The weight flow rate is
_
x ¼ A 1 A 0 p c
ð9:15Þ
In Eq. (9.15), gas flow coefficient is
A t ¼
ffiffiffiffiffiffiffi ffi
cg
RT c
r
2
c þ 1
cþ1
2 cÀ1
ð
Þ
ð9:16Þ
From the above equations, after sorting out, it can be obtained,
N ¼ E 1 À
p e
p c
m !
p c
ð9:17Þ
(2) Functional Relationship between Gas Thrust and Gas Pressure
Equation
F ¼ H 1 À
p e
p c
m ! 1
2
p c
ð9:18Þ
where
F Gas output thrust (N);
H
Coefficient, H ¼ c
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
2
cÀ1
2
c þ 1
cþ1 cÀ1
r
A 0 .
Simplify
If p e p c , 1 À
p e
p c
m
h
i 1
2 ! 1, Eq. (9.18) can be simplified to
F % Hp c
ð9:19Þ
Deduction
Because the gas thrust is
F ¼
_
x
g
v
ð9:20Þ
In Eq. (9.20), the weight flow rate is
_
x ¼
ffiffiffiffiffiffiffi ffi
cg
RT c
r
2
c þ 1
cþ1
2 cÀ1
ð
Þ
"
#
A 0 p c
ð9:21Þ
126
9 High-Temperature and High-Speed Gas Turbine Pump …