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2.2.2. Head loss in hydraulic installations

In the case of real liquids motion part of its energy is dissipated and transformed into thermal energy

(energie calorica), due to the internal friction in the liquid. The friction is produced by the viscosity,

turbulence of the motion, roughness of the pipe (rugozitatii tubului), and b several physical obstacles(fittings, valves, diameter changes etc.)

The head losses are of 2 types:

distributed losses (hd) along a flow with constant parameters (speed, cross-sections etc.) local losses (hl) taking place in the obstacles location. In these points the flow changes itsparameters.

With these the head loss hr1-2reads:

hr1-2=hd+hl

In Bernoullis equation all terms (v,p,z) can be analytically computed fairly easily, except head loss hdand hl as they depend on a lot of parameters.

For practical use of Bs equation, there are empirical formulas for the head losses inferred from

experimental investigations. There is a general formula for the head loss:

g

vhr

2

2

21 =

where is an adimentional coefficient experimentally computed for both the distributed and local loss.

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Distributed head lossesThe parameters that influence the distributed head loss are:

flow length: LIhd = ; L=flow length; hydraulic radius (R);

Rhd

1 ;

liquid nature; flow regime; roughness of the walls.

The last thing can be viewed as a geometrical property of the walls. It depends on the materials used,

on the degree of wall finishing (grad de prelucrare a peretilor), and on the pipe age.

There is a real roughness of any pipe which is difficult to define mathematically. Instead anEQUIVALENT ARTIFICAL ROUGHNESS is used, which can be expressed in terms of virtual

spheres diameters. From experimental investigations, conducted on real pipes (of a several diameters,

ages, materials) the distributed head losses have been measured. Pipes of same length diameter,

materials, with an artificial equivalent roughness (in the form of all spheres of certain diameters stuckon the pipe wall) producing the same head loss as the real ones have been used to equivalate the real

roughness. The artificial roughness is then transformed into a relative artificial roughness:

0r

for pipes

R

for unrestricted flow;

Finally, the general form of the distributed head loss becomes:

Ld

Ldg

vhd =

=

2

2

the coefficient expressing the inner friction (inside the liquid, between liquid and pipe), calledexchange coefficient (coeficient de rezistenta), also known as the coefficient Darcy-Weisbach.

=

0

,r

Rf e

The importance of led to a lot of experiments by many authors. The results show that the two

parametersRe and0r

have a different influence on .

To show this we take two extreme situations:

in case of laminar floweR

64=

in the case of a maximum (quadratic) turbulence2

71.3log4

1

=

d

In the case of an intermediate flow:

+=

dRe 71,3

51,2log2

1

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In Civil Engineering, we recommend 2 simple formulas:

in case of pressure flow2

0 QsI

lIhd

=

=(Sevelevs formula)

in case of unrestricted flowRC

vI

=

2

2

(Chezy formula)

where s0, , Care given coefficient depending on diameter, material, speed (see Laboratory classes)

Local head losses

g

vhe

2

2

= (general form of head losses)

depends on the specificity of the obstacles

has been experimentally computed for the entire set of obstacles met in hydraulic practice

(see Laboratory classes).

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A consequence of the definition is that in above Bernoullis equation the kinetic terms (av2/2g) and the

local head losses (he) can be neglected and the Bernoullis equation takes form:

2

210

21

QLszp

zp

=

+

+

which is a relative simple form easily to be used in the two problems of dimensioning or checking thesystems.

Short systems (sh.s) Definition: a sh.s is a system that along small distances changes its geometricaland hydraulic parameters. For example water supply distribution networks inside towns. A

consequence of this definition is that we can no longer neglect any terms in the Bernoullis equation,

and therefore two problems (dimensioning and checking) are more complicated, than in case of lg.s.

The Bernoullis has the general form.

Local systems (lc.s)

Definition: the lc.s is a concentrated system having a sudden head loss (o cadere brusca de presiune).Example mouthpieces (ajutaje), overfalls (deversoare), outlet openings (orificii).

A consequence of the definition is that in the general form of Bernoullis equation the distributed head

losses can be neglected and equation takes form:

g

v

g

v

g

vz

pz

pi

222

2

1

2

2

2

2

21

+=

+

+

In the following some specific computations (dimensioning, checking) is presented for lc.s. and sh.s.The computation for lg.s. will be presented during the laboratory classes as they are simple cases.