Cen370 Duct Sizing Dr. N. Zakhia Purpose
Cen370 Duct Sizing Dr. N. Zakhia Purpose
Zakhia
Purpose
Duct system delivers conditioned air to each diffuser in the desired
space at a specified total pressure, Pt. This can be done by selecting the
proper fan to overcome the total pressure losses in the system.
Pressures in ducts:
1
From Bernoulli’s equation: 𝑃 + 2 𝜌𝑉 2 + 𝜌𝑔𝑍 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
P = static pressure, Pst, pa
1
𝜌𝑉 2
≡ Pv ≡ theoretical dynamic or velocity pressure, Pa
2
𝜌𝑔𝑍 ≡ Elevation pressure, Pa ≈ 0
1
𝑃 + 2 𝜌𝑉 2 ≡ Pstag = stagnation or total pressure (Pt).
1
∴ 𝑃𝑠𝑡𝑎𝑔 − 𝑃𝑠𝑡 = 2 𝜌𝑉 2 ≡ 𝑃v ← velocity or dynamic pressure
For air at std, 𝜌 = 1.204 kg/m3 = 0.075 lbm/ft3. ⇒ thus, theoretically,
̅
𝑉 2 ̅
𝑉 2
𝜌 (1097) = (4005) ← 𝐸𝑛𝑔𝑙𝑖𝑠ℎ 𝑢𝑛𝑖𝑡𝑠, (𝑖𝑛. 𝑤𝑔)
𝑃v = { 2 2
̅
𝑉 ̅
𝑉
𝜌 (1.414) = (1.29) → 𝑆𝐼 𝑢𝑛𝑖𝑡𝑠 (𝑃𝑎)
2. Draw a layout on the plan showing AHU, ducts, diffusers, and grilles
3. Size the main duct and all branches
Calculation:
The fan specs are known before duct sizing (low, Medium or high static
fan unit) ⇒ thus, Pstatic,fan and 𝑚̇𝑓𝑎𝑛 are available from the catalogue.
Furthermore, ∆Plosses of all other elements of the system are known
except for the supply and return ducts.
Therefore, the Pnet,static available for the ducts is:
𝑷𝒏𝒆𝒕 𝒔𝒕𝒂𝒕𝒊𝒄,𝒅𝒖𝒄𝒕 = 𝑷𝒔𝒕𝒂𝒕𝒊𝒄 𝒇𝒂𝒏 − 𝑷𝒍𝒐𝒔𝒔𝒆𝒔
where: ∆𝑃𝑠𝑡𝑎𝑡𝑖𝑐,𝐹𝑎𝑛 = 𝑃𝑠𝑡,𝑑𝑢𝑐𝑡 + ∆𝑃𝑅 + 𝑃v
∆𝑃𝑓
• 𝑃𝑠𝑡,𝑑𝑢𝑐𝑡 = ∑ 𝐿𝑒𝑓𝑓 x ( ) + ∑ 𝑃𝑑 where:
𝑚
Leff = effective length = Lduct + Le
Le = total equivalent length of fittings …
∆Pf/meter = ∆P due to friction loss per meter of duct length,
from the flow chart
ΣPd = total dynamic losses for all fittings and equipment such
as fan coils, dampers, grills, …
• ∆𝑃𝑅 = Pressure drop in the Return duct, Pa.
̅2 2
𝑉
𝐶𝑜 (4005) → (𝑖𝑛𝑐ℎ. 𝑤𝑔) V = fan face velocity
• 𝑃v ≡ { 2 Co ≡ loss factors due to fittings
̅2
𝑉
𝐶𝑜 (1.29) → (𝑃𝑎) in the duct (tabulated)
Duct shape:
Round, oval, or rectangular shape can be used. However, rectangular
𝑙𝑒𝑛𝑔𝑡ℎ 𝑊
shape must have aspect ratio: 𝐴𝑅 = = < 4 to avoid vibration
𝑤𝑖𝑑𝑡ℎ 𝐻
and noises.
If AR > 4 ⇒ Expensive to fabricate, hard to
H
install due to large perimeters, high friction
W
losses and may produce vibration and noises
The formula that converts round pipes to rectangular shape:
(𝑊 x 𝐻)0.625
𝐷𝑒 = 1.3 [ ( ] where W = 4 H (see table 2 below)
𝑊+ 𝐻)0.25
cfm
Fa
n
1
2 3
The design of an air conditioning duct system in large buildings may
require the use of a computer software. However, the following
methods are most commonly used for simpler layouts such as the one
shown in the above figure.
Applications Methods
1. Equal Friction loss method.
Low and medium pressure 2. Velocity-reduction method
systems 3. Equal pressure drop method
(Balanced Capacity method)
High/large pressure system 4. Static regain method
1. Equal friction loss method
• This method is straight forward and easy to use.
• It gives an automatic reduction of the Vair throughout the system.
The reduced velocities are, in general, within the noise limits.
Advantages and disadvantages of the “equal friction loss method”:
• This method usually yields a better design than the “velocity-
reduction” method since ∆P is dissipated as friction in the duct
runs, rather than in the balancing dampers.
• This method is generally suitable when the ducts are not too long.
(i.e. residential applications). It can be used for both supply and
return ducts. However, similar to velocity method, the equal
friction method also requires partial closure of dampers in all but
the index run, which may generate noise.
• If the ducts are too long ⇒ the total pressure drop will be high
and due to dampening, ducts near the fan get over-pressurized.
• This method is not recommended for VAV systems and is better
suited for CAV (constant air volume) systems.
• It is usually applied for normal capacity (CFM < 2250 cfm) or
𝑄̇𝑐𝑜𝑜𝑙𝑖𝑛𝑔 < 60,000 Btu/h.
• The short runs will have to be damped, which may cause
considerable noise. The dampering pressure for supply and return
duct is found by deducting the total pressure from pressure losses
of coils, filter, grills, and accessory (all found in the manufacturer’s
catalogue). The remaining pressure is divided between the supply
and the return.
Procedure steps of “Equal Friction Pressure loss” method:
∆𝑃𝑓
This method assumes ( ) in the main and branch ducts is kept equal.
𝐿
∆𝑃𝑓 ∆𝑃𝑓 ∆𝑃𝑓 ∆𝑃𝑓
Meaning: ( 𝐿
) =( 𝐿
) =( 𝐿
) =( 𝐿
) =⋯
𝐴 𝐵 𝐶 𝐷
Steps are:
1. Compute the air flow rate in the main duct by summing the flow
rates of individual branches:
𝑄𝐴 = 𝑄1 + 𝑄2 + 𝑄3 + 𝑄4 + 𝑄5
∆𝑃𝑓
2. Select a suitable ( ) from the friction chart
𝐿
3. Calculate the diameter in the main duct, 𝑫𝒆𝒒,𝑨 ⇒ can be found from:
𝑄
• 𝑄𝐴 = 𝑉𝐴 𝐷𝐴 ⇒ 𝐷𝐴 = 𝑉𝐴 or
𝐴
∆𝑃𝑓
• Since ( ) is constant for all the duct runs, 𝐷𝐴 and all other 𝐷’𝑠
𝐿
can be found from the friction chart knowing Q for each duct.
4. Calculate the pressure drops for the longest run as:
∆𝑃𝑓 ∆𝑃𝑓
∆𝑃𝑓,𝐴 = ( ) . 𝐿𝐴 ; ∆𝑃𝑓,𝐵 = ( ) . 𝐿𝐵 ; …
𝐿 𝐿
5. Compute the dynamic pressure losses, Pv, due to fittings: 2 methods:
• Based on fitting types loss factor, Co (will be provided) or
• Using effective length method.
6. Check the pressure drops for the other branches and determine the
static head of the fan based on the highest ∆P.
7. Next, the fan is selected to suit the index run with the highest ∆P.
8. Finally, dampers will be selected and installed in all duct runs to
balance the total pressure loss.
Example:
consider a typical duct layout shown below. Use “Equal friction
method” to size this duct system. The velocity of air in the main duct is
8 m/s and ρair = 1.2 kg/m3. The fittings loss coefficients are:
𝐶𝑜 = 0.88 for the outlets
45° convergent Tee (WYE) Main duct
𝐶𝑏 = 0.515 for the branches
𝐶𝑚 = 0.18 for the main. VC Vm
45°
𝐶𝑒𝑙𝑏𝑜𝑤 = 0.53 for the 90° elbow.
Deduce the required FTP and the
1.5 Db
amount of dampering in each duct. Db
Vb Branch
2 m3/s 2 1 m3/s 3
Return
D F
15 m 12 m 18 m 66m
m
Fresh air
Outside
AHU A C E
+
FAN
66m
m
B 45° convergent Tee 90° Elbow
45° convergent Tee
1 m3/s 1
Solution:
1. Compute the total air flow rate of the main duct:
𝑄𝑡𝑜𝑡 = 𝑄𝐵 + 𝑄𝐷 + 𝑄𝐹 = 1 + 2 + 1 = 4 𝑚3 /𝑠 and V = 8 m/sec
∆𝑷𝒇
2. =? in the main duct (A): it can be found from the friction chart:
𝑳
∆𝑃𝑓,𝐴
At Q = 4 m3/sec and V = 8 m/s ⇒ ≈ 0.78 Pa/m. This method
𝐿
requires that ∆Pf/L is the same for all ducts.
3. Compute D’s =?
• DA =? can be read from the same figure 2 or calculated as:
𝑄 4
QA = VA. AA ⇒ 𝐴 = 𝑉 = 8 = 0,5 𝑚2 ⇒ 𝐷𝐴 = 0.798 m
All other D’s are found from the chart (figure 2), as:
∆𝑃𝑓,𝐴
• DB =?at QB = 1 m3/sec and = 0.78 ⇒ Deq,B =0.475 m
𝐿
∆𝑃𝑓,𝐴
• DC =? at QC = 3 m3/sec and = 0.78 ⇒ DB =0.72 m
𝐿
∆𝑃𝑓,𝐴
• Deq,D =? at QD = 2 m3/sec and = 0.78 ⇒ Deq,D =0.62 m
𝐿
∆𝑃𝑓,𝐴
• Deq,E =? at QE = 3 m3/sec and = 0.78 ⇒ Deq,E =0.475 m
𝐿
2 m3/s 2 1 m3/s 3
D F
15 m 12 m 18 m 66m
m
A C E
FAN 66m
m
B
1 m3/s 1
𝑉𝐵2
• ∆𝑃𝑒𝑙𝑏−𝑏 = 𝐶𝑐,𝑏 (𝜌 ) ⇒ VB =?
2
∆𝑃𝑓,𝐴
From the chart at = 0.78 and 𝑄̇𝐵 = 1 𝑚3 /𝑠 ⇒ VB ≈ 5.8 m/sec
𝐿𝐴
D F
15 m 12 m 18 m 66m
m
A C E
FAN 66m
m
B
1 m3/s 1
2 m3/s 2 1 m3/s 3
Damper (23.0 Pa)
D F
15 m 12 m 18 m 66m
m
A C E
FAN 66m
m
B
Velocity (m/s)
Residences Hotels Schools
Main supply 5 6 7.5
Main return 4 5 6
Branch supply 3 4 6
Branch return 3 4 5
Steps of calculation:
1. Select suitable velocities in the main and branch ducts from
ASHRAE Table.
2. Find the diameters of the main and branch ducts from airflow
rates and velocities for circular ducts.
3. From the velocities and duct dimensions obtained in the
previous step, find the ∆Pf for the main and branches using
friction chart or an equation.
4. From the duct layout, dimensions and airflow rates, find the Pv for
all the bends and fittings.
5. Select a fan that can provide sufficient Pst for the index run.
6. Balancing dampers have to be installed in each run. The damper in
the index run is left completely open, while the other dampers are
throttled to reduce the flow rate to the required design values.
Advantages/disadvantages of the velocity-reduction method:
It is a simple method to design both supply and return air-ducts.
However, selection of suitable velocities in different duct runs requires
experience. Wrong selection of velocities can lead to very large ducts,
which leads to occupying large space in the building and increases the
cost. Furthermore, if your selection of velocities led to very small ducts,
it will result in large pressure drop and hence necessitates the selection
of a large fan leading to higher fan cost and running cost. In addition,
the method is not very efficient as it requires partial closing of all the
dampers except the one in the longest or index run, so that the total
pressure drop in each run will be same.
Example: redo the previous example using the “velocity-reduction
method”
2 m3/s 2 1 m3/s 3
Return
D F
15 m 12 m 18 m 66m
m
Fresh air
Outside
AHU A C E
+
FAN
66m
m
B 45° convergent Tee 90° Elbow
45° convergent Tee
1 m3/s 1
Solution:
1. V =? Select a velocity of 5 m/s for the downstream and branches
while Vmain remains 8 m/sec.
2. D=?
Segment A: Flow rate, Q = 4 m3/s and VA = 8 m/s ⇒
AA = QA/VA = 4/8 = 0.5 m2 ⇒ DA = 0.798 m
Segment B: Flow rate, Q = 1 m3/s and VB = 5 m/s ⇒
AB = QB/VB = 1/5 = 0.2 m2 ⇒ DB = 0.505 m
Segment C: Flow rate, QC = 3 m3/s and VC = 5 m/s ⇒
AC = QC/VC = 3/5 = 0.6 m2 ⇒ DC = 0.874 m
Segment D: Flow rate, QD = 2 m3/s and VD = 5 m/s ⇒
AD = QD/VD = 2/5 = 0.4 m2 ⇒ DD = 0.714 m
Segments E&F: Flow rate, QE,F = 1 m3/s and VE,F = 5 m/s ⇒
AE = AF = QE/VE = 1/5 = 0.2 m2 ⇒ DE = DF = 0.505 m
3. Calculation of pressure drop (balancing the system):
Section A-B: ∆𝑃𝐴→𝐵 = ∆𝑃𝑓,𝐴 + ∆𝑃𝑓,𝐵 + ∆𝑃𝑒𝑙𝑏−𝑏 + ∆𝑃𝑜𝑢𝑡𝑙𝑒𝑡 1
∆𝑃𝑓,𝐴
∆𝑃𝑓,𝐴 =? at QA = 4 m3/s and VA = 8 m/s ⇒ = 0.78 Pa/m
𝐿
∆𝑃𝑓 𝐴
∆𝑃𝑓 𝐴 = ( ) 𝐿𝐴 = 0,78 𝑥 15 𝑚 = 11,7 Pa
𝐿
∆𝑃𝑓,𝐵
∆𝑃𝑓,𝐵 =? at Q = 1 m3/s and VB = 5 m/s ⇒ = 0.52 Pa/m
𝐿
∆𝑃𝑓 𝐵
∆𝑃𝑓 𝐵 = ( ) 𝐿𝐵 = 0,52 𝑥 6 𝑚 = 3,12 Pa
𝐿
𝜌𝑉𝐷2 1,2 x 52
∆𝑃𝑒𝑙𝑏−𝑏 = 𝐶𝑏 ( ) = 0,515 ( ) = 16,5 𝑃𝑎
2 2
𝜌𝑉𝐷2 1,2 x 52
∆𝑃𝑜𝑢𝑡𝑙𝑒𝑡(1) = 𝐶𝑜 ( ) = 0,88 ( ) = 13,2 𝑃𝑎
2 2
2
4
AHU 1 3
+
FAN
6m
AHU A 5m B 6m C 4m D
+ 1.10 m3/s
FAN
4m
Branch Fittings: F
Wye, 45 degree 0.20 m3/s
Solution:
1. Find the flow rates:
𝑄𝐴𝐵 = 0.6 + 0.2 + 1.1 = 1.9 𝑚3 /𝑠𝑒𝑐
𝑄𝐵𝐶 = 0.2 + 1.1 = 1.3 𝑚3 /𝑠𝑒𝑐
2. Calculate ∆P and the diameter in the main duct:
• Given Vmax = VAB = 5 m/sec in duct AB (next to the fan) ⇒ Thus:
4𝑄
𝑄𝐴𝐵 = 𝑉𝐴𝐵 x 𝐴𝐴𝐵 ⇒ 𝐷𝐴𝐵 = √𝜋 𝑉𝐴𝐵 = 0.70 𝑚 (or from the chart)
𝐴𝐵
• From the chart at 𝑄𝐴𝐵 = 1.9 m3/sec and VAB = 5 m/sec ⇒ read:
∆𝑃𝐴𝐵 ∆𝑃𝐴𝐵
= 0.36 Pa/m. This method requires that = 0.36 Pa/m
𝐿 𝐿
remains the same for all ducts to their exits.
Figure 2. Friction loss ∆Pf/m – SI units
Q = 4 m3/s
Air Quantity, m3/s
6m
AHU A 5m B 6m C 4m D
+ 1.10 m3/s
FAN
4m
Branch Fittings: F
Wye, 45 degree 0.20 m3/s
➢ Let’s first make ∆𝑃𝐴→𝐹 = ∆𝑃𝐴→𝐷 where:
∆𝑃𝐴→𝐹 = ∆𝑃𝐴→𝐵 + ∆𝑃𝐵→𝐶 + ∆𝑃𝐶→𝐹 This requires
∆𝑃𝐴→𝐷 = ∆𝑃𝐴→𝐵 + ∆𝑃𝐵→𝐶 + ∆𝑃𝐶→𝐷 ∆𝑃𝐶→𝐷 = ∆𝑃𝐶→𝐹
∆𝑃
• ∆𝑃𝐶→𝐷 =? Using the effective length method, ∆𝑃𝐶→𝐷 = ( 𝐿 ) . 𝐿𝑒𝑓𝑓
𝑒
𝐿
𝐿𝑒,𝑡ℎ𝑟𝑜𝑢𝑔ℎ = ( 𝐷𝑒| ) 𝐷𝐶𝐷 = 10 x 0.56 = 5.6 m
𝑡ℎ𝑟𝑜𝑢𝑔ℎ
∆𝑃
∴ 𝐿𝑒𝑓𝑓 = 4 + 5.8 = 9.8 m ⇒ ∆𝑃𝐶𝐹 = ( 𝐿 ) 𝐿𝑒𝑓𝑓 = 0.36 x 9.8 = 3.53 Pa.
𝑒
0.60 m3/s
E
Damper BE
6m
AHU A 5m 6m C 4m D
+ 1.10 m3/s
FAN B
4m
F Damper CD
0.20 m3/s
Table - 3
HVAC engineering Practice rules of thumb
1. Dampers.
a) Volume Control Dampers: used to control air
flow. They are of two types:
• Parallel blade dampers: The blades rotate in
one direction. These dampers are best suited to
fully-open or fully-close the air flow (cfm) or for
fine control between 80% to 100% full flow.
• Opposed blade dampers: The blades rotate in
opposite directions. These dampers are best
suited to regulate cfm over a wide range
AMCA (Air Movement and Control Association)
recommends using an opposed-blade damper when
volume control is needed.
Balancing/volume adjusting dampers should be installed close to the
main supply, as far away as possible from the outlets. Terminal
dampers such as those used in registers and diffusers should not be
considered in branch balancing as they are meant to be used for fine
adjustment only and would normally be in an almost fully open
position to prevent unnecessary noise.
b) Fire and Smoke Dampers
A fire damper is installed adjacent to duct outlets to interrupt the
passage of flame. Fire dampers are equipped with a fusible link {rated
for 165°F up to 286°F (74 °C to 141°C)} that holds the blades open until
the link melts.
Should the ductwork fall away, the damper needs to stay in the wall or
floor to maintain the integrity of the wall or floor. One should actually
think of the fire damper as part of the wall system itself.
Smoke dampers are defined as a device designed to resist the passage
of smoke through the HVAC system.
In today’s design, fire and smoke dampers come in one piece.
2. Diffusers, Grilles & Registers, plenum ceiling see EG and kbe files for
proper use and installation (posted on blackboard).
• Diffusers: They supply air in various directions through deflecting
vanes. 2 types: (see EG and kbe files on blackboard)
– Ceiling diffusers
– Slot diffusers
supply
air Diffuser
Length Airflow
Location of Air supply diffusers and Outlets (see table entitled “supply
air outlets performance” listed below)
The following key point should be noted:
a. Locate diffusers so that the T50 length is nearly equivalent to the
characteristic length.
b. When cooling is the dominant factor, install ceiling diffusers or
high wall outlets that discharge air parallel to the ceiling.
c. Place the returns high when cooling is the dominant factor, and
low when heating is the dominant factor.
d. Special applications such as bars, kitchens, lavatories, dining
rooms, club rooms, etc, the return and exhaust inlets must be
located near or at the ceiling level to collect the warm air "build-
up," odors, smoke, and fumes.
Supply Air Outlet Performance-Location
Diffuser Trunk
Branches
24 ft ≈ 7.3 m
(Single plenum)
24 ft 24 ft
maximum maximum
18 in.
minimum
Supply
plenum
18 in.
minimum
Perimeter outlets
18 in.
minimum 600 cfm
450 ft/min
Supply
plenum
4 ft
minimum
1200 cfm
900 ft/min
15 to 20 ft 24 ft
maximum
A Tee performs
AHU Supply the same function
as a reducer
Return
Return
spacing
For sheet metal ductwork, the space between the hangers should not
exceed the distances listed below: