7 Dynamic Similitude
272
roughness, the relative clearances and the relative thicknesses, so-called model laws
can be applied. Model laws are inspired by the finding that 1 h
− is proportional
to the friction losses and that these, according to the Moody diagram, vary within
the transition area with the Reynolds number to a power between − 0.25 and − 0.1.
Clearly, the exponent is a rough estimate. Thus, model laws have a weak foundation
and should not be overvalued.
Moody’s model law for hydraulic turbines is
(7.13)
Pfleiderer’s model law for centrifugal pumps is
(7.14)
In the first formula, D is the rotor diameter. In the last formula, D is the diameter of
the suction eye, expressed in mm. The subscript 0 refers to the model. Both formulae encompass a correction on the effect of the Reynolds number in order to take
the imperfect geometric similitude into account. For pumps, Re is determined with
the peripheral rotor speed (
)
Re
/ ,
2 2
u d
=
v for turbines with the spouting velocity
(
)
/ .
m 2
Re
2gH d
=
v
7.5 Series and Parallel Connection
If no single-rotor machine with an acceptable rotational speed can be found for a
particular combination of energy change and flow rate, series or parallel connection
may be considered. Connection may occur within the same machine. Series connection of rotors increases the overall energy exchange. Parallel connection increases
the flow rate. These internal connections are common with pumps. They will be
studied in the chapter concerned. Internal series connection is very common with
compressors, steam and gas turbines. Series or parallel connection of separate machines may be chosen to enable a flexible use of the machine group.
7.5.1 Parallel Connection of Fans
Figure 7.16 shows the flow rate addition of two parallel connected identical fans.
Flow rate is doubled with the same energy rise. With the load characteristic L1
(typically no static part with fans), the operating point is B for an individual fan. If
0.05
0.2
0
0
0
1
D
Re
.
1
D
Re
h
h
−
−
− =
−
1.5
0.1
0
1.5
0
0
1 70 / D
Re
1
( 1 [
]
)(
) .
Re
1 70 / D
h
h
−
−
− = − −
272
roughness, the relative clearances and the relative thicknesses, so-called model laws
can be applied. Model laws are inspired by the finding that 1 h
− is proportional
to the friction losses and that these, according to the Moody diagram, vary within
the transition area with the Reynolds number to a power between − 0.25 and − 0.1.
Clearly, the exponent is a rough estimate. Thus, model laws have a weak foundation
and should not be overvalued.
Moody’s model law for hydraulic turbines is
(7.13)
Pfleiderer’s model law for centrifugal pumps is
(7.14)
In the first formula, D is the rotor diameter. In the last formula, D is the diameter of
the suction eye, expressed in mm. The subscript 0 refers to the model. Both formulae encompass a correction on the effect of the Reynolds number in order to take
the imperfect geometric similitude into account. For pumps, Re is determined with
the peripheral rotor speed (
)
Re
/ ,
2 2
u d
=
v for turbines with the spouting velocity
(
)
/ .
m 2
Re
2gH d
=
v
7.5 Series and Parallel Connection
If no single-rotor machine with an acceptable rotational speed can be found for a
particular combination of energy change and flow rate, series or parallel connection
may be considered. Connection may occur within the same machine. Series connection of rotors increases the overall energy exchange. Parallel connection increases
the flow rate. These internal connections are common with pumps. They will be
studied in the chapter concerned. Internal series connection is very common with
compressors, steam and gas turbines. Series or parallel connection of separate machines may be chosen to enable a flexible use of the machine group.
7.5.1 Parallel Connection of Fans
Figure 7.16 shows the flow rate addition of two parallel connected identical fans.
Flow rate is doubled with the same energy rise. With the load characteristic L1
(typically no static part with fans), the operating point is B for an individual fan. If
0.05
0.2
0
0
0
1
D
Re
.
1
D
Re
h
h
−
−
− =
−
1.5
0.1
0
1.5
0
0
1 70 / D
Re
1
( 1 [
]
)(
) .
Re
1 70 / D
h
h
−
−
− = − −