Sanitary Engineering Lecture 7

Manning equation Many formulas are used to solve the flow parameters in sewers were discussed in the hydraulic course. The most used formula for sanitary sewers is Manning equation: R = Hydraulic radius (Area/ wetted parameter) S = slope. n = manning coefficient. D = pipe diameter. Q = flow rate. Note: Equation 1 is used for calculating the velocity in pipes either flowing full or partially full. Equation 2 same for flow rate. Vƒ = velocity flowing full VP = velocity flowing partially Note: Equations 3 and 4 are the same as Equation 1, but they are written using the subscript (ƒ) and (P), to indicate flowing full and partially full, respectively:

In sanitary sewers the flow is not constant; consequently the depth of flow is varying as mentioned above. In this case it is difficult to find the hydraulic radius to apply Manning’s equation. For partially full pipe the following relations are applied: D Ө d D d = partial flow depth. R = Hydraulic radius (P = partial, ƒ = full) Ө = flow angle in degrees. Maximum capacity of the pipe when d/D = 0.95 A = Flow area. Maximum velocity in the pipe occurs at d/D=0.81 Ө d

Example 2 Find the diameter of the pipe required to carry a design flow of 0.186 m3/s when flowing partially, d/D = 0.67, slope = 0.4%, n = 0.013 using the nomographs and partial flow curves . Solution

Partial Flow Curves d/D d/D Qp/Qf Vp/Vf d D

Partial Flow Curves Q &V d / D 1.1 2

Maximum & Minimum Velocity: Velocity is an important consideration in sewer design. The velocity must not be less than 0.90 m/s in order to prevent solids settlement. The velocity must not be grater than 3.0 m/s in order to prevent erosion of pipes and manholes. Maximum & Minimum Size:   Minimum size of pipes used at storm water is 200mm diameter (8") and the maximum size of pipes is 2000 mm (80"). For conducts we can use any dimensions that we needs.