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THE COMPUTER SOFTWARE FOR COMPUTATION HEAD LOSSES IN WATER SUPPLY SYSTEMS ACCORDING DARCY - WEISBAH FORMULA

 

Hydraulic losses in water supply systems depends in part upon velocity in the pipe and its diametar and roughness of the pipe, and occur along a whole pipe network. Local losses (valves, form losses bend, cross, etc) in long pipe installations are most 10% of linear losses. Head losses are computed according to the Darcy-Weisbach equation.. That equation for long pipe installations, where minor losses are 10% of linear losses, is represented as follows:


                                                             
where:  Δ h  is the head losses (pressure losses  measured as water meters),  L  is the  pipe length (m),  λ is the friction coefficient,  d  is the inside pipe diameter (m), V  is the flow velocity (m/s), and  g  is the gravitational acceleration (m/s).


In our engineer's usage, we compute the friction coefficient according to the equation innovated by professor Georgije Hajdin. This equation is an extension of Blazijus equation for smooth pipes and expressed as follows :
                         

 where: Re  is the Reynolds number and K is the roughness height (mm).

The Reynolds number is computed as:
                          
where: ν  is the kinematic viscosity which amounts  n =1.31 10-6 m2/s  for temperature of  10 C.

Typical pipe roughness values are shown in the following table. These values will vary depending on the manufacturer, workmanship, age, condition and other factors. For this reason, the following table should be used as a guideline only.

Material

Pipes condition

Roughness height      K (mm)

Glass, cooper, bronze, aluminum, plastic

New made pipes

0- 0.0015

PE

New made pipes- old pipes

0.002-0.004

PVC New made pipes- old pipes

0.006-0.012

Rolled steel New made pipes, technical smoothed

0.01- 0.05

Welded and from steel plate

New made pipes

0.05- 0.10

 

Old pipes - started scurf

0.15- 0.2

 

Matured scurf

max  3.0

Mettle

New made pipes

0.05

Gray cast

New made pipes, shifted

0- 0.12

 

New made pipes, no shifted

0.15

 

Old pipes, started scurf

max 1.5

 

Matured scurf

max 3

Asbestos cement

New made pipes

0- 0.3

Concrete

New made pipes,  reinforced, smoothed

0- 0.15

 

New made pipes, roughed

0- 0.8

 

Old pipes, good treated

0.2- 0.3


 

 

A  pipe-line name 

For a hydraulic resistance computation  in water supply penstocks necessity is enter next attributes of pipes in indicated gauge units.

The internal pipe diametar                   d (mm)  

The roughness height                           K (mm) 

The assumed flow                               Q (l/s)   

The pipe length -                                 L (m)                
                       

The cross-sectional area of a pipe                           F (m2) 

The flow velocity through a pipe                               v (m/s)

The Reynolds number                                                Re    

The friction coefficient                                                  l    

The hydraulic head losses (head losses in water meters)              D h (m)