The sewers are generally designed as open channels except when it is specially required to design them as conduits carrying sewage under pressure as in the case of inverted siphons. Thus various empirical formulae which are used for the design of open channels are used for the design of sewers.
The following empirical hydraulic formulae are commonly used for the design of sewers:
(1) Chezy’s Formula:
Chezy (1775) gave the following formula for velocity of flow:
In which
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V = velocity of flow in m/s;
R = hydraulic mean depth or hydraulic radius in m;
S = slope of the sewer or hydraulic gradient; and
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C = Chezy’s coefficient
The hydraulic mean depth or hydraulic radius R is given by the following expression
R = A/P
In which
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A is area of flow section or wetted area in m2; and
P is wetted perimeter in m
The Chezy’s coefficient C depends on various factors such as roughness of inner surface of sewer, hydraulic mean depth, size and shape of sewer, etc.
The value of Chezy’s coefficient C can be obtained by using Ganguillet-Kutter formula or Bazin formula given below:
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(a) Ganguillet-Kutter’s Formula:
Two Swiss engineers Ganguillet and Kutter (1869) gave the following expression for Chezy’s coefficient C:
In which
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R and S are same as defined earlier; and
n is roughness coefficient or rugosity coefficient.
The roughness coefficient n is known as Kutter’s n.
The value of n varies widely depending upon the nature of inside surface of the sewer and its condition. Values of n for different types of surfaces commonly encountered in practice are given in Table 4.2.
(b) Bazin’s Formula:
Bazin (1897) gave the following expression for Chezy’s coefficient C:
In which
R is same as defined earlier; and
m is Bazin’s roughness coefficient
Some of the values of m proposed by Bazin are given in Table 4.1.
(2) Manning’s Formula:
Manning (1889) gave the following formula for velocity of flow-
In which V, n, R and S are same as defined earlier.
The values of Manning’s n are same as those of Kutter’s n and hence the values of n given in Table 4.2 may be used in both Kutter’s as well as Manning’s formulae.
If Manning’s formula is compared with Chezy’s formula it can be seen that-
Equation 4.5 provides a relationship between Chezy’s C and Manning’s n.
(3) Crimp and Bruge’s Formula:
This formula gives velocity of flow as-
V = 83.47 R2/3 S1/2 …(4.6)
Where V, R and S are same as defined earlier.
Comparing this formula with Manning’s formula, we obtain
1 / n = 83.47 n
or n =0.012
Hence when n = 0.012, Manning’s formula becomes Crimp and Bruge’s formula. This formula is commonly used in England.
(4) Hazen-Wiliiams Formula:
Hazen and Williams (1902) gave the following formula for velocity of flow-
V = 0.849 CH R0.63 S0.54 … (4.7)
In which
V, R and S are same a defined earlier; and
CH is Hazen-Williams coefficient.
The values of Hazen-Williams coefficient CH for new conduit materials and the values to be adopted for design purposes are given in Table 4.3.
The Hazen-Williams formula is mainly used for the design of conduits carrying liquid under pressure.
The area of flow section of a sewer required to carry a given discharge can be determined by the following general formula based on the principle of continuity:
Q = A x V
Where
Q is discharge in m3/s;
A is area of flow section in m2; and
V is velocity of flow in m/s, which may be determined by the various formulae indicated earlier.
Based on the various formulae indicated earlier nomograms, charts and tables have been prepared which may be used for the design of sewers.