Calculation of Potential Energy Stored in Compressed Water.

Consider a cylinder capped on one end with an end cap and on the other end
with a piston (see Fig. 3). The cylinder
is filled with a mass, , of water which is pressurized by applying a
force, , to the piston. The force that must be applied is where
is the area of the piston and is the water pressure. The work done
in compressing the water is ,

The fact that the mass of water is fixed can be used to determine the
relationship between the piston position and the water pressure. Note that
a fixed mass implies that

where is the compressibility of water. Table 3 demonstrates that the compressibility is nearly constant over the range of pressures relevant to the PTV.

The density can also be expressed as
where is the
cross-sectional-area of the vessel. Substituting this into (11)
yields the following equivalent relationships between the pressure and the
piston position,

(13) |

Equation (14) is exact but unnecessarily complicated. Note that even at a maximum pressure of 10 kpsi then and therefore . Computing the Taylor series of (14) and neglecting third and higher order terms yields a greatly simplified expression with an error of approximately only 3%: