31
1.6 Energy Analysis of Turbomachines
So
or
As with the turbine, the gravitational potential energy consumed is converted into
kinetic energy and pressure energy, with losses. Figure 1.12 shows a pump that is
mounted below the suction level (submerged). If the pump is mounted above the
suction level, with a suction pipe, g(  z 0– z 1 ) is negative. The above expression may
then be better written as
2
a
1
1
1
0
irr01
p
p
v
g( z z )
q
.
2
r
−
=
−
+
+
The interpretation is then that the suction height is overcome due to pressure lowering at the suction side of the pump and that kinetic energy is generated, with losses.
Rotor: 1 → 2
In the absolute frame:
2
1
irr
2
1
dW d v
dp dU dq .
r
=
+
+
+
So
The work done on the fluid results into mechanical energy increase, with losses.
2
1
a
1
1
0
irr01
p p
v
0
g( z z ) 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
−
−
=
+
+
1
2
0
3
u
u
1
v
2
v
1
w
2
w
Fig. 1.12 Energy analysis of an axial pump