27
1.6 Energy Analysis of Turbomachines
So
or
The gravitational potential energy consumed is converted into kinetic energy
and pressure energy, with losses. The inlet supplies the kinetic energy and pressure
energy to the rotor.
Rotor: 1 → 2
In the absolute frame:
2
1
irr
2
1
dW d v
dp dU dq .
r
=
+
+
+
So
or
Kinetic energy and pressure energy (= mechanical energy) are consumed in the
flow in order to generate mechanical energy on the rotor (  -ΔW), with losses. Kinetic
2
1
a
1
1
0
irr01
p p
v
0
gz gz q
0,
2
r
−
− +
+
−
+
=
2
1
a
1
0
1
irr01
p p
v
g( z z )
q
.
2
r
−
−
=
+
+
2
2
2
1
2
1
irr12
v v
p
p
W
q
,
2
D
r
−
−
=
+
+
2
2
1
2
1
2
irr12
v v
p p
W q
.
2
D
r
−
−
+
= −
+
0
1
2
3
z
u
u
0
v
1
v
2
v
1
w
2
w
Fig. 1.9 Energy analysis of an axial hydraulic turbine