2 Aerodynamics
121
where dq is the heat transferred from the outside to the system, de is the
internal energy increment of the system, pd
1
ρ
is the expansion work of
the system to the outside,
1
ρ
d p is the pressure difference work of the
moving system, and V dV is the kinetic energy increment of the system,
which can also be written as
dq = d(e +
p
ρ
+
V 2
2
)
In the case of adiabatic flow, the energy equation becomes
e +
p
ρ
+
V 2
2
= C
The above formula shows that the sum of internal energy, pressure
energy, and kinetic energy per unit mass of gas is constant along the same
streamline in a one-dimensional steady flow. In a compressible gas, the
enthalpy is defined as
h = e +
p
ρ
, h = C p T
where h is the sum of internal energy and pressure energy of unit
mass gas. C p is the specific heat coefficient of constant pressure (=
1004.7 N.m/(kg.K)). The energy equation of a one-dimensional steady
adiabatic flow is
C p T +
V 2
2
= C
The internal energy of unit mass gas can be expressed as
e = C v T, C v = 717.6 N.m/(kg.K)
where C v is the constant volume specific heat coefficient of unit mass gas.
Introducing specific heat ratio γ = C p / C v , the energy equation can be
written as
γ RT
γ − 1
+
V 2
2
= C,
a 2
γ − 1
+
V 2
2
= C,
γ
γ − 1
p
ρ
+
V 2
2
= C