120
P. Liu
Fig. 2.57 Ernst Mach (1836–1916, Austrian physicist)
In one-dimensional steady compressible flow, because the flow parameters increase from two to four, it needs four basic equations to solve. The
basic control equations needed are as follows: state equation, continuous
equation, momentum equation, and energy equation of ideal flow.
The equation of state for a complete gas is
p = ρ RT
where p is the pressure, ρ is the density, T is the temperature, and R is
the gas characteristic constant (= 287.053 N.m/(kg.K)).
The continuity equation is
ρ AV = const.,
dρ
ρ
+
dV
V
+
d A
A
= 0
where A is the pipe area. The momentum equation is
d p
ρ
= −V dV
For the moving system of unit mass gas, the energy equation can be
obtained from the first law of thermodynamics
dq = de + pd
1
ρ
+
1
ρ
d p + V dV
P. Liu
Fig. 2.57 Ernst Mach (1836–1916, Austrian physicist)
In one-dimensional steady compressible flow, because the flow parameters increase from two to four, it needs four basic equations to solve. The
basic control equations needed are as follows: state equation, continuous
equation, momentum equation, and energy equation of ideal flow.
The equation of state for a complete gas is
p = ρ RT
where p is the pressure, ρ is the density, T is the temperature, and R is
the gas characteristic constant (= 287.053 N.m/(kg.K)).
The continuity equation is
ρ AV = const.,
dρ
ρ
+
dV
V
+
d A
A
= 0
where A is the pipe area. The momentum equation is
d p
ρ
= −V dV
For the moving system of unit mass gas, the energy equation can be
obtained from the first law of thermodynamics
dq = de + pd
1
ρ
+
1
ρ
d p + V dV