D0 Silicon Upgrade: Liquid and Gas Nitrogen Line Sizing for D-Zero Upgrade

This engineering note documents the calculations done to properly size the liquid/gas nitrogen piping system for the D-Zero refrigerator, solenoid, and VLPC upgrade. See the line sketch of the system on the next page. The sketch shows the chosen line sizes, estimated lengths of piping runs, estimated steady state flow rates and pressure drops for each pipe section. The raw calculations are attached as an appendix. The estimated steady state flow rates were developed in D-Zero EN-421, 'Helium and LN2 Storage Requirements for the D-Zero Upgrade'. The pressure drop calculations take into account the two phase property of the fluid on the inlet piping. The outlet piping is sized for saturated vapor. These calculations supplement sizing that was done in D-Zero EN-416, rev. 6/26/95, 'Pipe Sizing for Solenoid/VLPC Cryogenic Systems', EN-416 only looked at the Solenoid and VLPC sections of the system. In a previous EN-430, 'LN2 control valve sizing', a calculation was done to address the cool down flow rate necessary. The minimum cooldown flow rate needed for a simultaneous, serial cooldown of the refrigerator, solenoid and VLPC system was 6.4 g/s. This warm flow would get choked by an opening less than 0.175-inch in diameter. All the piping/tubing sizes exceed this size, so cooldown will not be a problem. The available pressure drop for the VLPC and solenoid control valves was calculated to be 5.5 psid and 27 psid respectively. The actual delta P is expected to be larger because the conservativeness of using maximum flow rates and fluid properties that yield pressure drops on the high side.