DESIGN OF RAW WATER TANK

From Stokes’s law, the velocity of settling of small discrete particles is given by:
            v=418(s-s_1 ) d^2 (3T+70)/100                               ………….6.2
Where v = velocity of settling in mm/sec
    s = specific gravity of particle
    s1= specific gravity of water
    d = diameter of particle in mm
    T = temperature in degree Celsius.
Assuming each settleable particle in water is discrete with an average diameter of 0.09 mm and specific gravity 1.75 in water at 25oC;

        v=418(1.75-1.00)〖(0.09)〗^2  ((3x25+70))/100
        v = 3.6821 mm/s
Thus, the velocity of each settling particle is 3.6821 mm/s.
Number of tanks required = 2
Geometry of tank: Cylindrical, of uniform cross section
Height of tank = 5.6 m
Radius of tank = 14.2 m
Point of entry of raw water = 3.5 m above the tank floor.
In quiescent water, the time for a particle to move to the bottom of the tank is given by
        time =(velocity of particle )/(height of entry of water)
            =(3500 mm )/(3.6821mm/s)
             = 950.5445 s
             = 15.84 min.
Capacity (volume) of each tank =  〖πD〗^2/4 H
                    =〖22 x 28.4〗^2/(7 x 4)  x 5.6
            = 3,548.864 m3.
To know the point where the discharge of raw water on the tank to the treatment plant will be, the accumulated height of sludge after a month is calculated.
To calculate the volume of sludge produced per tank:
From material balance, 998.1214394 m3 of raw water produces 418 kg of sludge

Therefore, 3,548.864 m3 of raw water will produce 3,548.864 x 418 kg of sludge
                                                             998.1214394
                                                         = 1,486.2171 kg of sludge
Volume of sludge/day =(mass of sludge )/(density of sludge)
                             =(1,486.2171  )/(1,750)
               = 0.8493 m3 of sludge.
Height of sludge/day  =(Volume of sludge )/(Area of tank)
Where area of tank = πr^2
                   =(0.8493 x 7)/(22 x14.2 x 14.2)
              = 1.3402 x 10-3 m
              = 1.3402 mm/day
The height of sludge after 31 days = 31 x 1.3402
                      = 41.5462 mm
                      = 0.0415 m
The water outlet from the tank will be placed at a height of 0.3 m above the floor of the tank.
An emergency overflow weir will be placed at a distance of 0.1 m from the top of the open tank.
Thus, the effective water holding capacity of the tank =  〖22 x 28.4〗^2/(7 x 4)   x 5.2
                           = 3,295.3737 m3.