Important terms and formulae

TERMS:

• Design period 't' is the number of years in future for which the given facility is available to meet the demand. Design period is provided because
• It is very difficult or impossible to provide frequent extension.
• It is cheaper to provide a single large unit rather to construct a number of small units.
• The factors affecting design period are
• Life of the structure
• Ease or difficulty in extension
• Rate of population growth
• Time from concept to implementation
• Economy
• Time for testing
• Designed capacity refers to the volume that be handled by the treatment unit without overflowing. The plant should be designed for an additional capacity to take care of future population growth
• Sewage characteristics refer to the physical, chemical and biological  characteristics of the sewage
• Surface loading is one of the most important factors affecting the effectiveness of sedimentation process. It is used to determine if the sedimentation tanks and clarifiers are under or overloaded. The tanks are considered overloaded if the actual surface loading is greater than the design values. It is also called Surface settling or Surface Overflow Rate
• Weir loading rate is the amount of water being pushed over the weirs.    Weir loading rate = (surface loading * weir length) /  (Tank surface area)
• Hydraulic loading is defined in a wastewater treatment process as the volume of wastewater applied to the surface of the process unit per time period. It is expressed as l/d/m2

FORMULAE & ASSUMPTIONS:

• Maximum daily demand = 1.8 * Average demand
• Hydraulic radius = Area of cross-sectional flow / Wetted perimeter
• Overflow rate = Flow rate / Settling surface area
• For rapid sand filters filtration rate is assumed to be 4000 to 12000 l/hr/m2
• Efficiency of a settling basin = Settling velocity of particles (Vs)
•                                                      Surface overflow rate (Vo)
• Surface Overflow rate (Vo) = Sewage to be treated (Q)
•                                                   Plan of tank (A)
• Surface loading rate is given by hydraulic loading per unit surface area of tank in unit time (units - m3/d/m2)
• Per capita demand = Total yearly requirement of water of a city in litres
•                                                               365 * Design population
• Total solids - Suspended solids = Dissolved solids
• Equivalent weight = Molecular weight
•                                      Valency
• Carbonate hardness is the minimum of total hardness and alkalinity
• Non carbonate hardness = Total hardness - Alkalinity
• Overflow rate for
• Plain sedimentation = 12,000 to 18,000 l/m2/d
• Sedimentation with coagulation = 24,000 to 30,000 l/m2/d

• Velocity of flow (V) = Discharge (Q) / [Width (B) * Height (H)]
• Detention time for
• Plain sedimentation = 4 to 8 hours
• Sedimentation with coagulation = 2 to 4 hours
• Detention time
• For rectangular tank 't' = (Width * Length * Depth) / Discharge (Q)
• For circular tank 't' = d^2(0.11d + 0.785H) / Q
• d - Diameter of tank
• H - Vertical depth of wall or side water depth
•  Displacement efficiency = Flowing through period / Detention period
• Scour velocity (Vd) is given by    
• For filters, Plan area = Discharge / Rate of filtration
• For rapid sand filters, N = 1.22 * (Q)^0.5 
• N - Number of units required
• Q - Plant capacity in MLD
• Depth of sand layers = 60 to 90 cm
• Depth of tank = 2.5 to 3.5 m
• Area = 10 to 80 m2 per unit
• Rate of filtration = 3,000 to 6,000 l/m2/hr (30 times of slow sand filter)
• Cross-sectional area of manifold = 2 * cross-sectional area of lateral
• Cross-sectional area of each lateral = 2 to 4 times cross-sectional area of perforations in it
• Total cross-sectional area of perforation = 0.2% of total area of one filter bed
• Length of lateral / Diameter of lateral > 60
• 4.5% of filtered water is used as backwash
• 30 minutes used for backwash operation

• CHEZY's FORMULA

The formula was developed by Chezy in 1775 and states that

V = c * √(r*s) where 

V is velocity of flow in channel in m/s 

r is the hydraulic mean radius            

or hydraulic mean depth of the channel

It is equal to the ratio of area of channel to its wetted perimeter

For a circular sewer running full, "r = D/4"

s = Hydraulic gradient which is the

 ground slope for uniform flows

It is equal to the head drop between two points divided by the length

'c' is the Chezy's constant

• Chezy's constant depends on various factors such as
• Size and shape of channel
• Roughness of channel surface
• Hydrauliic characteristics of the channel etc
• The value of Chezy's constant can be obtained by Kutter's formula or Bazin's formulla as given below.
• KUTTER's FORMULA 

c = (23 + 0.00155/s) + 1/n     
                       (23 + 0.00155/s) * (n/√r)                
                                                                   where

n - Rugosity coefficient

s - Bed slope                

n depends upon the type of channel surface

r is the hydraulic mean depth

r = a/p                                    

• BAZIN's FORMULA 

c =           157.6 

         1.81 + (K/√r)

where                         

K is Bazin's constant                          

r is hydraulic mean depth of channel

• WILLIAM HAZEN's FORMULA

         This formula is used for flows under pressure (water supply pipes) and rarely used for designing sewers. According to this formula

 

V = 0.85 * CH * r^0.63 * s^0.54

• SHIELD's EXPRESSION FOR SELF CLEANSING VELOCITY

Self cleansing invert slope by

s = (k/r) * (G - 1) * d'

where

k is a dimensional constant that indicates an important characteristic of the sediment solid present in sewage. It varies from a minimum od 0.04 to 0.8

 

 Self cleansing velocity is given by 

Vs = (1/n) * r^0.166 * √(k * d' * (G - 1)

where

Vs is the self cleansing velocity in m/s

n is the porosity of the sediment

n = e/(1+e). e is the void ratio of the sediment

r is the hydraulic radius

k is a dimensional constant varying from 0.04 (min) to 0.8

d' is the depth of the sewage

G is the specific gravity of the sediment

According to the above equation, it can be computed that

• Inorganic particles of diameter 1 mm and specific gravity 2.65, and organic particles of 5 mm and a specific gravity 1.2 can be removed with a minimum velocity of 0.45 m/s
• It is necessary that a minimum velocity of 0.45 and an average velocity of 0.9 m/s is developed  in sewers
• In the design of sewers, the flow velocity at full design depth is generally assumed 0.8 m/s
• Minimum velocity generated in sewers helps
• to keep the sewer size under control
• in preventing the sewage from getting stale and thus prevents evolution of foul gases
• Velocity of flow developed in a sewer depends only upon 
• hydraulic mean depth of sewer and
• slope on which sewer has been laid