Question

At a small water treatment plant which has 4 filters, the rate of filtration and backwashing are $200m^3/d/m^2$ and $1000m^3/d/m^2$, respectively. Backwashing is done for 15 min per day. The maturation, which occurs initially as the filter is put back into service after cleaning, takes 30 min. It is proposed to recover the water being wasted during backwashing and maturation. The percentage increase in the filtered water produced (up to two decimal places) would be

• A. 7.53

Answer 1

The correct option is A 7.53
Rate of filteration = $200m^3/d/m^2$
Backwashing rate = $1000m^3/d/m^2$
Time for backwashing = 15 min/day
Time wasted in maturation = 30min
Let the area of filter be unity

Total water to be produced

$=200m^3/d/m^2\times \frac{23.25}{24}=193.75$

The water wasted in backwashing

$\frac{1000\times 15}{24\times 60}=10.4167m^3$

The water wasted during maturation

$=\frac{200\times 30}{24\times 60}$

$=4.1667m^3$


Total filter water to be produced

$=193.75+10.4167+4.1667$

$=208.3334m^3$

Hence percentage increase in filtered water produced

$=\frac{208.3334-193.75}{193.75}$

$=7.53\%$