Ductwork elements

In the design of a ductwork system it is the practice to add the resistance of all the elements in the index leg together, to deter­mine the total (or static) pressure loss. The fan must develop this pressure at the design flowrate. The system and fan will then be in harmony. (See Chapter 4.)

Where:

подпись: where:The resistance of duct fittings and straight ducting is invariably determined from the Guides produced by CIBSE or ASHRAE. Both bodies have a similar approach and treat the pressure losses as a function of the local velocity pressure. This function is usually regarded as a constant and thus the loss becomes:

PLf

= pressure loss (Pa)

KF

= constant

P

= local air density (kg/m3)

(usually taken as standard 1.2)

V

= local velocity (m/s)

1 9

Pl =kF X2PV Equ3.26

Whilst this may be reasonably true in the normal working range, it is important to know that kF has a Reynolds Number depend­ence and that at low Reynolds Numbers kF can increase enor­mously, whilst in fully turbulent flow, if ever attained, the value could be less.

There are very few textbooks which even admit this variation. The only one of note is Idelchik’s Handbook of Hydraulic Resis­tance which gives a very detailed exposition of the subject and is noteworthy for its comprehensiveness. Miller’s Internal Flow Systems is also recommended.

It might be thought that the topic is somewhat esoteric, but it is suggested that with the increasing use of inverters and other variable flow devices, it is important to know that at high turn­down ratios, the system resistance curve diverges ever more from the oft quoted pL °c Q2. Thus power absorbed is not x fan speed N3, even if there were no bearing, transmission and con­trol losses.

In like manner, the loss in straight ducting is usually quoted as

Diameter

D

M

Average

Velocity

V

M/s

Reynolds No

R.= P*

N

Relative

Roughness

K

D

Friction

Factor

F

Flow quality

0.1

2.5

16492

0.0015

0.0076

Tr

5

32985

0.0067

10

65970

0.0063

15

98955

0.0059

20

131940

0.0057

0.25

2.5

41231

0.0006

0.006

Tr

5

82463

0.0055

10

164926

0.005

15

247388

0.0048

20

329851

0.0047

0.315

5

103903

0.00048

0.0051

Tr

10

207806

0.0047

15

311710

0.0046

20

415613

0.0045

25

519516

0.0044

0.63

5

207806

0.00024

0.0043

Tr

10

415613

0.0042

15

623419

0.0039

20

831226

0.0038

25

1039032

0.0036

1

5

329851

0.00015

0.0039

Tr

10

659703

0.0037

15

989555

0.0036

20

1319406

0.0035

25

1649258

0.0034

2

10

1319406

0.000075

0.0033

Tr

15

1979109

0.0032

20

2638812

0.0031

25

3298516

0.003

30

3958218

0.00295

2.5

15

2473887

0.00006

0.00295

Tr

20

3298516

0.0029

25

4123144

0.00285

30

4947773

0.0028

40

6597031

0.0028

Table 3.1 Friction factors versus duct size and velocity

Note 1 : Values apply to standard air

Note 2: All values are in the transitional range

FL 1 o

Pls = ^ Pv Equ 3.27

M 2

And — is taken to be a constant ks m

Where:

L = length of straight duct (m)

M = mean hydraulic depth (m)

~ — for circular cross-sections 4

F = friction factor

Again, as L and m are constants and f is assumed to be con­stant, the loss is taken to be

PLs=ks^Pv2 Equ 3.28

And thus another problem is created, for f is not a constant but rather a function of absolute roughness and Reynolds Number.

The Moody chart shown in Figure 3.13 shows that in the transi­tional and lower zones f * constant, and that again, as flow en­ters the critical zone there are significant increases in f, then a sudden drop, before climbing again in the laminar zone.

Referring now to Table 3.1, this covers the range of sizes and velocities encountered in HVAC practice. Assuming an abso­lute roughness applicable to g. s.s. (galvanised sheet steel), it can be seen that in all these cases the flow is transitional. The relative roughness and friction factor therefore vary enor­mously as shown. Thus with decreasing flow, and therefore ve­locity, the reducing velocity pressure is partially offset by the in­crease in f.

A system resistance curve is likely to be of the form shown in Figure 3.14 although for most HVAC systems the flow at which instability occurs is very close to zero flow. For mine ventilation, where the size of roadways can be considerable and the

Ductwork elements

Figure 3.14 A system resistance curve

0,025

подпись: 0,025

0,004

подпись: 0,004

0,002

подпись: 0,002

7 89 2 34567 89

Iff 104

подпись: 7 89 2 34567 89
iff 104

2 3 4 5 6 789

подпись: 2 3 4 5 6 789

105

подпись: 105

2 3 4 5 6 789

подпись: 2 3 4 5 6 789

106

подпись: 106

2 3 4 5 6 789

подпись: 2 3 4 5 6 789

10:

подпись: 10:

2 3 4 5 6 789

подпись: 2 3 4 5 6 789

108

подпись: 108

P vd

Reynolds number Re = —— Figure 3.13 Friction factor versus Reynolds number — Moody chart

подпись: p vd
reynolds number re = —— figure 3.13 friction factor versus reynolds number - moody chart
Ductwork elements

K(mm)

Riveted steel

1-10

Concrete

0,3-3

Vtood slave

0,2-1

Cast iron

0,25

Galvanised steel

0,15

AsphaRed cast iron

0,12

Commercial steel

Or wrought iron

0,045

Drawn tubing

0,0015

подпись: k(mm)
riveted steel 1-10
concrete 0,3-3
vtood slave 0,2-1
cast iron 0,25
galvanised steel 0,15
asphared cast iron 0,12
commercial steel 
or wrought iron 0,045
drawn tubing 0,0015
Reynolds Number is higher, this shape of system resistance curve has been recognised for at least 50 years. Somewhat later in Section 3.4.1 it will be shown how the formula has been tailored to fit the facts by reducing the index of v velocity from 2 down to 1.9 or even less.

Vigilant readers of this text will have detected that the author is somewhat cynical and he would suggest that it hardly seems worth the struggle to reach the truth, if there is any! Better to go back to basics. In this computer age, it should be possible to de­velop a programme to give the correct f for the velocity, diame­ter and roughness. Whether the effort is applauded, however, may still be debatable.

Norman Bolton at NEL, East Kilbride, was responsible for a programme of work which measured the resistance of suppos­edly identical ducts and fitting from three different manufactur­ers. The variation in pressure loss pL was enormous, thus prov­ing that quality is everything. It also suggests that so-called balancing of systems is not enough and that, to use “manage­ment speak”, a full system audit should be carried out.

The results should be fed back into the company design data­base. Some aspects of ductwork design are rarely mentioned in

^v2

VA2y

1-

— Ps1 + Pv1

+ Pv2

A,

Eps

1-

So, the static regain psr or addition to the initial fan static pres-

V2

Which is exactly the same as

Sure psi is the term pv1

(Pv1~Pv2>

As the efficiency of conversion is never 100%, the actual regain will be:

1-

VA2

Because velocity pressure is inversely proportional to area2. Then

“ ,2"

A,

Pv1 Pv1

+ Pv2

Ps1 Pv1 Ps1 "

Textbooks. The Sections which followare a mixture of basic fluid dynamics and practical “nous".

Posted in Fans Ventilation A Practical Guide


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