8 Pumps
288
(8.7)
When cavitation occurs on the location considered, pressure equals the vapour pressure. We may then replace
p
C
−
with σ according to (8.1). The NPSH value required
to avoid cavitation should meet
(8.8)
The NPSH value is always positive and that feature is referred to in the terminology.
The highest, and thus most critical value of NPSH, is attained for the most unfavourable combination of v 1 and w 1 . With a centrifugal pump, the most unfavourable combination is at the casing.
Henceforth we reason with centrifugal pumps. The hub side may be most critical
with axial pumps. This complicates the reasoning, but the results derived hereafter
may be applied qualitatively to axial pumps as well. We reason with a pump with
supply to the suction eye in line with the shaft, as in Fig. 1.13 of Chap. 1. The reasoning is the same for a mixed-flow pump (see the further Fig. 8.12) or for an axial
pump (see Fig. 1.3 in Chap. 1) with a similar suction eye. We note the highest value
of NPSH r as
(8.9)
w
d
th
n
,
i
a
2
2
2
1
1
1
1
1
d
w
u v
u
2
W
= +
=
where d 1 is the diameter of the rotor inlet at the casing or the rotor shroud. The value
of λ ≈ 1.1. The velocity v 1 at the corresponding position may be estimated from the
velocity v 0 at the inlet of the eye of the rotor by a velocity factor:
(8.10)
We take here into account that the leakage flow in a pump is negligible. The diameter of the suction eye of the rotor is denoted with d 0 . The factor k is the square of the
ratio ( d 0 /d 1 ), typically about (0.9)
2
. If the shaft passes through the suction eye, this
factor must also take into account the obstruction by the hub around the shaft. With
(8.10), we use a similar notation as we did with the optimisation of the inlet of the
rotor of a radial fan (Sect. 3.4.10). Generally, the velocity factor ζ is unity in a pump
r
−
−
=
1
p
2
1
1
2
p p
C
.
w
with
.
x
s
= +
>
+
2
2
1
1
r
r
v
w
gNPSH
NPSH NPS
1
2
H
(
)
2
l
s
=
+
2
2
1
1
r
v
w
gNPSH
,
2
2
with
.
1
0
0
2
o
4Q
v
v
d
v
z
p
=
=
.
Thus:
1
2
1
Q
v 4(
)
k d
z
p
=
288
(8.7)
When cavitation occurs on the location considered, pressure equals the vapour pressure. We may then replace
p
C
−
with σ according to (8.1). The NPSH value required
to avoid cavitation should meet
(8.8)
The NPSH value is always positive and that feature is referred to in the terminology.
The highest, and thus most critical value of NPSH, is attained for the most unfavourable combination of v 1 and w 1 . With a centrifugal pump, the most unfavourable combination is at the casing.
Henceforth we reason with centrifugal pumps. The hub side may be most critical
with axial pumps. This complicates the reasoning, but the results derived hereafter
may be applied qualitatively to axial pumps as well. We reason with a pump with
supply to the suction eye in line with the shaft, as in Fig. 1.13 of Chap. 1. The reasoning is the same for a mixed-flow pump (see the further Fig. 8.12) or for an axial
pump (see Fig. 1.3 in Chap. 1) with a similar suction eye. We note the highest value
of NPSH r as
(8.9)
w
d
th
n
,
i
a
2
2
2
1
1
1
1
1
d
w
u v
u
2
W
= +
=
where d 1 is the diameter of the rotor inlet at the casing or the rotor shroud. The value
of λ ≈ 1.1. The velocity v 1 at the corresponding position may be estimated from the
velocity v 0 at the inlet of the eye of the rotor by a velocity factor:
(8.10)
We take here into account that the leakage flow in a pump is negligible. The diameter of the suction eye of the rotor is denoted with d 0 . The factor k is the square of the
ratio ( d 0 /d 1 ), typically about (0.9)
2
. If the shaft passes through the suction eye, this
factor must also take into account the obstruction by the hub around the shaft. With
(8.10), we use a similar notation as we did with the optimisation of the inlet of the
rotor of a radial fan (Sect. 3.4.10). Generally, the velocity factor ζ is unity in a pump
r
−
−
=
1
p
2
1
1
2
p p
C
.
w
with
.
x
s
= +
>
+
2
2
1
1
r
r
v
w
gNPSH
NPSH NPS
1
2
H
(
)
2
l
s
=
+
2
2
1
1
r
v
w
gNPSH
,
2
2
with
.
1
0
0
2
o
4Q
v
v
d
v
z
p
=
=
.
Thus:
1
2
1
Q
v 4(
)
k d
z
p
=