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94 3. Heterogeneous Processes and Reactor Analysis

3.3.5 Hydraulics

Hydrodynamic analysis of agitated vessels
The impeller Reynolds number is defined as follo ws:
DN 2 a L
N (3.104)

Re
L
where:
N the impeller rotational speed, r/s
D the impeller diameter m ,
a
the liquid density kg/m , 3
L
the dynamic liquid viscosity Pa s. ,
L
The flow is called turbulent in the case N 10,000, whereas the flow is laminar in the
Re
case N 10. In the case 10 N 1000, the flow is characterized as transient (Perry
Re Re
and Green, 1999).
The following equations relate velocity head, pumping rate, and po wer under turb ulent-
flow conditions:
Q Q a 3 (3.105)
N ND
2 2
NN D
H P a (3.106)
Ng Q
D  5  g
a
P N P N L 3  g  c   L HQ g c (3.107)

where:
Q the impeller discharge rate, m 3 /s
N the discharge coef dimensionless icient, f
Q
N po dimensionless, wer number ,
P
H the velocity head, m
P the po Nm/s = J/s = , wer W
g 1 when using SI units
c
g the gravitational acceleration, m/s 2 .
It should be noted that for relatively dilute solid–liquid mixtures, e xcept for f ibrous solids,
the power to agitate at a given speed is essentially the same as for the clear liquid (Treybal,
1980). Concentrated slurries and suspensions of fibrous solids are likely to be non-
Newtonian in character.
Given the delivered power P and the friction losses, the required motor po wer P can be
m
calculated as
P
P (3.108)
m
100 losses %