Question

A water treatment plant is designed to treat 1 m³/s of raw water. It has 14 sand filters. Surface area of each filter is 50 m². What is the loading rate \(% MathType!MTEF!2!1!+- % feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qadaqadaWdaeaapeGaamyAaiaad6gadaWcaaWdaeaapeGaamyBa8aa % daahaaWcbeqaa8qacaaIZaaaaaGcpaqaa8qacaWGKbGaamyyaiaadM % hacaGGGcGaamyBa8aadaahaaWcbeqaa8qacaaIYaaaaaaaaOGaayjk % aiaawMcaaaaa!41E8! \left( {in\ \frac{{{m^3}}}{{day\;{m^2}}}} \right)\) with two filters out of service for routine backwashing? 

Answer 1

Concept:

1) Surface Loading Rate (SLR) or Surface Overflow Rate (SOR) 

Volume of water applied in unit time per unit surface area of settling tank is known as Surface Loading Rate. It is also denoted by Vo.

\({\rm{SOR\;or\;}}{{\rm{V}}_{\rm{o}}} = \frac{{\frac{{{\rm{Volume\;of\;water\;}}}}{{{\rm{Time}}}}}}{{{\rm{Surface\;area}}}} = \frac{{{\rm{Discharge\;}}}}{{{\rm{Surface\;area}}}}\)

∴ \({\rm{Surface\ area\ of\ filter}} = \frac{{{\rm{Discharge\;}}}}{{{\rm{SOR}}}}\)

It is expressed in m3/d/m2

2) The number of filters required.

\({\rm{n}} = \frac{{{\rm{Total\;surface\;area}}}}{{{\rm{Area\;of\;each\;filter}}}}\)

Calculation:

Area of one filter = 50 m2

Total number of filters working during backwashing = 14 - 2 = 12 filters

Total water filtered in a day= 60 × 60 × 24 = 86400 m3/day

Total surface area of filter working during backwash = 12 × 50 = 600 m2

∴ The required loading rate = \(\frac{{{\rm{86400\;}}}}{{{\rm{600}}}} = 144 \frac{{{m^3}}}{{day\;{m^2}}}\)