Environmental Engg. 3(2+1)

Lesson-17 Hydraulic design of sewers

General approach for the design of sewer is the same as that of water mains.  But the following are the two main differences between the basic principles of design of sewers and those of water mains.

Presence of particles  The water carried by water mains is practically free from particles of any solid matter – organic and inorganic.  Sewage, on the other hand, contains such particles in suspension and the heavy particles settle down at the bottom of sewers which may ultimately result in the clogging of sewers.  The sewers are, therefore, to be laid down at gradient and they should be capable of resisting the wear and tear due to abrasion of these particles.

Pressure  The water mains normally carry water under pressure and hence, within certain limits, they may be carried up and down the hill.  The sewers, on the other hand, are treated as open channels and they must, therefore, be laid at continuous gradient in downward direction.  If sewage has to be carried under pressure, it will require elaborate equipment at each house which is to be connected to the drainage system.

Minimum and Maximum velocities

The silting or deposition of particles of solid matter is undesirable in sewers and hence, the sewers should be laid at such a gradient that a minimum velocity which will prevent the silting of particles in sewers is developed over a wide variation in discharge of sewage.  Such a minimum velocity is known as self-cleansing velocity and for keeping the sewers free from any trouble, this velocity should be developed at least once in a day, preferably twice a day.

The self-cleansing velocity depends on the nature of suspended matter in sewage and the size of the sewer.  The following table shows the self-cleansing velocities for different materials in suspension as recommended by Beardmore.

 

Name of the material	Self-cleansing velocity in cm/sec
Angular stones	100
Round pebbles	60
Fine gravel	30
Coarse sand	20
Fine sand and clay	15

The following table shows the self-cleaning velocities for sewers for different sizes as recommended by Badwin Latham. Usually, a self-cleaning velocity of about 80 cm to 90 cm per second is adopted for normal sewage.

 

Diameter of sewer in cm	Self-cleansing velocity in cm/sec
15 to 25	100
30 to 60	75
Above 60	60

The maximum velocity of flow is also to be taken in to consideration.  If the velocity of flow exceeds a certain limit, the particles of solid matter start to damage the inside smooth surface of sewers or in other words, a scouring action takes place.  The maximum permissible velocity at which no such scouring action will occur is known as non-scouring velocity and it will mainly depend on the material used in the construction of sewers.  The following table shows the non-scouring velocities for common sewer materials.

 

Material of sewer	Non-scouring velocity in cm/sec
Earthen channels	60 to 120
Brick-lined sewers	150 to 240
Cement Concrete sewers	240 to 300
Stoneware sewers	300 to 450

The velocity which can cause automatic self-cleansing can be found out by the following formula given by Shield:

\[V=\sqrt{\frac{{8k}}{f}\left[{\frac{{{P_s}-P}}{P}}\right]gd}\]

Where. f = Darcy’s coefficient of friction having a value of 0.05 for usual type of sewers.

            k = Characteristics of solid particles carried in suspension by the sewage. .

            P_s= Specific gravity of the particles.

            P =  specific gravity of transporting liquid which is water in the case of sewage.

            g = acceleration due to gravity.

           d = diameter of the particle in mm to be carried in suspension.

From general observation and also from Shield’s formula, it is clear that heavier and sticky particles need larger velocity for their transportation, while smaller particles need smaller velocity.  This aspect can be made clear from irrigation canals also.  During rainy days water flowing in canals carries more coarser silt and thus silting of the canals takes place only in rainy season.

In sewers, the velocity of flow depends, on the following factors:

• Longitudinal slope or gradient in the sewer

• Hydraulic mean depth

• Coefficient of roughness of internal surface of the sewers

The sewage to be transported is mostly liquid containing 0.1 to 0.2 % solid matter in the form of organic matter, sediments and minerals

Following are the six common empirical formulae used in the determination of velocity of flow.

Chezy’s formula:

The formula given by Chezy in 1775 as follows:

\[=V\sqrt{RS}\]

Where,            V = velocity of flow in metres per second

                        R = hydraulic mean depth in metres

                        S = slope or hydraulic gradient

                        C = Chezy’s constant

 Bazin’s formula

            According to Bazin, the value of constant C in chezy’s formula can be obtained by the following equation

\[C = \frac{{157.6}}{{1.81 + \frac{K}{{\sqrt R }}}}\]

Where,            R = hydraulic mean depth in metres

                        K = Bazin’s constant

 Manning’s formula

            This formula, as given by Manning, is as follows:

\[V = \frac{1}{n}{R^{0.66}}{S^{0.50}}\]

Where,            R = hydraulic mean depth in metres

                        S = slope or hydraulic gradient

Crimp and Bruges formula

\[V=\frac{1}{n}{R^{0.66}}{S^{0.50}}\]

Where,             R = hydraulic mean depth in metres

                        S = slope or hydraulic gradient

Hazen and Williams formula

\[V=0.85{R^{0.63}}{S^{0.54}}\]

Where,          C =  friction coefficient based on the type and the condition of sewer

                     R = hydraulic mean depth in metres

                          S = slope or hydraulic gradient

Size of sewers

The minimum size of a sewer depends upon the practice followed in the locality.  Usually, sewers of 10 cm diameter are allowed upto a maximum length of 6 m or so.  But when the length of sewer line exceeds about 6 m, a sewer of minimum diameter 15 cm is allowed.  The smaller the diameter of sewer, the greater will be the slope and hence, in order to take advantage of available fall, sewers of large diameter are sometimes used.

The design of sewers should be made in such a way that it ends in sections of sewers which are commercially available.  The non-commercial sizes are difficult to obtain and they prove to be costly.  For sewers to be constructed on site of work, this problem does not arise.

There is no upper limit for the size of sewer.  It is however submitted that it is desirable to lay duplicate sewer line when sewer diameter exceeds about 3 m or so.

 Time of concentration

This term is used in connection with the design of storm water drains.  As the rain falls on the ground, all the area to be served by the sewer does not start to contribute immediately to the flow of sewer.  But the flow is build-up gradually as follows:

• The area just near the sewer line will start contributing first and it will go on increasing as more and more area starts to contribute.
• When the whole area is contributing to the flow of sewer, the maximum limit of flow will be reached and it will be equal to the rate of precipitation of rain water.
• The maximum flow continues until the storm stops.  The flow then gradually falls down as the area near the sewer line stops contributing firstly, while flow continues to come for considerable time from the distant areas.

The importance of time of concentration in the design of storm water sewers lies in the fact that out of all the storms of equal frequency of occurrence, that storm which has duration equal to the time of concentration, produces maximum flow in sewer.