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ALTERNATIVE SEDIMENTATION THEORY FOR SETTLING TANKS DESIGN

by Sadyrbek DJIGHITEKOV, ( Sagi ), Ph.D

That theory was described in the book which has written in Russian in 1991 / 2 /. Thanks to Alternative Sedimentation Theory it is possible to calculate accurate sizes of Settling Tanks. The new calculation method is more correct and effective than traditional approach. Now, for English readers author is offering the main formulas for Rectangular Tanks design. 1. Definition of the Rectangular Tank’s depth a) Definition the value of the sedimentation zone height:        ______________________________ Ho = 5,2√ ν t / ln [ Cн / ( Cн – Cк ) ] ( 1 )

where 5,2 is a constant coefficient of resistance to settling particles in process laminar flow regime in tank; ν is a kinematic coefficient of viscosity, мм2 / sec; t is a detention time to reach desired underflow concentration, sec; Cн и Cк are the initial and desired water concentrations, mg/L.

b) Definition the value of the sludge zone height:

_________________________________ Hoc = 2√ ν t / ln [ Cнo / ( Cнo – Cкo ) ] ( 2 )

where 2 is a constant coefficient of resistance to settling particles in the inactive water environment Cнo и Cкo are the initial and desired sludge concentrations, mg/L.

c) Definition the value of the Rectangular Tanks depth:

H = Ho + Hoc ( 3 )

2. Definition of the Rectangular Tanks width:

B = Q / 3,6 υ H ( 4 )

where Q is a total water inflow, m³ / hr; υ is a downstream velocity in Rectangular Tank, mm/sec

3. Definition of the Rectangular Tanks length:

L = H² υ ln [ Cн / ( Cн – Cк ) ] /(5,2)² ν ( 5 )

Example. Determine the Rectangular Tank’s sizes if:

- total water inflow: Q = 2000 m³/ hr; - initial water concentration: Cн = 400 mg/L; - desired water concentration: Cк = 10 mg/L; - initial sludge concentration: Cнo = 6000 mg/L; - desired sludge concentration: Cкo = 16000 mg/L; - detention time to reach desired concentration: t = 2 hr or 7200 sec - temperature of the turbid water of 16°C and kinematic coefficient of viscosity: ν = 1,1 mm2/sec; - downstream velocity: υ = 10 mm/sec

Solution.

1. Determine the value of the Rectangular Tank’s depth: _________________________________ a) Ho = 5,2√ 1,1 × 7200/ ln [400/ (400 - 10)] = 2909 mm

_______________________________________ b) Hoc = 2√ 1,1 × 7200/ ln [6000/ ( 6000 – 16000)] = 249 mm

c) H = Ho + Hoc = 2909 + 249 = 3158 mm or 3,16 m

2. Determine the value of the Rectangular Tank’s width:

B = 2000/ (3,6 × 10 × 3,158) = 17,58 m

3. Determine the value of the Rectangular Tanks length:

L = ( 3158 )² × 10 × ln [400/ (400 - 10)]/ (5,2)² × 1.1 = 84829 mm or 85 m

On basis of the Alternative Sedimentation Theory it is possible to calculate sizes of the other types of Settling Tanks.

References

1. Loyzianski, A. M,& Lurye, A. I., 1983. Kurs teoreticheskoi mehaniki. T. 2. Dinamika – M.: Nayka 2. Djighitekov, S. 1991. Osnovy tehnologicheskogo rascheta otstoinikov. Bishkek: KyrgNIINTI