Water tools

Vertical turbine flocculator: power, impeller speed and Gt

Flocculation is set by the velocity gradient G and the time. From those two, the stage volume and the impeller's power number give the motor and the speed it must turn at.

Plant flowm³/d

Total flocculation timemin20 to 45 min before settling, 10 to 20 before direct filtration, 5 to 15 before flotation.

Parallel trains

Stages in series2 to 4 for turbines.

Velocity gradient G1/sVertical turbines 10 to 80; taper down through the stages.

Water temperature°C

Impeller

Impeller diameter / tank diameter0.4 to 0.5 preferred.

Per stage

Water power per stage

545W

Impeller speed

23.7rev/min

Tip speed

2.53m/s

Stage volume

65.1m³

Side of a cubic stage

4.02m

Impeller diameter

2.04m

Reynolds number

1,257,895

Turnover time

39s

Plant

Total water power

8.72kW

Gt over the flocculator

96,000

A derived figure, not a design criterion in itself.

How it works

The root-mean-square velocity gradient relates power, viscosity and volume:

G = \sqrt{\frac{P}{μ V}} P = G^{2} μ V

(1)

For a turbine in fully turbulent flow the power number is constant, which fixes the speed for the impeller diameter chosen (0.4 to 0.5 of the equivalent tank diameter):

N_{p} = \frac{P}{ρ N^{3} D^{5}} N = {(\frac{P}{N_{p} ρ D^{5}})}^{1 / 3} R e = \frac{D^{2} N ρ}{μ}

(2)

where

$G$: root-mean-square velocity gradient, 1/s
$P$: water power, W
$μ$: water viscosity, kg/m·s
$V$: stage volume, m³
$N_{p}$: impeller power number
$ρ$: water density, kg/m³
$N$: impeller speed, rev/s
$D$: impeller diameter, m
$R e$: impeller Reynolds number

Power numbers: hydrofoil about 0.25, pitched-blade turbine 1.26, flat-blade turbine 3.6, disc turbine about 5. The speed inside the power number is in revolutions per second. G is a basin average; taper it down stage by stage and keep the first-stage tip speed under about 2.5 m/s and the last under 0.6 m/s. Horizontal paddle wheels use a drag relation instead and run at 0.5 to 3 rev/min.

Vertical turbine flocculator: power, impeller speed and Gt

How it works

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