Computation of Water-Discharge Volumes.

Jets of high pressure water from the PTV pose a potential risk to people and property. To appreciate the potential risk, consider that a 3000 psi water jet from a properly shaped nozzle can cut heavy steel plate. The PTV is pressurized by forcing more water into the vessel than it can hold at atmospheric pressure. As more water is forced into the PTV, the pressure rises and the water is compressed. If the air-bleed valve on the pressurized PTV were mistakenly opened then a high pressure jet would expel this excess water. A baffle has been installed on the air-bleed valve to prevent damage or injury.

Appendix A.2 demonstrates that the pressure vessel is incompressible compared to water -- the volume of the PTV remains essentially constant with pressure. This fact can be used to compute the volume of water expelled while discharging the PTV. The mass of water in the PTV at atmospheric pressure is $M_o = V\rho_o$ where $V$ is the water volume and $\rho_o$ is the water density at atmospheric pressure. Similarly, the mass of water at pressure $p$ is $M = V\rho(p)$. Subtracting these two expressions yields the mass of water that is discharged: $\delta M = V \left[\rho(p) - \rho_o\right]$. Dividing by $\rho_o$ gives the volume of water expelled while discharging the PTV:

  $$\delta V = V \left[ \frac{\rho(p)}{\rho_o} - 1 \right]~.$$ (1)

Table 1: The discharge volume for the PTV at various pressures. The last four table columns correspond to the PTV with 3, 2, 1, or 0 aluminum ingots installed to reduce the compressible volume.

p

Discharge Volume (gal)
(psi)	$\frac{1}{4} V$	$\frac{1}{2} V$	$\frac{3}{4} V$	$V$
1000	0.2	0.3	0.5	0.6
2000	0.3	0.6	0.9	1.2
3000	0.5	0.9	1.4	1.8
4000	0.6	1.2	1.8	2.4
5000	0.7	1.5	2.2	3.0
6000	0.9	1.8	2.6	3.5
7000	1.0	2.0	3.1	4.1
8000	1.2	2.3	3.5	4.6
9000	1.3	2.6	3.9	5.2
10000	1.4	2.9	4.3	5.7

Table 1 shows that the discharge volume is roughly one-half gallon per kpsi for the PTV at full volume.