Flow Formulae

It is the design practice to use the Manning's formula for open channel flow and the Hazen-Williams formulae for closed conduit or pressure flow.

Manning's Formula

V = 1/n × R^{2/ 3} × S^{1/ 2}

For circular conduits

V = 1/n × 3.968 × 10^{- 3} × D^{2 / 3} × S^{1/ 2}

Q = 1/n × 3.118 × 10^{- 6} × D^{2 / 3} × S^{1/ 2}

where,            Q = Discharge in litres per seconds,

S = Slope of hydraulic gradient,

D = Internal diameter of pipe line in mm,

R = Hydraulic radius in metre,

V = Velocity in metre per seconds, and

n = Manning's coefficient of roughness.

Hazen-Williams Formula is expressed as follows:

V = 0.849 × C × R^0.63 × S ^0.54

For circular conduits, the expression becomes

V = 4.567 × 10^{- 3} × C × D^0.63 × S ^0.54

and     Q = 3.1 × 10^{- 4} × C × D^2.63 × S^0.54

where,            Q = Discharge in kilo litre per day,

D = Internal diameter of pipe in mm,

V = Velocity in metre per seconds,

R = Hydraulic radius in metre,

S = Slope of hydraulic gradient, and

C = Hazen-Williams coefficient.

The Charts based on Manning's and William Hazen formulae for circular pipe flowing full is mostly used in design work. Given any two values of four parameters (quantity of flow, diameter of pipe, slope of pipe or velocity) the remaining two can be determined. Manual on Sewerage and Sewage Treatment may be referred for design calculations.