Example 4 - Cafeteria

Size the index run for the ductwork system shown below and give the total pressure drop for the system.

Size the fan for the system.

The building is a Cafeteria.

The index run includes sections A,B,C,D.

SectionAir Flow Rate

(m3/s)Length

(m)

A 1.20 10

B 0.90 3

C 0.60 6

D 0.30 8

NOTES:

1. Keep one side 350 mm high.2. Ductwork to be rectangular galvanised steel.3. There are no additional pressure losses.4. Tapered reductions are at 45 degrees.

Duct Sizing Table

1 2 3 4 5 6 7 8 9 10101010 11 12

Section Length Flow PressurePressurePressurePressure Duct Velocity Velocity Fittings Pressure Loss Total Cumulative

(m)

Rate

(m3/s)

drop perdrop perdrop perdrop per

metremetremetremetre

(Pa/m)

Size(mm)

(m/s)PressurePressurePressurePressure

(Pa)

pressure lossfactor or

zzzz (zeta) factor

PressureLoss(Pa)

PressureLoss(Pa)

Fittings(Pa)

StraightDuct(Pa)

A 10 1.2 1.0 0.47 m dia.

p(0.47/2)2 /0.350 =0.4957500 x350mm

1.2 / (0.5x 0.35)=6.86

0.5 x 1.2 x

6.862 =28.2

Intake louvre = 6.5see drg.Bend = 0.67Reduction to sectionB will go indownstream section(B).TOTAL = 7.17

28.2 x7.17 =202

1.0 x 10

= 10202 + 10= 212

212

B 3 0.9 1.0 0.43 m dia.425 x350mm

6.05 22.0 Branch IndexCircuit is straightthrough (VP1 to

VP2) .

The VP ratioVP2/VP1

= 22 / 28.2= 0.78The z zeta factor fromEXAMPLES OF z zetaFACTORS is 0.09Reduction z = 0.2for taper on one side.TOTAL = 0.29

0.29 x 22= 6

3

9

221

C 6 0.6 1.0 0.37 m dia.325 x350mm

5.28 16.7 BranchVP ratio = 16.7 / 22= 0.76zzeta factor = 0.16by interpolationReduction z = 0.2for taper on one side.TOTAL = 0.36

6

6

12

233

D 8 0.3 1.0 0.28 m dia.175 x350mm

4.90 14.4 BranchVP ratio = 14.4 /16.7 = 0.86zzeta factor = 0.08by interpolationReduction z = 0.2for taper on one side.Bend = 0.67Outlet diffuser =3.5 see drg.TOTAL = 4.45

64

8

72

305

It is a good idea to look at the velocities in each section.

If the air velocity is high, then noise may be a problem.

Acceptable noise levels depend on the areas to be ventilated.

The Table below may help to decide if the velocity is too high or not.

The velocity for the main ducts, section A,B,C do not exceed 9 m/s from the Table.

The velocity for the branch duct, section D also does not exceed the value of 6 m/s from the Table.

BuildingAir Velocity (m/s)

Main Duct Branch

Domestic 3 2

Auditoria 4 3

Hotel bedroom, Conference hall 5 3

Private office, Library, Hospital ward 6 4

General office, Restaurant, Dept. store 7.5 5

Cafeteria, Supermarket, Machine room 9 6Factory, Workshop 10-12 7.5

The fan should be capable of delivering 1.2 m3/s against a pressure of 305 Pa.

A percentage addition may be added to these figures for a design margin.

Fan Selection

To choose a fan go to; www.flaktwoods.com.Type: JM Aerofoil axial flow fan, or go to http://www.flaktwoods.com/169/0/1/076c8cda-f44c-4779-ab73-8ede6304a028 for a technicalcatalogue.

The fan code: 35JM/16/2/5 size: 355 mm diameter, 28o blade pitch angle, 2840 rev/min 5 Blades 50 Hz would fit the criteria for duty and

output pressure; 1.2 m3/s against a pressure of 305 Pa. Since this fan is running quite fast at 2840 rev/min it is somewhat noisy at about 86 dB (less corrections).A quieter fan would probably be better. System Resistance The system resistance of 305 Pa is mainly from section A at 212 Pa.If we examine this section on the Duct Sizing Table we can see that most of the resistance comes from the Intake Louvre.

The Intake Louvre pressure drop is; Intake Louvre - z x V.P. = 6.5 x 28.2 = 183 Pa.We could choose a louvre with a lower resistance.Go to; www.gilbertsblackpool.com. series wg louvres.Or go to http://www.gilbertsblackpool.com/UserFiles/File/louvres/SERIES%20WG%20-%20Jan%202006.pdf.

If a 700mm wide x 500mm high louvre is used then the sizing nomogram gives a pressure drop of 69 Pa for a air flow rate of 1.2 m3/s.This is a lot less than the previously calculated pressure drop of 183 Pa so this louvre would significantly reduce fan pressure. We could also examine the outlet diffuser resistance.The Outlet Diffuser pressure drop is; Outlet Diffuser - z x V.P. = 3.5 x 14.4 = 50 Pa. Go to www.waterloo.co.uk. Aircell polymer louvre faced diffuser.

The air flow rate in section D is 0.3 m3/s = 300 l/s.If a M600 diffuser is used it will fit into a ceiling tile and have less pressure drop than a M450.The performance Table for a 4 way diffuser supplying 315 l/s gives a Ps (Static pressure drop) of 9 Pa.

This is a lot less than the previously calculated pressure drop of 50 Pa so this diffuser would also reduce fan pressure. The new fan pressure is; 305 - 183 - 50 + 69 + 9 = 150 Pa.

The new fan rating is; 1.2 m3/s against a pressure of 150 Pa.

The new fan code: 45JM/16/4/5 size: 450 mm diameter, 28o blade pitch angle, 1420 rev/min 5 Blades 50 Hz, would fit the criteria for duty

and output pressure; 1.2 m3/s against a pressure of 150 Pa.Since this fan is running at half the previous fan speed it produces less noise at about 79 dB (less corrections), but is a more expensive fan. To be more accurate we could add resistances for; transformation pieces at the Intake louvre and fan, VCD’s (volume control dampers),flexibles at fan, plenum box at outlet diffuser.