Several equations have been developed to describe the flow of clean water through a porous medium. Carman-Kozeny equation used to calculate head loss is as follows:
h= f (1-a)Lvs2
h= f p(1-a)Lvs2 fa3dgg
f =150 (1-a) + 1.75
Ng Ng= fdvsr m
where, h = headloss, m
f = friction factor
a = porosity
f = particle shape factor (1.0 for spheres, 0.82 for rounded sand, 0.75 for average sand,0.73 for crushed coal and angular sand)
L = depth of filter bed or layer, m
d = grain size diameter, m
vs = superficial (approach) filtration velocity, m/s
g = accelaration due to gravity, 9.81 m/s2
p = fraction of particles ( based on mass) within adjacent sieve sizes
dg = geometric mean diameter between sieve sizes d1 and d2
Ng = Reynolds number
m = viscosity, N-s/m2
For a filter to operate efficiently, it must be cleaned before the next filter run. If the water applied to a filter is of very good quality, the filter runs can be very long. Some filters can operate longer than one week before needing to be backwashed. However, this is not recommended as long filter runs can cause the filter media to pack down so that it is difficult to expand the bed during the backwash.
Treated water from storage is used for the backwash cycle. This treated water is generally taken from elevated storage tanks or pumped in from the clear well.
The filter backwash rate has to be great enough to expand and agitate the filter media and suspend the floc in the water for removal. However, if the filter backwash rate is too high, media will be washed from the filter into the troughs and out of the filter.
When the filter is newly commissioned, the loss of head of water percolating through the filter is generally very small. However, the loss of head goes on increasing as more and more impurities get trapped into it.
A stage is finally reached when the frictional resistance offered by the filter media exceeds the static head of water above the and bed. Most of this resistance is offered by the top 10 to 15 cm sand layer. The bottom sand acts like a vacuum, and water is sucked through the filter media rather than getting filtered through it.
The negative pressure so developed, tends to release the dissolved air and other gases present in water. The formation of bubbles takes place which stick to the sand grains. This phenomenon is known as Air Binding as the air binds the filter and stops its functioning.
To avoid such troubles, the filters are cleaned as soon as the head loss exceeds the optimum allowable value.
Formation of Mud Balls :
The mud from the atmosphere usually accumulates on the sand surface to form a dense mat. During inadequate washing this mud may sink down into the sand bed and stick to the sand grains and other arrested impurities, thereby forming mud balls.
Cracking of Filters :
The fine sand contained in the top layers of the filter bed shrinks and causes the development of shrinkage cracks in the sand bed. With the use of filter, the loss of head and, therefore, pressure on thesand bed goes on increasing, which further goes on widening these cracks.
Breaking the top fine mud layer with rakes and washing off the particles.
Washing the filter with a solution of caustic soda.
Removing, cleaning and replacing the damaged filter sand.
Standard design practice of Rapid Sand filter: Maximum length of lateral = not less than 60 times its diameter. Spacing of holes = 6 mm holes at 7.5 cm c/c or 13 at 15 c/c. C.S area of lateral = not less than 2 times area of perforations. C.S area of manifold = 2 times total area of laterals. Maximum loss of head = 2 to 5 m. Spacing of laterals = 15 to 30 cm c/c. Pressure of wash water at perforations = not greater than 1.05 kg/cm2. Velocity of flow in lateral = 2 m/s. Velocity of flow in manifold = 2.25 m/s. Velocity of flow in manifold for washwater= 1.8 to 2.5 m/s. Velocity of rising washwater= 0.5 to 1.0 m/min. Amount of washwater = 0.2 to 0.4% of total filtered water. Time of backwashing = 10 to 15 min. Head of water over the filter = 1.5 to 2.5 m. Free board = 60 cm. Bottom slope = 1 to 60 towards manifold.
Q = (1.71 x b x h3/2)
where Q is in m3/s, b is in m, h is in m. L:B = 1.25 to 1.33:1 .