Question

Water Supply

The design loading rate to a filter is 200 m3/d.m2. How much filter surface area should be provided for a design flow rate of 0.5 m3/s. For the given data, design the required filter depth Filter coeff. = 0.06 cm-1 % R = 99 If the surface area per filter is limited to 50 m2, how many filters are required?

Answer 1

Here for a filter we have,

Design flow rate,Q =0.5 m³/s = 0.5×60×60×24 m³/d = 43200 m³/d

Design loading rate of filter or surface overflow rate(SOR) =200m³/d.m²

Filter coefficient,λ = 0.06 cm​​​-1

Percentage removal ,%R = 99

Surface area per filter = 50 m²

• TOTAL AREA OF FILTER REQUIRED

Total filter area required = Q/SOR = 43200/200 m² = 216 m²

• DEPTH OF FILTER REQUIRED

From Iwasaki's equation we have,

$\frac{dC}{dz} = -\lambda C$

Integrating the above equation from C​​​​​​o (Initial concentration) to C(Final concentration ) for 0 to L, depth of filter we have,

$\ln \frac{C}{C_o} = -\lambda .L$

Now as percentage removal is 99 this C/C​​​​​​o = 1/100 , thus

$\ln \frac{1}{100} = -(0.06 cm^{-1}).L$

• NUMBER OF FILTER REQUIRED

NUMBER OF FILTERS REQUIRED = 216/50 = 4.32 ≈ 5

Thus atleast 5 filters of 50 m² of depth more than 76.75 cm are required for 99 % removal.

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