static balance duct design method r1 balance.pdf · 4.0 static balance duct design method the...

STATIC BALANCE DUCT SIZING

METHOD

Author:

Engr. K.H., Kong is Mechanical Engineer

(IEM member, No: M21065)

Bachelor’s Degree with Honors with Distinction in Mechanical Engineering

STATIC BALANCE DUCT DESIGN METHOD

Copyright © 2008 by Kok-Haw Kong

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ABSTRACT

Generally, the duct design methods for low velocity supply air system that are

currently used include

1. Velocity reduction

2. Equal Friction, and

3. Static Regain

In this write up, a novel duct design method, known as the static balance duct

design method, is introduced. In this method, the duct looping or network principle is

applied to achieve static balance. The Static balance method is an intelligent self-

balance method to achieve minimum static losses across the ducting network. In turn,

energy consumption is reduced.

Static balance method is also well applicable to the variable air volume (VAV)

system. It reduces the system response time, the operating static losses within the duct

network system, and enhances the energy saving.

1.0 INTRODUCTION

In this write up, the description for the conventional and static balance duct

design method is presented in chapter 2. The Equal friction and static balance

methods are compared and discussed in detail. Chapter 3 discusses about the equal

friction method. A few equations involved in the development of the equal friction

method are presented. In chapter 4, the development and the principal of static

balance method are discussed in relation to the equal friction method. Comparisons of

the equal friction and static balance are discussed in chapter 5. Chapter 6 brings up the

advantages of the static balance method for VAV system and followed by a final

conclusion.



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2.0 DUCT DESIGN METHOD

The conventional duct design method includes:

1. the velocity reduction method

2. the equal friction method, and

3. the static regain method.

The novel duct design method is static balance method.

In the velocity reduction duct design method, the controlling factor is the air

velocity in the duct. This is mainly to prevent noise due to high air velocity. Basically,

the duct velocity is determined before the duct size is selected. With the air velocity,

the duct diameter size is computed. Then, the actual round or rectangular duct size is

selected and the relevant static loss is calculated accordingly.

The Equal friction method is widely used due to its simplicity and flexibility.

This method is based on the assumption that the friction loss per unit of length is

consistent for the entire system. Usually, the initial friction loss per unit of length is

determined. Then the duct size throughout the entire ducting system is selected

according to the air flow rate relative to the determined friction loss. The total friction

loss in the duct system is calculated based on the duct run with the highest resistance,

including the friction loss through all elbows and fittings in the section. For any site

coordination or adjustment, the duct size is changed based on the same static loss

coefficient. However, the drawback of the equal friction method is that the system is

difficult to balance if the design has a mixture of short and long runs. Where the

pressure difference between short and long runs is large, and requires considerable

dampering on system.

In the static regain method, the duct is designed in such a way that at each

branch, the available static pressure is used to offset the friction loss on the

subsequent section of duct. The static pressure remains constant before each terminal

and at each branch. This method requires more complicated and time consuming

design procedures and methods. It also uses more duct materials as compared to the

equal friction method.



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The Static balance duct design method presented here comprises a duct

looping network, which consists of ducts of various sizes, geometric orientations, and

fittings. It is designed based on the principle of equal friction method which offers

lower friction losses but more duct work. Similarly to all networks system, this

method implements the continuity and the work-energy principles throughout the

network. The solution of the static balance method is obtained through a trial-and-

correction or iteration process.

3.0 EQUAL FRICTION DUCT DESIGN METHOD

The Equal friction method uses the same friction loss per unit of length for the

entire system. In any duct section in which the air is flowing through, there is a static

loss. This loss is named as the friction loss which is related to the followings:

1) Duct size,

2) Interior surface roughness,

3) Air flow rate, and

4) Duct length

The relationship of these factors is represented by the following equation:

82.122.1

1000

118.67

=

∆ V

df

L

P

e

… eq. 3.1

or

=

∆86.4

82.17103

ed

Qfx

L

P … eq. 3.2

where ∆P = friction loss (Pa)

f = interior surface roughness

L = duct length (m)

de = duct diameter or equivalent diameter for rectangular duct (mm)

V = air velocity (m/s)

Q = air flow rate (l/s)

The equivalent diameter for a rectangular duct can be further related as follows:



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( )

( ) 25.0

625.0

3.1ba

abd e

+=

… eq. 3.3

where de = duct diameter or equivalent diameter for a rectangular duct (mm)

a and b = duct size (mm)

Another useful parameter derived from the velocity pressure is the velocity head,

26137.0 Vhv = … eq. 3.4

or

4

26

101e

vd

Qxh = … eq. 3.5

where hv = velocity head (Pa),

V = air velocity (m/s)

Q = air flow rate (l/s)

de = duct diameter or equivalent diameter for rectangular duct (mm)

The friction loss of fittings can be related to the velocity pressure by adding a

multiplier or coefficient. The coefficient for various fittings is tabulated below:

Fittings Coefficient, C

Transition 0.25

Elbow 0.27

Wye 0.30

Tee 0.37

The static loss through fittings is represented by the following equation:

vf ChP =∆ … eq. 3.6

where ∆Pf = static loss through fittings, (Pa)

hv = velocity head (Pa),

C = fitting coefficient

In any duct system for the equal friction method, the duct is sized based on a

desired friction loss per unit length of duct. The equations shown above are used to

calculate the static loss. The static loss of each section of the duct runs is

accumulated. Only the duct runs with highest resistance is calculated, where this is the



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static required for the fan to overcome it. The highest static loss may not be the

longest duct run, rather it can be a shorter duct with more bends and fittings.

3.1 Example for Equal Friction Duct Design Method

Figure 3.1 shows a simple duct system for hospital ward rooms. In this

simulation, the ward rooms are located at perimeter whereas offices, the procedure

room and the nurse station are located at center of the zone.

Referring to figure 3.1, the fan discharge air flow rate is 4800 l/s and there are

16 branches or air terminals with 300 l/s each. The friction loss is limited to 1 Pa/m.

Duct is made of galvanized sheet with the interior surface roughness of 0.9.

The duct runs with the highest static loss is from point O to P. The static loss

calculation is tabulated in table 3.1 and the duct design is shown in figure 3.2. Here,

the friction loss per unit length is selected to be 1 Pa/m. In actual situation, due to the

limitation of discrete duct sizes, the friction loss is re-calculated according to the duct

size selected.

From calculation, the accumulated static loss is 64 Pa from point O to P.



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Item Point Description

Air

Flow

(L/S)

Design

Static

Loss

(Pa/m)

Duct Size (mm)

W x H

Air

Velocity

(m/s)

Calc.

Static

Loss / L

(Pa/m)

Straight

Duct

Length

(m)

Static

Loss

(Pa)

C hv

(Pa)

Fitting

Static

Loss

(Pa)

Total

Static

Loss

(Pa)

Cumulative

Static Loss

(Pa)

Static

Loss

(in.

wg)

1 OA Straight duct Q0 4800 1.0 1,300 x 450 9.35 0.751 5.0 3.757 0.00 42.41 0.0 3.8 3.8 0.0148

2 Tee 0.37 42.41 15.7 15.7 19.4 0.0766

3 AF Straight duct Q5 2100 1.0 700 x 450 7.19 0.874 5.0 4.372 0.00 31.72 0.0 4.4 23.8 0.0938

4 FJ Straight duct Q8 1500 1.0 600 x 400 6.73 0.913 5.0 4.567 0.00 27.78 0.0 4.6 28.4 0.1118

5 Tee 0.37 27.78 10.3 10.3 38.7 0.1522

6 JK Straight duct Q11 1200 1.0 500 x 400 6.41 0.932 5.0 4.658 0.00 25.24 0.0 4.7 43.3 0.1706

7 KL Straight duct Q12 900 1.0 450 x 350 5.94 0.988 5.0 4.941 0.00 22.93 0.0 4.9 48.3 0.1900

8 LM Straight duct Q13 600 1.0 400 x 300 5.35 0.918 5.0 4.588 0.00 17.60 0.0 4.6 52.9 0.2081

9 MN Straight duct Q14 300 1.0 250 x 300 4.27 0.808 5.0 4.041 0.00 11.19 0.0 4.0 56.9 0.2240

10 Elbow 0.27 11.19 3.0 3.0 59.9 0.2359

11 NP Straight duct Q15 300 1.0 250 x 300 4.27 0.808 5.0 4.041 0.00 11.19 0.0 4.0 64.0 0.2518

Table 3.1 – Static loss calculated result using equal friction duct design method.



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4.0 STATIC BALANCE DUCT DESIGN METHOD

The Static balance duct design method uses the duct network principle. For all

network problems, it satisfies the continuity and the work-energy principles

throughout the network. The continuity principle states that the vector summation of

air flow rate into any junction must be equal to zero. The continuity principle is

represented by the following equation:

∑ =± 0Q … eq. 4.1

The network-energy principle states that the vector summation of static loss

around any single loop of the network must be equal to zero. The vector summation of

static loss applies to any section of the duct within the loop. The static loss is additive

if air flow direction is parallel with the loop direction, but deductive if air flow

direction is opposite the loop direction. The network-energy is represented by the

following equation:

∑ =∆± 0P … eq. 4.2

Equation 4.2 can be further divided to two portions. The static loss through

straight duct and fittings is shown as follows:

( ) ( )∑ ∑ =∆±+∆± 0fittingsPductstraightP f … eq. 4.3

From equation 3.2, it is known that the static loss is related to 4 factors, which

are the duct length, the friction factor, the duct size and the air flow rate. Thus, ∆P is a

function of (L, f, de and Q).

Using the equal friction principle, the friction loss per unit of length is

constant. The friction factor, f, is a constant depending on the duct material. Giving

that the air flow rate, Q, the duct equivalent diameter, de can be calculated. Therefore,

it can be summarized that the friction loss, ∆P, is determined by the air flow rate, Q.

As for all network problems, the solution of the static balance method is

obtained through a trial-and-correction or iteration process. There are several ways to



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solve these flow rates, the simplest and easiest to understand being the Hardy Cross

method.

The essence of the method is to start with an estimated set of initial values, Q0,

that fulfills the continuity at each junction. The difference between the estimated and

the updated value is represented by a correction factor, ∆L. The updated value is the

summation of estimated value and the correction factor as shown below.

Li QQ ∆±= 0 … eq. 4.4

where the sign (±) depends on the directions assumed for Q0.

In cases where one duct is depending on two loops, the new air flow rate

should include the summation of both correction factors from two loops.

Then, the next iteration is carried out with a new successive set of values.

Iterations are repeated until the iteration results are converged and satisfied.

From equation 4.3, the static loss equation is,

( ) ( )∑ ∑ =∆±+∆± 0fittingsPductstraightP f

where the sign (±) depends on the directions assumed for Q0.

The static loss through a straight duct is represented by equation (3.2), and the

static loss through fittings is represented by equation (3.5) and (3.6). In general, a

common equation as follows is obtained,

∑ ∑ =±=∆± 0n

KQP … eq. 4.5

where K is the coefficient of static loss, which depends on the duct length, the duct

equivalent diameter and the friction factor.

Introducing eq. 4.4 into eq. 4.5, and obtain

( )∑ ∑ =∆±±=∆± 00

n

LQKP



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Expanding this equation by the binomial theorem and neglecting all terms

containing ∆L raised to a higher power, because ∆L is presumed to be small. For the

first iteration,

( )∑ ∑ =+∆±±=∆±−

01

00 negligiblenQQKP L

nn

Solving for ∆L, the first correction factor becomes

∑∑

−

±−=∆

1

0

0

n

n

L

nKQ

KQ … eq. 4.6

The absolute value must be used in the denominator to ensure that the proper

sign for ∆L. This equation is used to compute the flow rate correction factor, ∆L, for

each loop in the network. From equation 4.6, it can be further simplified as follows to

the satisfaction of usage,

∑∑

∆

∆±−=∆

0QPn

PL … eq. 4.7

For iterative processes, the value of (1/n) is categorized as an over-relaxation

factor, which can be varied within certain limit to enhance the iteration process. In

this case, referring to eq. 3.2 and 3.5, due to the different value of ‘n’ for straight duct

and fittings, the value of 2 for ‘n’ is selected to proceed with the iterative process.

Hence, eq. 4.7 becomes

∑∑

∆

∆±−=∆

02 QP

PL … eq. 4.8

In every iterative process, the air flow rate must be updated with a successive

set of values computed until the values of Q converge with suitable accuracy to final

values.

Due to the limitation of discrete duct sizes, there will be residual where the

value of Q may not converge to zero, but alter within a small value for the same duct

sizes. In this case, the iteration is considered converged. The converged set value of Q

will be used to determine the static loss across the ducting system.



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4.1 Example for Static Balance Duct Design Method

Figure 4.1 shows a duct system which uses the static balance duct design

method. Figure 4.1 has the same layout as described in figure 3.1, with a duct looping

network. The friction loss is limited to 1 Pa/m. A set of initial air flow rate across

each duct section is estimated and tabulated in table 4.1 below. The air flow rate must

satisfy the continuity principle.

Item Point Designation Air flow rate (l/s)

1 OA Q0 4800

2 AB Q1 2700

3 BC Q2 2400

4 CD Q3 1350

5 DE Q4 1050

6 AF Q5 1800

7 CG Q6 750

8 EH Q7 750

9 FJ Q8 1200

10 GL Q9 150

11 HN Q10 150

12 JK Q11 900

13 KL Q12 600

14 LM Q13 450

15 MN Q14 150

Table 4.1 – Initial estimated air flow rate across each section of duct.

The first iteration is carried out and the static loss calculation is tabulated. The

iteration for loop (I) is tabulated in table 4.2 and the iteration for loop (II) is shown in

table 4.3.

From eq. 4.8, the correction factor for loop I is,

( ) ∑∑

∆

∆±−=∆

02 QP

PIL

( )

++++++

++++++

−−−−−−−+++++−=

01085.000765.000523.000778.000388.000262.0

00414.001556.002049.000548.000574.000204.000165.02

5.66.47.43.97.47.49.193.21.31.48.139.44.4



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( )( )09311.02

8.21−−=

sl /117=

Similarly, the correction factor for loop II is,

( ) ∑∑

∆

∆±−=∆

02 QP

PIIL

( )

++++++

++++++

−−−−−−−+++++−=

01556.002049.000828.001556.002049.000548.0

00574.001556.002049.000548.000718.000479.000342.02

3.21.37.33.21.31.48.133.21.31.45.70.56.4

( )

( )14852.02

8.5−−=

sl /19=



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Air

Flow

(L/S)

Design

Static

Loss

(Pa/m)

Duct Size (mm)

W x H

Air

Velocity

(m/s)

Calc.

Static

Loss / L

(Pa/m)

Straight.

Duct

Length

(m)

Static

Loss

(Pa)

C hv

(Pa)

Fitting

Static

Loss

(Pa)

Total

Static

Loss, ∆P

(Pa)

∆P/Q

First Iteration Loop I

1 AB Straight duct Q1 2700 1.0 850 x 450 7.71 0.889 5.0 4.445 0.00 36.48 0.0 4.4 0.00165

2 BC Straight duct Q2 2400 1.0 850 x 400 7.79 0.978 5.0 4.891 0.00 37.21 0.0 4.9 0.00204

3 C Tee 2400 0.37 37.21 13.8 13.8 0.00574

4 CG Straight duct Q6 750 1.0 500 x 300 5.41 0.822 5.0 4.112 0.00 17.99 0.0 4.1 0.00548

5 GL Straight duct Q9 150 1.0 250 x 200 3.21 0.615 5.0 3.073 0.00 6.31 0.0 3.1 0.02049

6 L Tee 150 0.37 6.31 2.3 2.3 0.01556

7 A Tee 4800 0.37 53.66 19.9 19.9 0.00414

8 AF Straight duct Q5 1800 1.0 600 x 450 7.14 0.944 5.0 4.722 0.00 31.28 0.0 4.7 0.00262

9 FJ Straight duct Q8 1200 1.0 500 x 400 6.41 0.932 5.0 4.658 0.00 25.24 0.0 4.7 0.00388

10 J Tee 1200 0.37 25.24 9.3 9.3 0.00778

11 JK Straight duct Q11 900 1.0 400 x 400 5.99 0.942 5.0 4.710 0.00 22.04 0.0 4.7 0.00523

12 KL Straight duct Q12 600 1.0 400 x 300 5.35 0.918 5.0 4.588 0.00 17.60 0.0 4.6 0.00765

13 L Tee 600 0.37 17.60 6.5 6.5 0.01085

Table 4.2 – First iteration for loop I.



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Air

Flow

(L/S)

Design

Static

Loss

(Pa/m)

Duct Size

(mm)

W x H

Air

Velocity

(m/s)

Calc.

Static

Loss / L

(Pa/m)

Straight.

Duct

Length

(m)

Static

Loss

(Pa)

C hv

(Pa)

Fitting

Static

Loss

(Pa)

Total

Static

Loss, ∆P

(Pa)

∆P/Q

First Iteration Loop II

14 CD Straight duct Q3 1350 1.0 550 x 400 6.58 0.923 5.0 4.614 0.00 26.567 0.0 4.6 0.00342

15 DE Straight duct Q4 1050 1.0 600 x 300 6.40 1.006 5.0 5.031 0.00 25.144 0.0 5.0 0.00479

16 E Wye 1050 0.30 25.144 7.5 7.5 0.00718

17 EH Straight duct Q7 750 1.0 500 x 300 5.41 0.822 5.0 4.112 0.00 17.988 0.0 4.1 0.00548

18 HN Straight duct Q10 150 1.0 250 x 200 3.21 0.615 5.0 3.073 0.00 6.309 0.0 3.1 0.02049

19 N Tee 150 0.37 6.309 2.3 2.3 0.01556

20 C Tee 2400 0.37 37.208 13.8 13.8 0.00574



23 L Tee 150 0.37 6.309 2.3 2.3 0.01556

24 LM Straight duct Q13 450 1.0 350 x 300 4.57 0.745 5.0 3.726 0.00 12.834 0.0 3.7 0.00828

25 MN Straight duct Q14 150 1.0 250 x 200 3.21 0.615 5.0 3.073 0.00 6.309 0.0 3.1 0.02049

26 N Tee 150 0.37 6.309 2.3 2.3 0.01556

Table 4.3 – First iteration for loop II.



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From the two correction factors obtained above, the estimated flow rate is

updated and tabulated in table 4.4.

Item Point Designation

Initial Air

flow rate (l/s)

Correction Updated Air

flow rate (l/s)

1 OA Q0 4800 Q0 4800

2 AB Q1 2700 Q1 = Q1 +∆L(I) 2817

3 BC Q2 2400 Q2 = Q2 +∆L(I) 2517

4 CD Q3 1350 Q3 = Q3 +∆L(II) 1369

5 DE Q4 1050 Q4 = Q4 +∆L(II) 1069

6 AF Q5 1800 Q5 = Q5 - ∆L(I) 1683

7 CG Q6 750 Q6 = Q6 +∆L(I) - ∆L(II) 848

8 EH Q7 750 Q7 = Q7 +∆L(II) 769

9 FJ Q8 1200 Q8 = Q8 - ∆L(I) 1083

10 GL Q9 150 Q9 = Q9 +∆L(I) - ∆L(II) 248

11 HN Q10 150 Q10 = Q10 +∆L(II) 169

12 JK Q11 900 Q11 = Q11 - ∆L(I) 783

13 KL Q12 600 Q12 = Q12 - ∆L(I) 483

14 LM Q13 450 Q13 = Q13 - ∆L(II) 431

15 MN Q14 150 Q14 = Q14 - ∆L(II) 131

Table 4.4 – Updated estimated air flow rate after first iteration.

The iteration is continued and the correction factor is tabulated in table 4.5.

The iteration is converged and the duct sizes are maintained from iteration of Ninth

onwards. The converged value of Q is tabulated in table 4.6. The duct design is shown

in figure 4.2.

Item Iteration

Number

Correction factor Loop I,

∆L(I) (l/s)

Correction factor Loop II,

∆L(II) (l/s)

1 First 117 19

2 Second 90 15

3 Third 63 33

4 Forth 77 26

5 Fifth 42 23

6 Sixth 42 21

7 Seventh 50 13

8 Eighth 29 5

9 Ninth 23 1

Table 4.5 – Correction factors obtained from iterations.



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At the eighth iteration, it is found that the air flow rate direction for duct

section MN, Q14, is changed, from M->N to N->M. This is due to the accumulated

static loss from O to N is lower than from O to M. The air flow rate across the duct

section MN is very low, showing that the pressure at point M and N is almost balance

or the air flow is almost stagnant.

From the static balance duct design method, it is discovered that the highest

static loss is from O to Q. This static loss shall be overcome by the supply fan. An

interesting phenomenon is found that the static loss from O to Q is almost the same

regardless of the paths of air flow, either through A-J, C-L or E-N. This complies with

the work-energy principle. The static loss calculation is tabulated in table 4.7. The

minor variation of static loss is due to the residual air in discrete duct sizes. The

variation can be reduced with more iterations. The average accumulated static loss

from O to Q is 56 Pa.

Item Point Designation Air flow rate (l/s) Duct Size, W x H (mm)

1 OA Q0 4800

2 AB Q1 3234 950 x 450

3 BC Q2 2934 900 x 450

4 CD Q3 1507 600 x 400

5 DE Q4 1207 600 x 350

6 AF Q5 1266 450 x 450

7 CG Q6 1127 650 x 300

8 EH Q7 907 550 x 300

9 FJ Q8 666 400 x 350

10 GL Q9 527 350 x 300

11 HN Q10 307 250 x 300

12 JK Q11 366 300 x 300

13 KL Q12 66 150 x 150

14 LM Q13 293 250 x 300

15 MN Q14 7 100 x 50

Table 4.6 – Converged air flow rate across each section of duct.

The air flow rate through duct section KL and MN is small. For equal friction

method, these sections can be neglected and omitted. However, they have advantages

for the static balance duct design method. This will be discussed more in chapter 6.



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Air

Flow

(L/S)

Design

Static

Loss

(Pa/m)

Duct Size (mm)

W x H

Air

Velocity

(m/s)

Straight

Duct

Length

(m)

Static

Loss

(Pa)

C hv

(Pa)

Fitting

Static

Loss

(Pa)

Total

Static

Loss

(Pa)

Cumulative

Static Loss

(Pa)

Static

Loss

(in.

wg)

Static Loss through path E-N

1 OA Straight duct Q0 4800 1.0 1,300 x 450 9.35 5.0 5.000 0.00 53.66 0.0 5.0 5.0 0.0197



4 CD Straight duct Q3 1507 1.0 600 x 400 6.76 5.0 4.606 0.00 28.04 0.0 4.6 19.0 0.0747

5 DE Straight duct Q4 1207 1.0 600 x 350 6.23 5.0 4.335 0.00 23.86 0.0 4.3 23.3 0.0918

6 Wye 0.30 23.86 7.2 7.2 30.5 0.1199

7 EH Straight duct Q7 907 1.0 550 x 300 5.99 5.0 4.683 0.00 22.03 0.0 4.7 35.1 0.1384

8 HN Straight duct Q9 307 1.0 250 x 300 4.37 5.0 4.214 0.00 11.72 0.0 4.2 39.4 0.1550

9 Tee 0.37 11.72 4.3 4.3 43.7 0.1721

10 NM Straight duct Q14 7 1.0 100 x 50 1.54 5.0 3.334 0.00 1.45 0.0 3.3 47.0 0.1852

11 Tee 0.37 1.45 0.5 0.5 47.6 0.1873

12 MQ Straight duct Q16 300 1.0 250 x 300 4.27 5.0 4.041 0.00 11.19 0.0 4.0 51.6 0.2032

Static Loss through path A-J

1 OA Straight duct Q0 4800 1.0 1,300 x 450 9.35 5.0 5.000 0.00 53.66 0.0 5.0 5.0 0.0197

2 Tee 0.37 53.66 19.9 19.9 24.9 0.0978

3 AF Straight duct Q5 1266 1.0 450 x 450 6.66 5.0 4.945 0.00 27.23 0.0 4.9 29.8 0.1173

4 FJ Straight duct Q8 666 1.0 400 x 350 5.07 5.0 3.777 0.00 15.80 0.0 3.8 33.6 0.1322

5 Tee 0.37 15.80 5.8 5.8 39.4 0.1552

6 JK Straight duct Q11 366 1.0 300 x 300 4.33 5.0 3.707 0.00 11.52 0.0 3.7 43.1 0.1698

7 KL Straight duct Q12 66 1.0 150 x 150 3.13 5.0 4.765 0.00 5.99 0.0 4.8 47.9 0.1886


9 Tee 0.37 10.68 4.0 4.0 55.7 0.2194




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Air

Flow

(L/S)

Design

Static

Loss

(Pa/m)

Duct Size (mm)

W x H

Air

Velocity

(m/s)

Straight

Duct

Length

(m)

Static

Loss

(Pa)

C hv

(Pa)

Fitting

Static

Loss

(Pa)

Total

Static

Loss

(Pa)

Cumulative

Static Loss

(Pa)

Static

Loss

(in.

wg)

Static Loss through path C-L

1 OA Straight duct Q0 4800 1.0 450 x 1,300 9.35 5.0 5.000 0.00 53.66 0.0 5.0 5.0 0.0197



4 Tee 0.37 38.78 14.3 14.3 28.7 0.1131



7 Tee 0.370 17.60 6.5 6.5 44.2 0.1740


9 Tee 0.37 10.68 4.0 4.0 52.0 0.2048


Table 4.7 – Static loss calculated result using static balance duct design method from point O to Q.



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5.0 COMPARISON BETWEEN THE STATIC BALANCE AND THE EQUAL

FRICTION DUCT DESIGN METHOD

Chapter 3.1 and 4.1 show two examples of the duct design method for the same

layout. The static balance duct design method uses the equal friction principle to develop

the duct network.

Table 5.1 shows a comparison of the total static loss for the two methods. The

static loss across duct work for the equal friction method is 64 Pa. This represents the

external static pressure that a supply fan needs to overcome. However, the static balance

method is 56 Pa, indicating that the friction loss in the equal friction duct method is 12.5%

higher than the static balance method. The total static loss inclusive of equipment and

terminal pressure for the equal friction method is approximately 1.7% higher than the

static balance method. The reduction of static loss for static balance method may be

significant for a large duct network system.

Item Description Equal Friction

method, (Pa)

Static balance

method, (Pa)

1 Air Handling Unit 380 380

2 Duct friction 64 55

3 Terminal pressure 35 35

Total 479 470

Difference on friction across duct. (%) 12.5

Difference on total static loss. (%) 1.7

Table 5.1 – comparison on the total static loss for two duct design method.



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Item Section Q

Flow

rate

Duct size

(mm) Length Qty

Surface

area Gauge Weight

(l/s) W x H (m) (m2) (U.S.) (kg)

1 OA Q0 4800 1300 x 450 5 1 17.5 22 120.40

2 AB Q1 2400 750 x 450 5 1 12.0 22 82.56

3 BC Q2 2100 750 x 400 5 1 11.5 24 65.05

4 CD Q3 1200 500 x 400 5 1 9.0 26 39.90

5 DE Q4 900 450 x 350 5 1 8.0 26 35.47

6 AF Q5 2100 700 x 450 5 1 11.5 24 65.05

7 CG Q6 600 400 x 300 5 1 7.0 26 31.03

8 EH Q7 600 400 x 300 5 1 7.0 26 31.03

9 FJ Q8 1500 600 x 400 5 1 10.0 26 44.33

10 JK Q11 1200 500 x 400 5 1 9.0 26 39.90

11 KL Q12 900 450 x 350 5 1 8.0 26 35.47

12 LM Q13 600 400 x 300 5 1 7.0 26 31.03

13 MN Q14 300 250 x 300 5 1 5.5 28 21.02

14 NP Q15 300 250 x 300 5 16 88.0 28 336.30

Total = 978.53

15% scrap = 146.78

Total weight = 1125.31

Table 5.2 – Duct size and weight for equal friction duct design method.

Item Section Q

Flow

rate

Duct size

(mm) Length Qty

Surface

area Gauge Weight

(l/s) W x H m m2 (U.S.) (kg)

1 OA Q0 4800 1300 x 450 5 1 17.5 22 120.40

2 AB Q1 3234 950 x 450 5 1 14.0 22 96.32

3 BC Q2 2934 900 x 450 5 1 13.5 22 92.88

4 CD Q3 1507 600 x 400 5 1 10.0 26 44.33

5 DE Q4 1207 600 x 350 5 1 9.5 26 42.12

6 AF Q5 1266 450 x 450 5 1 9.0 26 39.90

7 CG Q6 1127 650 x 300 5 1 9.5 24 53.74

8 EH Q7 907 550 x 300 5 1 8.5 26 37.68

9 FJ Q8 666 400 x 350 5 1 7.5 26 33.25

10 GL Q9 527 350 x 300 5 1 6.5 26 28.82

11 HN Q10 307 250 x 300 5 1 5.5 28 21.02

12 JK Q11 366 300 x 300 5 1 6.0 26 26.60

13 KL Q12 66 150 x 150 5 1 3.0 28 11.46

14 LM Q13 293 250 x 300 5 1 5.5 28 21.02

15 MN Q14 7 100 x 50 5 1 1.5 28 5.73

16 NP Q15 300 250 x 300 5 16 88.0 28 336.30

Total = 1011.56

15% scrap = 151.73

Total weight = 1163.29

Table 5.3 – Duct sizes and weight for static balance duct design method.



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Table 5.2 and 5.3 show the duct sizes and weights established by the two methods

respectively. The weight of sheet metal required for the system design by the static

balance method is approximately 3.4% higher than the equal friction method. However,

the minimal increase of cost is offset by the long-term operating cost.

5.1 Alternative Equal Friction Duct Design Method

From the static balance method, it is found that the duct orientation for equal

friction can be changed to achieve lower static loss. The alternative duct design is shown

in figure 5.1. The highest static loss is from point O to Q, which is 56 Pa. It has the same

static loss obtained for the static balance method.

This result is acceptable because the static balance method is developed based on

the equal friction principle. Furthermore, this system is almost symmetrical, and therefore,

the static variation is not significant. For a more complex system, the static balance

method always has the lowest static loss.

5.2 Site Coordination

In general, the equal friction method is always the most popular among the 3

conventional duct design methods. This is because the equal friction method is the

simplest and fastest way to design, easy to change or modify to suit any site modification.

The static balance method also uses equal friction principle in developing the duct network.

Therefore, it possesses the same advantageous characteristics of the equal friction method

for site modifications.

In addition, the static balance method offers more advantages. Referring to figures

3.2, for example, if the duct size at section F-J is modified to avoid obstruction, any

changes on the duct size will increase the total static loss, which shall be overcome by the

supply fan. The increase of the static loss may cause an insufficient air flow from point O

to P and require a higher fan static.

Referring to figure 4.2, if the static balance method is applied, with the same

modification on section F-J, the air will achieve self-balancing so that more air will flow



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through section C-L and E-N to achieve static balance phenomenon. The increase of static

loss is one-third of the equal friction method. Hence, the disturbance may not be

significant and the increase of fan size may not be required.

5.3 Testing and Commissioning

The static balance method is easier to balance as compared to the equal friction

method. The Equal friction method requires more commissioning time in the air balancing

at branches, due to the air flow is limited within the same length of duct. For the static

balance method, the air flow is self-balance within the duct network and the static

variation by minor disturbances is not significant.

6.0 THE STATIC BALANCE FOR VARIABLE AIR VOLUME (VAV) SYSTEM

The Static balance duct design method offers many advantages and well applicable

for the VAV system. For any partial loading of the VAV system, the air flow rate will self-

balance to achieve the lowest static loss across the duct network. Therefore, it enhances

energy saving on the fan operating cost. Furthermore, the response time of pressure

variation for VAV system is much faster compared to the conventional system due to the

shorter duct length.

6.1 The Equal Friction Method for VAV system

For a VAV system, the supply fan speed is controlled by a variable speed drive

(VSD), corresponding to a pressure sensor located in the duct. Referring to figure 3.2, for

example, the pressure sensor is located between sections L-M. If a VAV terminal unit

located at H is shut off, the pressure sensor will sense the variation and feedback to the

supply fan in reducing the speed. However, the static loss that is required to be overcome

by the supply fan remains unchanged because the air supply from point O to P is

unchanged. The fan reduces air flow rate and maintain the static.

Furthermore, the response time of pressure variation from point H to point L is

long because of the long duct works through path H-E-D-C-B-A-F-J-K-L.



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6.2 The Static Balance Method for VAV System

A Similar case of the equal friction method for VAV system is applied to the static

balance method. Referring to figure 4.2, the pressure sensor is located at L-M. If the VAV

terminal unit located at H is shut off, the pressure sensor will sense the variation and

feedback to the supply fan in reducing the speed. In this case, the air flow within the duct

network will perform self-balancing to reduce the total overall static loss. The air flow

within each section of duct of the network is reduced. It reduces the overall static loss

from point O to Q and the energy consumption.

In addition, lower air flow through bigger duct size reduces the friction factor per

unit of length. As a result, static balance method further reduces the static that required to

be overcome by the supply fan. It further reduces the fan speed and enhances energy

saving. In static balance method, the fan reduces the air flow and the static as well.

The pressure variation response time of the pressure sensor from point H to point L

is short through path H-N-M-L.



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CONCLUSION

The static balance is a novel duct design method which has advantages over

conventional duct design methods. The static balance is a duct network system that

implements the continuity and work-energy principles throughout the network.

The static balance method is an intelligent self-balance method by achieving

minimum static losses across the ducting network. Although the initial cost for the static

balance method is higher than the equal friction method, it is offset by the long term

operating cost. The static balance method also minimizes the increase of static losses,

which causes by site modifications, within the duct network. The commissioning of the

static balance is easier and faster than the equal friction method.

Furthermore, the static balance method is well applicable to the variable air volume

(VAV) system. It enhances the functionality of VAV system. It reduces the system

response time. Due to its intelligent self-static balance characteristic, it further reduces the

overall static losses within the duct network system and achieves higher energy saving.

REFERENCES

1. Carrier, “Handbook of Air Conditioning System Design.” McGraw-Hill, New York.

2. SMACNA, “HVAC Duct Construction Standards.” 1985. SMACNA, USA

3. R.L. Street, “Elementary Fluid Mechanicals.” 1996. (7th

Ed.) John Wiley & Sons, New

York.

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