṁ_A is the accumulator flow out of the junction. The ṁ_in terms are obtained from the positive compatibility equation, while the ṁ_out terms are obtained from the negative equation.

Similar to a pipe interior node, when the vapor volume is negative, the cavity collapses and the fluid pressure then rises above the vapor pressure.