Question

You are the engineer asked to design a rapid sand filtration system for a small water treatment plant. It has the following characteristics: Hydraulic loading rate = 6 m/h Total volumetric flow rate of the plant = 3 MGD Effective filtration rate = 5.8 m/h Production efficiency = 97% Complete (filtration, rinsing, and backwashing) filter cycle duration = 48 h a) What is the area of your square filtration system? What are the surface dimensions of the filter? b) What volume of water is needed for backwashing plus rinsing the filter in each rinsing cycle?

Answer 1

given,

hydraulic loading rate = 6 m/h

total Volumetric flow rate = 3 MGD

Effective filtration rate = 5.8 m/h

Production efficiency = 97%

filter cycle duration = 48 h

3 MGD = 3 x 0.04381 = 0.131 m³/s = 471.6 m³/hr

`Q = V_a A_f`

Q = 6 x A_f

471.6 = 6 x A_f

A_f = 78.6

x² = 78.6

x = 8.86 m

b) Production efficiency

`\eta_f = (V_f-V_b-V_r)/(V_f)`

`0.97 = (V_f-V_b-V_r)/(V_f)`..........(1)

eff. filtration rate

`5.8 = (V_f-(V_b+V_r))/(A_ft_c)`

`0.97 V_f = 5.8 * A_f * t_c`

`V_f = 22559\ m^3`

from equation (1)

volume of water required for back washing = V_b + V_r

= 676.77 m³