The gas outlet velocity is
v ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2gr
r À 1
RT 1 À
p e
p c
m !
s
ð9:22Þ
From the above equations, after sorting out, it can be obtained,
F ¼ H 1 À
p e
p c
m ! 1
2
p c
ð9:23Þ
(3) Functional Relationship between Gas Pressure and Characteristic Area
Equation
p c ¼ k
2 A b
A 0
2
ð9:24Þ
where
A 0 Area of nozzle throat (cm
2 );
K Coefficient, K ¼ d
a 1
A t
;
d Grains weight (g=cm
3 );
a t Burning rate temperature coefficient mm= s Á MPa
ð
Þ
½
Š ;
a 1 ¼ a 0 1 þ a T T À T 0
ð
Þ
½
Š
ð 9:25Þ
a 0 Temperature coefficient of burning rate at room temperature
mm= s Á MPa
ð
Þ
½
Š ;
a T Temperature sensitivity coefficient (1=K);
T Environmental temperature (K);
T 0 Room temperature, T 0 ¼ 293 K.
Deduction
Because the nozzle weight flow rate is
_
x 0 ¼ A 1 A 0 p c
ð9:26Þ
The weight flow rate of the grain is
_
x d ¼ dA b r
ð9:27Þ
9.3 Design Principle of Gas Generator
127