32
1 Working Principles
In the relative frame:
2
2
2
1
2
1
irr12
w w
p
p q
0.
2
r
−
−
+
+
=
The kinetic energy increase in the absolute frame is visible in the velocity triangles.
The pressure increase follows from the kinetic energy decrease in the relative frame.
It follows as well that
2
2
2
2
2
1
1
2
v v
w w
W
.
2
2
D
−
−
=
+
The first part of the expression is the action part, the second one the reaction part.
The work done equals the total enthalpy increase (in adiabatic flow). The reaction
part of the work equals the static enthalpy increase (in adiabatic flow).
The degree of reaction is
Guide ring and delivery pipe: 2 → 3
In the absolute frame:
2
1
irr
2
1
0 d v
dp dU dq .
r
=
+
+
+
So
or
The kinetic energy and the pressure energy available downstream of the rotor are
converted, with losses, into increase of gravitational potential energy.
Addition of the three relations results in
or
The internal efficiency of the whole installation is
The losses in the pipes connected to the pump can be taken out of the definition
by placing manometers at the inlet and outlet of the pump and by determining the
manometric head. In the example of Fig. 1.12, the inlet is mostly considered as part
of the pump. If two manometers are mounted, the manometric head of the pump H m
is determined by
2
1
02
01
h h
R
.
h
h
−
=
−
2
a
2
2
3
2
irr 23
p
p
v
0 0
g( z z ) q
,
2
r
−
= − +
+
−
+
2
2
a
2
3
2
irr 23
p
p
v
g( z z ) q
.
2
r
−
+
=
−
+
0
1
3
2
irr03
W g( z z ) g( z z ) q
,
D +
−
=
−
+
3
0
irr03
W g( z z ) q
.
D =
−
+
3
0
i
g( z z ) .
W
h
D
−
=