Pressure losses distributed in the
pipes

The calculation of the linear pressure loss, that corresponding
to the general flow in a rectilinear conduit, is given by the following
general formula:
 Dp =
pressure loss in Pa
 L = friction factor
(a number without dimension)
 p = density of water in kg/m3
 V = flow rate in m/s
 D = pipe diameter in m
 L = pipe length in m
The expression above shows that calculations of pressure losses
rest entirely on the determination of the coefficient L.
The nature of the type of flow of a fluid is determined by the
value of the Reynolds number.
The various types of flows are visualized by the chart of the diagram
of Moody using the Reynolds number for the x axis and the factor
of friction F for the y axis.
The mode of flow of a fluid is characterized in 3 forms:
Laminar mode 
Reynolds number lower than 2000 indicates than
the flow is calm and regular 
Turbulent mode 
Reynolds number higher than 4000 indicates than
the flow is in the form of swirl and of movement. 
Zone critique 
Reynolds number located 2000 and 4000 indicates
that the flow is unstable between the laminar mode and the turbulent
mode. 
Calculation of the Reynolds number 
The Reynolds number is no dimensional (thus without units). It
combines 3 significant characteristics of the flow and the fluid:
speed, density and viscosity. The diameter is necessary to make
the number no dimensional. One calls the diameter the characteristic
length. A Reynolds number of 2000 or less indicates a flow in laminar
mode while a number of 4000 where more a turbulent flow indicates.
The Reynolds number is defined is:
According to kinematics viscosity

According to dynamics viscosity



 V = flow rate in m/s
 d = pipe diameter in mm
 v = viscosity of water in mm²/s (or
centistokes)
(legal System (S.I) in m²/s = 1000000 centistokes or
mm²/s)

 p = density in kg/m3
 V =speed in m/s
 D = hydraulic diameter of the pipe in m
 µ = dynamic viscosity in Pa.s (or kg/m.s)
(kg/m.s = One tenth of a poise = 10 poises)

Reynolds number is inversely proportional to kinematics viscosity.
The viscosity of a fluid is a characteristic which makes it possible
to determine resistance to the movement of the fluid. The higher
kinematic viscosity will be and the more difficult it will be to
move the fluid in the pipe.
Kinematics viscosity (v is the ratio of dynamic viscosity on the
density of the fluid.
Kinematics viscosity in m2/s

kinematics viscosity in mm²/s (or centistokes)



 v = kinematics viscosity in mm²/s
(or centistokes)  (legal system (S.I) in m²/s =
1000000 centistokes)
 µ = viscosity dynamic of water Pa.s or
(kg/m S)
 p = density of water in kg/m3

Laminar flow (Re £ 2000)
In rate of laminar, the nature or the surface quality of the interior
walls of the lines does not intervene in the calculation of the
pressure loss.
The loss pressure is determined by the following function:
 L = friction factor
(a number without dimension)
 Re = Reynolds number
The laminar flow meets in practice only in the transport and the
handling of the viscous fluids, such as the crude oil, fuel oil,
oils, etc.
Turbulent flow (Re > 2000)
In the critical zone, i.e. between 2000 and 4000 Reynolds the formula
of computation employed will be treated in the manner that in situation
of mode of turbulent flow.
In rate of turbulent, the factor of friction is translated by the
formula of Colebrook considered as that which translates best
the phenomena of flow into turbulent mode.
It is noted that this formula is in implicit form; consequently
search can be done only by successive approaches (iterative calculation)
With:
 L = friction factor
(a number without dimension)
 D = pressure loss coefficient.
 k = index of roughness of the pipe.
 d = pipe diameter in mm.
 Re = Reynolds number.
Usual value index of roughness (k) in mm


Nature of interior surface

Index roughness K

1

Copper, lead, brass, stainless

0,001 to 0,002

2

PVC pipe

0,0015

3

Stainless steel

0,015

4

Steel commercial pipe

0,045 à 0,09

5

Stretched steel

0,015

6

Weld steel

0,045

7

Galvanized steel

0,15

8

Rusted steel

0,1 to 1

9

New cast iron

0,25 to 0,8

10

Worn cast iron

0,8 to 1,5

11

Rusty cast iron

1,5 to 2,5

12

Sheet or asphalted cast iron

0,01 to 0,015

13

Smoothed cement

0,3

14

Ordinary concrete

1

15

Coarse concrete

5

16

Well planed wood

5

17

Ordinary wood

1

Influence rate of antifreeze (glycol) 
In the case of an addition of antifreeze (glycol) to water, kinematics
viscosity (into centistokes) varies in the following way:
 t = temperature at 0°C
 a = percentage of glycol
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