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Comparison of Liąuid Propellant Rocket Engine Feed Systems - 1 - 6

0/F

m_f p_fv_f

- -\^mp = ^mp

p_a \\+OIF)

1

p_f \ \ + 0! F

m _p = a _r m _p

(2.1.5)

(2.1.6)

(2.1.7)

where, v_o & v _f: Oxidizer or fuel volumetric flow as designated with “o” or “f ’ (m³/s).

m„ &m/: Oxidizer or fuel mass flow as designated with “o” or “f ’ (kg/s). p₀ & pf. Oxidizer or fuel density (kg/rn³).

O/F: Propellant mixture ratio. m_p: Propellant total mass (kg).

Notę that once defined the a₀ and ajconstants is possible to write:

a_Q + a_f = a    (2.1.8)

V_p = V_c + V_f = a„m_p + a_tm_r = a m_p    (2.1.#)

Finally, a safety constant k_g is defined, which provides a margin to account the gas mass that, at the end of the operation cycle, will stay inside the gas tank and in the feed system pipes. Thus, the eąuation 2.1.1 becomes:

,=^kg^kpk_uy_ga

^mp Pc Pc

1 -k

Po)

(2.1.10)

2.2. Tanks mass

The tanks’ masses can be estimated multiplying each tank volume by its constituting materiał density. Thus, the next expression is obtained:

m, = p,S, e,    (2.2.1)

donde, m,: Tank mass (kg).

S,: Tank surface (m²).

e,: Tank wali thickness (m).

p,: Tank materiał density (kg/m³).

Using the Laplace 's Law is possible to relate the wali stress of a body, under the effect of a determined pressure, whit their physical dimensions. In particular, if a spherical tank is considered, the next relationship is derived: