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Comparison ofLiąuid Propellant Rocket Engine Feed Systems -1-7

(N II £	(2.2.2)
where, Ap: Sphere outside to inside pressure fali. T: Sphere wali stress. r. Sphere radius
In tum, the maximum stress that the wali supports is proportional to their thickness. The maximum allowable stress for a rigid materiał can be obtained using the UTS parameter (Ultimate Tensile Strength) which is temperaturę dependent. Thus:
Tmx =°^e	(2.2.3)
where, Tmax- Maximum allowable materiał stress. er. UTS (Pa). e\ materiał thickness (m).
Assuming a spherical tank, the next expressions tum out:
4 , V. = n rf 3	(2.2.4)
S, = 4 ir,^1	(2.2.5)

2.2.1. Pressurizing gas tank mass

Now this mass estimation can be faced, assuming that the tank volume is completely filled by the gas:

(2.2.6)

_gR_uT₀

PM_g

Then, combining the expressions 2.2.2, 2.2.3, 2.2.4 and 2.2.6:

^e, —

Po

2 <7,

4 7cp_QM_g j

(2.2.7)

Finally, an eąuation to estimate the mass of the spherical tank can be obtained combining the expressions 2.1.10, 2.2.1, 2.2.5 y 2.2.7:

^{m,s =} ^Ł^k«^k*^kr^k'^r*^a

^mp Pc

1 -k_m ^Fc

Po J

(2.2.8)

where k,_g is a constant that provides a safety margin to the estimated mass.