In this article we will discuss about the velocity of flow in sewers.
Minimum Velocity of Flow in Sewers – Self Cleansing Velocity:
A sewer should be so designed that the solid matter present in the sewage is not deposited at the bottom of the sewer and thus clogging of the sewer is prevented. The deposition of the solid matter and the resulting clogging of the sewer can be prevented if the solid matter is held in suspension in the flowing sewage.
In order to keep the solid matter in suspension certain minimum velocity of flow of sewage is required. Such a minimum velocity of flow is known as self-cleansing velocity. Thus self-cleansing velocity may be defined as the minimum velocity of flow at which the solid particles present in the sewage will be held in suspension and also at which the scour of the deposited particles will take place so that the sewer will be kept clean.
The self-cleansing velocity depends on the size of the solid particles present in the sewage and their specific gravity. It is, however, not possible to maintain the self-cleansing velocity throughout the day because of fluctuations in the quantity of sewage flow. During minimum flow of sewage the velocity of flow will be less than the self-cleansing velocity.
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However, the design should be such that self-cleansing velocity is maintained in the sewer at least once in a day so that the solid particles which might have deposited gets eroded and transported by the flowing sewage, and the sewer is rendered clean.
Shields Formula for Self-Cleansing Velocity:
From the findings of Shields, Camp has derived a formula for self-cleansing velocity which as defined earlier is the velocity of flow required to scour and transport the solid particles (heavier than water) deposited at the invert of a sewer.
The Shields formula for self-cleansing velocity has been derived by equating the forces tending to cause the motion and those opposing the motion of the deposited particles as indicated below-
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Consider a layer of sediment of unit length, unit width and thickness t deposited at the invert of a sewer as shown in Fig. 4.1. Let the slope of the sewer be α.
The water flowing in the sewer exerts a force, on the sediment in the direction of flow, which tends to move the sediment. This force is known as tractive force (or drag force or shear force) and it is given by the expression
= wRS … (i)
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In which
is tractive force per unit area;
w is unit weight of water;
R is hydraulic mean depth or hydraulic radius; and
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S is slope of sewer or head loss per unit length of sewer.
The motion of the sediment is opposed by the frictional resistance F. When the sediment is just on the point of moving the frictional resistance is given by the expression.
F = W sin θ … (ii)
In which
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W is effective weight of the sediment; and
θ is angle of repose or angle of internal friction of sediment.
The effective weight of the sediment under consideration is equal to its submerged weight and hence
W = wsub x 1 x 1 x t … (iii)
Where wsub is submerged unit weight of sediment.
The submerged unit weight of sediment is given by the expression-
In which
Gs is specific gravity of sediment;
e is void ratio of sediment deposit; and
n is porosity of sediment deposit.
In order to obtain the value of Chezy’s coefficient C, Darcy-Weisbach equation for head loss HL is used, from which for channel flow
Substituting this value of C in equation (ix), we get
Alternatively the value of Chezy’s coefficient C is also given by equation 4.5 as
Substituting this value of C in equation (ix), we get
Equations 4.8 and 4.9 give two alternate forms of the Shields formula for self-cleansing velocity in which-
The Shields formula indicates that velocity required to transport material in sewers is only slightly dependent on shape of sewer and depth of flow but mainly dependent on the particle size and specific weight. A velocity of 0.60 m/s would be required to transport sand particles of diameter 0.10 mm with a specific gravity of 2.65.
Hence the sanitary sewers (i.e., the sewers which carry only domestic or sanitary sewage) should have a minimum velocity of 0.6 m/s for present peak flow and a minimum velocity of 0.8 m/s at design peak flow.
According to Beardmore the minimum velocities of flow required to move solid particles of different materials are as given in Table 4.4.
Further the effect of specific gravity of the material on the velocity of flow required to transport the material has been determined experimentally and the same is indicated in Table 4.5.
Badwin Latham indicated that in order to prevent the deposition of silt in sewers the minimum or self- cleansing velocities required to be provided varies according to the diameters of the sewers. Table 4.6 indicates the minimum or self-cleansing velocities for sewers of different diameters as recommended by Badwin Latham.
Maximum Velocity of Flow in Sewers:
Just as it is necessary to provide minimum velocity of flow of sewage or self-cleansing velocity in a sewer to prevent its clogging, it is also necessary that velocity of flow of sewage in a sewer should not be excessive to cause scouring or erosion of its inner surface. At higher velocities of flow beyond certain limit scouring or erosion will be caused due to abrasive action of harder materials like sand, grit, gravel, etc., present in the sewage and this will damage the inner surface of the sewer.
The maximum velocity of flow up to which no scouring or erosion of the inner surface of the sewer will take place is known as non-scouring velocity or limiting velocity. The non-scouring or limiting velocity depends on the materials used for the construction of sewers. Table 4.7 indicates the values of the non-scouring velocity for the various materials commonly used for the construction of sewers.
Out of the various materials used for sewer construction vitrified tiles and glazed bricks are more resistant to erosion as compared to ordinary bricks or concrete. As such the ordinary brick or concrete sewers are sometimes coated with vitrified tiles or glazed bricks at their bottoms where the abrasion is maximum, because sand, grit, gravel, etc. are heavy and travel along the bottom of the sewers.
However, in order to prevent erosion of inner surface of sewers the maximum velocity of flow in a sewer is recommended not to exceed 3.0 m/s.