Brochure

74
74
4. Pump theory
4.8 Specific speed of a pump
As described in chapter 1, pumps are classified in many dierent ways for
examplebyusageorangesize.Seenfromauidmechanicalpointofview,
this is, however, not very practical because it makes it almost impossible to
compare pumps which are designed and used dierently.
A model number, the specific speed (n
q
), is therefore used to classify pumps.
Specicspeed is givenindierent units. InEuropethe following formis
commonly used:
n
n
n
(4.21)
(4.22)
(4.23)
vmF ⋅ =
⋅
2
vAvmI ⋅⋅=⋅=∆ ρ
⋅
FI = ∆
(4.21)
(4.22)
(4.23)
Q
g bD
U
g
U
H
⋅
⋅ ⋅⋅
⋅
−=
22
2
2
2
2
) tan(
π
β
Scaling of
rotational speed
n
PP
QQ
HH

















⋅ =






⋅ =






⋅ =
3
2
Geometric
scaling
bD
bD
PP
bD
bD
Q
D
D
HH



















⋅
⋅
⋅=







⋅
⋅
⋅=






⋅=
4
4
2
2
2
u,Am,A
C
A
B
AB
CU
= =
(4.24)
(4.25)
(4.26)
(4.27)
(4.28)
2,A
DnU ⋅
=
2,A AA
2
2,A2,AA2,A2,A2,A2,A
222
nb
2,B B
nb
D
2,B
D
DnbDC
C
bDQ
B
Q
CbDCAQ
2m,A
2m,B
2m2m
⋅ ⋅








=
⋅⋅⋅⋅
= ⋅
⋅⋅
=
⋅⋅⋅ = ⋅ =
π
2,BB2,B2,B
DnbD ⋅⋅⋅⋅ π
π
2,B2,B
bD ⋅⋅ π
π
2 2
2,A2,A2,A22,A22,A
22,A
⋅















=
⋅⋅⋅
=
⋅
=
⋅⋅
=
⋅
=
nDDnDnCU gCU H
H
g
CU
H
U,A
22,B
⋅ CU
U,B
AA
B
A
2,B
nD
B
A
2,B2,B
⋅⋅⋅ DnDn
B B
U,A
22,B
⋅⋅ gCU
U,B
U,A
3
4
2,A 2,A A22,A22,A
22
⋅














= ⋅ =
⋅
⋅ =
⋅ ⋅ ⋅
=
⋅⋅⋅=
n
B
n
b
2,B
b
D
2,B
D
HQCUQ
Q
CUQP
CUQP
U,A
22,B
⋅ CU
U,B
A A
HQ
B B
U,AA
P
B
A A
B
U
ρ
22,B
⋅ ⋅ ⋅ CUQ
U,BB
ρ
ρ
4
3
2
1
H
Q
nn
q
⋅=
(4.29)
(4.20)
g
U
H =
2 2U
[ ]
⋅ C
m
[ ]
N
[ ]
N
[ ]
N
[ ]
m
B
B
P
A
n
B
A
n
B
A
B
A
A
B A
A
Q
B
AB
AA
BB
AA
BB
A
u,B
d
d
d
m,B
CCU
B
A A
2,B
DnU ⋅
B B
Where
n
d
= rotational speed in the design point [min
-1
]
Q
d
= Flow at the design point [m
3
/s]
H
d
= Head at the design point [m]
The expression for n
q
can be derived from equation (4.22) and (4.23) as the
speed which yields a head of 1 m at a flow of 1 m
3
/s.
The impeller and the shape of the pump curves can be predicted based on the
specific speed, see figur 4.17.
Pumps with low specific speed, so-called low n
q
pumps, have a radial out-
let with large outlet diameter compared to inlet diameter. The head curves
are relatively flat, and the power curve has a positive slope in the entire flow
area.
On the contrary, pumps with high specific speed, so-called high n
q
pumps,
have an increasingly axial outlet, with small outlet diameter compared to the
width. Head curves are typically descending and have a tendency to create
saddle points. Performance curves decreases when flow increases. Dierent
pump sizes and pump types have dierent maximum eciency.