Page 188 - Fluid mechanics, heat transfer, and mass transfer

MIXING
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Power number as a function of Reynolds number for different turbine impellers. D: impeller diameter; W: blade width.
FIGURE 6.1
sensitive to anything that changes flow patterns & Figure 6.1 illustrates the relationship between N Re
produced by the impeller. and P o .
& Power number is inversely proportional to N Re in the & In most industrial situations, power number of an
laminar regime, has weaker dependence on N Re in the impeller is constant under turbulent conditions. This
means that under turbulent conditions, power is pro-
transition regime, and is almost independent of N Re
under highly turbulent conditions. portionaltofluiddensityandindependentofviscosity.
& Power number will be low for impellers that produce & Under laminar conditions, power number is inversely
a uniform flow with relatively low levels of local proportional to Reynolds number, which means that
turbulence (e.g., narrow blade hydrofoils, P o ffi 0.3) power is proportional to viscosity and independent of
and much higher for impellers that produce a highly density.
nonuniform flow with high local turbulence intensity & Under transitional conditions, impeller power is
(e.g., the disk turbine, P o ffi 5). influenced by both viscosity and density.
& It is used to predict impeller power directly and & Under turbulent conditions, typical power numbers
torque indirectly. are listed in Table 6.1 for different impeller designs.
. How is power number related to Reynolds number for . What is pumping number/flow number?
mixing? N Q ¼ Q=ND : ð6:7Þ
3
m
n
P o ¼ KðN Re Þ ðN Fr Þ : ð6:5Þ
& It is a dimensionless number used to represent actual
& K, n, and m are constants, whosevalues depend on the
flow during mixing in a vessel.
type of impeller. For example, for a propeller with a
pitch equal to the diameter, n ¼ 1 and K ¼ 41,
according to one reference, based on experimental
TABLE 6.1 Power Numbers for Different Impeller Designs
data.
Number Power
& The Froude number correlates the effects of gravi-
Impeller Type of Blades Number
tational forces and it becomes significant only when

the propeller disturbs the liquid surface. Below 45 pitched blade turbine 4 1.37
Reynolds numbers of about 300, the Froude number Straight blade turbine 4 3.96
Straight blade turbine 6 4.92
is found to have little or no effect and
Disk turbine 6 5.0
n
P o KðN Re Þ : ð6:6Þ Hydrofoil impeller 3 0.31