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LECTURE-11

FAN AND DUCT SYSTEM-2

Fr iction Factor for Ducts:

The value of friction factor, for smooth ducts may be obtained by using the

following expressions:

1. For laminar flow, the friction factor

� � ����

…………………………………15

2. For turbulent flow, the friction factor

� � �.�

���.��…………………………………16

In case of rough pipes or ducts the friction factor depends upon the roughness

factor (e/D), where (e) is the absolute roughness of the surface and (D) is the

diameter of duct. The friction factor for rough pipes or ducts is:

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� �

.����������� ��

�…………………………………17

Fr iction Chart for Circular Ducts:

From equations 11 and 13 the frictional pressure loss for circular ducts

�� � ������

���

� ����

�� (N/m2)……………………..…………….18

The frictional pressure loss for circular ducts (mm of water ) for various

velocities (m/s) and duct diameter (m) may be obtained directly from the friction

chart. In these charts, the vertical ordinates represent volume flow rate of air and the

.horizontal ordinates represent frictional pressure loss in mm of water per unit length

of the circular duct (Pf/L).

Dynamic Losses in Ducts:

The dynamic losses are caused due to the change in direction or magnitude of

velocity of the fluid in the duct. The change in direction of velocity occurs at bends

and elbows. The dynamic pressure loss,

�� � ��� � �� ��.��

��

…………………………(19)

Where (C) is the dynamic loss coefficient.

The dynamic pressure loss expressed in terms of an additional equivalent

length (Le) of the duct is given by:

�� � ���

�� � ���

� �

�.���

� in mm of water……………(20)

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From equations 19 and 20, the relationship between the dynamic loss

coefficient (C) and equivalent additional length is

� � ���

�! �� � � �

……………………………….…….…(21)

Duct Design:

The object of duct design is to determine the dimensions of all ducts in the

given system. The ducts should carry the necessary volume of conditioned air from

the fan outlet to the conditioned space with minimum frictional and dynamic losses.

The area changes must be gradual where possible and limited to not more than

20o for diverging area and 60o for convergent area. For rectangular ducts the

aspect ratio of 4 and less is desirable but it should not be greater than 8 in any

case.

The velocities in the ducts must be high enough to reduce the size of the ducts

but it should be low enough to reduce the noise and pressure losses to economize

power requirement as table (1)

Designation

Recommended Velocities in m/s

Residences School, theater and

public building Industrial building

Outdoor air intakes 2.5 2.5 2.5

Filters 1.25 1.5 1.75

Heating coil 2.25 2.5 3

Air washers 2.5 2.5 2.5

Fan Outlet 5-8 6.6-10 8-12

Main Duct 3.3-5 5-6.6 5.8-9.1

Branch Duct 3 3-4.5 4-5

Branch Risers 2.5 3-3.5 4

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Methods for Determination of Duct Size:

The following three methods for determination of duct size are important as:

1. Velocity Reduction Method

The various steps involved in this method are:

i. Select suitable velocities in the main and branch ducts

ii. Find the diameters of main and branch ducts from airflow rates and velocities

for circular ducts. For rectangular ducts, find the cross-sectional area from flow

rate and velocity, and then by fixing the aspect ratio, find the two sides of the

rectangular duct.

iii. From the velocities and duct dimensions obtained in the previous step, find the

frictional pressure drop for main and branch ducts using friction chart or

equation.

iv. From the duct layout, dimensions and airflow rates, find the dynamic pressure

losses for all the bends and fittings.

v. Select a fan that can provide sufficient Flow for the index run

vi. 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.

The Velocity Method Proper air flow velocities for the application

considering the environment are selected. Sizes of ducts are then given by the

continuity equation like:

A = q / v …………………………..(22)

A = duct area (m2)

q = air flow rate (m3/s)

v= air speed (m/s)

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A proper velocity will depend on the application and the environment. The

table below indicate commonly used velocity

2. Equal fr iction method

In this method the frictional pressure drop per unit length in the main

and branch ducts (∆pf/L) are kept same

Then the stepwise procedure for designing the duct system is as follows:

i. Select a suitable frictional pressure drop per unit length

the combined initial and running costs are minimized.

ii. Then the equivalent diameter of the main duct (A) is obtained from the

selected value of (∆

air flow rate in the main duct is equal to the sum total of airflow rates to

all the conditioned zones.

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A proper velocity will depend on the application and the environment. The

table below indicate commonly used velocity limits:

In this method the frictional pressure drop per unit length in the main

/L ) are kept same,

……………………………(23)

Then the stepwise procedure for designing the duct system is as follows:

Select a suitable frictional pressure drop per unit length (∆

the combined initial and running costs are minimized.

Then the equivalent diameter of the main duct (A) is obtained from the

(∆pf/L ) and the air flow rate. As shown in Figure (1),

the main duct is equal to the sum total of airflow rates to

all the conditioned zones.

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A proper velocity will depend on the application and the environment. The

In this method the frictional pressure drop per unit length in the main

……………………………(23)

Then the stepwise procedure for designing the duct system is as follows:

(∆pf/L) so that

Then the equivalent diameter of the main duct (A) is obtained from the

wn in Figure (1),

the main duct is equal to the sum total of airflow rates to

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ix. Next the dynamic pressure losses in each duct run are obtained based on

the type of bends or fittings used in that run.

x. Next the total pressure drop in each duct

the frictional and dynamic losses of that run:

xi. Next the fan is selected to suit the index run with the highest pressure

loss. Dampers are installed in all the duct runs to balance the total

pressure loss.

The major loss, or friction loss, in a circular duct in galvanized steel with

turbulent flow can for imperial units be expressed

∆p = (0.109136 q

∆p = friction (head or pressure loss) (inches water gauge/100 ft of duct)

de = equivalent duct diameter (inches)

q = air volume flow - (cfm

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……………………………(2

Next the dynamic pressure losses in each duct run are obtained based on

the type of bends or fittings used in that run.

Next the total pressure drop in each duct run is obtained by summing up

the frictional and dynamic losses of that run:

……………………………(2

Next the fan is selected to suit the index run with the highest pressure

loss. Dampers are installed in all the duct runs to balance the total

The major loss, or friction loss, in a circular duct in galvanized steel with

turbulent flow can for imperial units be expressed

p = (0.109136 q1.9) / de5.02………………….

friction (head or pressure loss) (inches water gauge/100 ft of duct)

equivalent duct diameter (inches)

(cfm - cubic feet per minute)

O F M E CH A N ICA L E N G IN E E R INO F M E CH A N ICA L E N G IN E E R INO F M E CH A N ICA L E N G IN E E R INO F M E CH A N ICA L E N G IN E E R IN

……………………………(27)

Next the dynamic pressure losses in each duct run are obtained based on

run is obtained by summing up

……………………………(28)

Next the fan is selected to suit the index run with the highest pressure

loss. Dampers are installed in all the duct runs to balance the total

The major loss, or friction loss, in a circular duct in galvanized steel with

…………. )29(

friction (head or pressure loss) (inches water gauge/100 ft of duct)