154
4 Compressible Fluids
We consider a flow without work exchange (  dW = 0) and as yet without losses (  dq irr
= 0). Gravitational potential energy may always be ignored for a compressible fluid
in a flow with significant pressure variation. This follows from the typical low density value (e.g. air under atmospheric conditions ρ ≈ 1.20 kg/m
3
). Example: a 1 m
height change is a change in potential energy of about 10 J/kg. The corresponding
pressure change is dp = ρdU ≈ 12 Pa. We simplify the work equation to
(4.2)
The energy equation in absence of work exchange and heat exchange is
The influence of potential energy may be ignored again. Example: a 10 J/kg enthalpy change represents a temperature change of dT ≈ 0.01 K (  c p = 1005 J/ kgK for
air under atmospheric conditions). We simplify the energy equation to
(4.3)
A total differential is formed in the energy equation. We therefore introduce the
concept of total enthalpy, defined by
(4.4)
1
1
2
dW d v
dp dU dq .
irr
2
r
=
+
+
+
2
1
dp
d v
0.
2
r
+
=
2
1
0 dh d v dU .
2
= +
+
2
1
dh d v
0.
2
+
=
2
0
1
h h
v .
2
= +
Fig. 4.1 Nozzle between two
spaces (0 and 1)