APPENDIX V
DERIVATION OF EQUATION FOR BYPASS TUBE PRESSURE
1. Assuming that the propellant is all-burnt at the time the bypass port is uncovered, the equation of state is
given by
Where:
Pf =pressure in the device just before the port is uncovered
Vd =volume of the device
C =propellant charge weight
F =propellant impetus
1 = fraction of the total energy, CF, taken from the propellant gas by work and heat loss just before the port is
uncovered (this quantity can vary from about 0.35 to nearly 1.0, depending on the amount of work done and
the nature of the thruster design)
2. After the port is uncovered, the system again achieves an approximate equilibrium condition. The equation of
state becomes:
Where:
Vt = tube volume
Pt = tube pressure (pressure in complete system)
2= fraction of total energy lost as heat transferred to walls of tube after port is uncovered
3. It is assumed that external work has been completed at the time the port is uncovered, and that the process
can be represented as a quasi-static adiabatic expansion where the work done, W, is proportional to the internal surface
area of the tube, St, i.e., W = htSt where ht, is an empirical proportionality constant. Therefore,
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