# Belgrade, 27. Marta 71, tel. +38163207646, balby@bitsyu.net

#### SEWER SYSTEMS ACCORDING TO PRANTL-KOLBRUK'S FORMULA

The head losses in sewer systems can be computed by the Prandtl-Colebrook's formula, expressed as:

where:
Re  is the Reynolds number, l  is the friction coefficient, D  is the inside pipe diametar  (m),
K is the  roughness coefficient  (m)

The critical value of Reynolds number Re  is computed by the next formula:

By combine the Prandtl-Colebrook's formula and  Chezy's formulas provides formula for the maximum velocity

in sewers system with circular section, expressed as:

where: v is the maximum velocity (m/s) and g is gravitational acceleration (m/s”)

we obtain the value of maximum velocity and the value of maximum flow through a pipe.

For computing  the value of maximum velocity and the value of maximum flow in soil pipes,

necessary is enter next attributes of pipes in indicated gauge units .

Enter the longitudinal pipes slope                                                  - I()

Enter the pipes diameter                                                               - D (mm)

Enter the roughness coefficient of pipes (1mm or 1.5 mm)        - K (mm)

Enter number of decimal places for determining values of velocity and flow

Maximum velocity of flow through pipes -  vmax (m/s)

Maximum flow of water through  pipes   -  Qmax (l/s)

Pipes in  sewerages are mostly not  full up and because of that we have to  compute values

of velocity and flow in partially filled profile.

Water elevation's dependence on flow in pipes  is represented at table 1.

 Relation Q/Qmax Degree of   pipes filling  h/hmax 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 N. F. Fedorov 0.020 0.073 0.175 0.311 0.468 0.628 0.765 0.890 0.975 1.000

Velocity's dependence on water elevation in  pipes is represented at table 2.

 Relation v/vmax Degree of   pipes filling h /hmax 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 N. F. Fedorov 0.340 0.550 0.710 0.835 0.920 0.980 1.030 1.040 1.034 1.000

For computing  the value of maximum velocity and the value of maximum flow in soil pipes,

necessary is enter next attributes of pipes in indicated gauge units .

Enter the real flow in  pipes         - Qr (l/s)

Enter the maximum flow in  pipes  - Qmax (l/s)

Enter the pipes diametar                 - D (mm)

Enter the maximum velocity of flow in  pipes        - vmax (m/s)

Enter number of decimal places for determining the real elevation

Relation of flows in pipes   - Qr/Qmax  (-)

Relation of pipes filling - hr/hmax  (-)

Real elevation of pipes filling  -  hr (m)

Relation of velocities  in pipes - vr/vmax  (-)

Real velocity in  pipes -  vr (m)