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Lecture 3 - Fans and Blowers

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3/6/2024
Republic of the Philippines
Tarlac State University
COLLEGE OF ENGINEERING
Department of Mechanical Engineering
MEF343:
FLUID MACHINERIES
Engr. Marc Florenz P. Arnaldo
Faculty, Department of Mechanical Engineering
1
Republic of the Philippines
Tarlac State University
COLLEGE OF ENGINEERING
Department of Mechanical Engineering
LECTURE 3:
FUNDAMENTAL PRINCIPLES
OF FANS AND BLOWERS
Engr. Marc Florenz P. Arnaldo
Faculty, Department of Mechanical Engineering
2
1
3/6/2024
LEARNING OUTCOMES
After completion of the discussion, the students should be able to:
• Explain the types, concepts, and principles related to fans and
blowers
• Identify the different types and components of fans and
blowers
• Perform energy analysis to solve related fans and blowers
problems
For more inquiries, message:
mfarnaldo@tsu.edu.ph
3
FUNDAMENTAL PRINCIPLES OF FANS AND BLOWERS
FAN
A fan is a machine used to apply power
to a gas to increase its energy content
thereby causing it to flow or move.
BLOWER
A blower is a fan used to force air under
pressure, that is, the resistance to gas
flow is imposed primarily upon the
discharge.
Tube Axial Fan
Centrifugal Blower
Source: Industrial Plant Engineering by Capote, R. and Mandawe, J.
4
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FUNDAMENTAL PRINCIPLES OF FANS AND BLOWERS
EXHAUSTER
An exhauster is a fan used to withdraw
air under pressure which means
resistance to gas flow is imposed upon
suction.
BLOWER
A blower is a fan used to force air under
pressure, that is, the resistance to gas
flow is imposed primarily upon the
discharge.
Source: Industrial Plant Engineering by Capote, R. and Mandawe, J.
5
FUNDAMENTAL PRINCIPLES OF FANS AND BLOWERS
DIFFERENCE BETWEEN FANS AND BLOWERS
The American Society of Mechanical Engineers (ASME) has defined fans
and blowers based on their discharge pressure and suction pressure ratio.
This way they have also defined compressors, and in a way distinguished
between all these three devices. According to ASME, a fan is a device
with a pressure ratio of up to 1.11.
Source: Fans by American Society of Mechanical Engineers (ASME)
6
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FUNDAMENTAL PRINCIPLES OF FANS AND BLOWERS
TYPES OF FANS:
1. Centrifugal Fan
It is a machine which pumping action is accomplished by imparting
kinetic energy to the fluid by a high speed revolving impeller with
vanes and subsequently converting this kinetic energy into pressure
energy either by passing through a volute casing or through a diffuser
vanes.
Source: Industrial Plant Engineering by Capote, R. and Mandawe, J.
7
FUNDAMENTAL PRINCIPLES OF FANS AND BLOWERS
TYPES OF FANS:
2. Axial Fan
It is a machine which pumping action is accomplished by imparting
kinetic energy to the fluid by a high speed revolving impeller with
vanes and subsequently converting this kinetic energy into pressure
energy either by passing through a volute casing or through a diffuser
vanes.
Source: Industrial Plant Engineering by Capote, R. and Mandawe, J.
8
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FUNDAMENTAL PRINCIPLES OF FANS AND BLOWERS
TYPES OF FANS:
2. Axial Fan
Source: Industrial Plant Engineering by Capote, R. and Mandawe, J.
9
FUNDAMENTAL PRINCIPLES OF FANS AND BLOWERS
BLOWERS:
Blower is equipment or a device which increases the velocity of air or
gas when it is passed through equipped impellers. They are mainly
used for flow of air/gas required for exhausting, aspirating, cooling,
ventilating, conveying etc. Blower is also commonly known as
Centrifugal Fans in industry. In a blower, the inlet pressure is low and
is higher at the outlet. The kinetic energy of the blades increases the
pressure of the air at the outlet. Blowers are mainly used in industries
for moderate pressure requirements where the pressure is more than
the fan and less than the compressor.
Source: Fans and Blowers by Power Zone Equipment, Inc.
10
5
3/6/2024
FUNDAMENTAL PRINCIPLES OF FANS AND BLOWERS
TYPES OF BLOWERS:
Blowers can also be classified as Dynamic and Positive
Displacement Blowers. Like fans, blowers use blades in various
designs such as backward curved, forward curved and radial. They
are mostly driven by electric motor. They can be single or multistage
units and use high speed impellers to create velocity to air or other
gases.
Positive displacement blowers are similar to PDP pumps, which
squeezes fluid that in turn increases pressure. This kind of blower is
preferred over a centrifugal blower where high pressure is required in
a process.
Source: Fans and Blowers by Power Zone Equipment, Inc.
11
FUNDAMENTAL PRINCIPLES OF FANS AND BLOWERS
APPLICATIONS OF FANS AND BLOWERS:
Fans and Blowers are mostly used for processes such as Air
Ventilation, Material Handling, Air Drying etc.
Source: Fans and Blowers by Power Zone Equipment, Inc.
12
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3/6/2024
FUNDAMENTAL PRINCIPLES OF FANS AND BLOWERS
APPLICATIONS OF FANS AND BLOWERS:
Industrial fans are also used in a variety of applications such as
chemical, medical, automotive, agricultural, mining, food processing,
and construction industries, which can each utilize industrial fans for
their respective processes. They are mainly used in many cooling and
drying applications.
Source: Fans and Blowers by Power Zone Equipment, Inc.
13
FUNDAMENTAL PRINCIPLES OF FANS AND BLOWERS
APPLICATIONS OF FANS AND BLOWERS:
Centrifugal blowers are routinely used for applications such as dust
control, combustion air supplies, on cooling, drying systems, for fluid
bed aerators with air conveyor systems etc. Positive displacement
blowers are often used in pneumatic conveying, and for sewage
aeration, filter flushing, and gas boosting, as well as for moving gases
of all kinds in the petrochemical industries.
Source: Fans and Blowers by Power Zone Equipment, Inc.
14
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3/6/2024
FUNDAMENTAL PRINCIPLES OF FANS AND BLOWERS
APPLICATIONS OF FANS AND BLOWERS:
Therefore, fans, and blowers, largely cover Municipal, Manufacturing,
Oil & Gas, Mining, Agriculture Industry for their various applications,
simple or complex in nature.
These are available from various manufacturers in different designs.
Few of the well-known brands are Yashiba, Hoffman, Bosch,
Sutterbuilt, Sullair and Joy.
Source: Fans and Blowers by Power Zone Equipment, Inc.
15
FUNDAMENTAL PRINCIPLES OF FANS AND BLOWERS
APPLICATIONS OF FANS AND BLOWERS:
A detailed study of all the designs and specifications is required to
buy an appropriate fan or a blower that is available in the market so
that it can match the requirements of your process and ensure
reliability and durability at the same time.
Source: Fans and Blowers by Power Zone Equipment, Inc.
16
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3/6/2024
FUNDAMENTAL PRINCIPLES OF FANS AND BLOWERS
BASIC DIFFERENCES
COMPRESSORS:
OF
FANS
&
BLOWERS,
AND
EQUIPMENT
SPECIFIC RATIO
PRESSURE RAISE
(mmHg)
Fans
Up to 1.11
1136
Blowers
1.11 – 1.20
1136 – 2066
Compressors
More than 1.20
More than 2066
Source: Centrifugal Pumps by Michael Smith Engineers Co. UK
17
FUNDAMENTAL PRINCIPLES OF FANS AND BLOWERS
ANALYSIS OF FANS AND BLOWERS:
1. Static Head, 𝒉𝒔
Static Head is the height of the surface of the fluid above the gauge
point. This can also be interpreted as the pressure head in the case of
fans and blowers, since change in elevation is not a factor in the
analysis.
β„Ž =β„Ž =
𝛾 β„Ž
𝛾
2. Velocity Head, 𝒉𝒗
Velocity Head is the head required to produce the flow of fluid.
β„Ž =
𝑉 −𝑉
2𝑔
Source: Industrial Plant Engineering by Capote, R. and Mandawe, J.
18
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FUNDAMENTAL PRINCIPLES OF FANS AND BLOWERS
ANALYSIS OF FANS AND BLOWERS:
3. Total Head, 𝑯
Total Head is the sum of the static head and velocity head.
𝐻 =β„Ž +β„Ž
𝑃 −𝑃
𝑉 −𝑉
+
𝛾
2𝑔
𝛾 (β„Ž , − β„Ž , ) 𝑉 − 𝑉
𝐻=
+
𝛾
2𝑔
𝐻=
4. Capacity of the Fan, 𝑸
The capacity of the fan is the volume flow rate measured at the fan
outlet.
𝑄 = 𝐴𝑉
Source: Industrial Plant Engineering by Capote, R. and Mandawe, J.
19
FUNDAMENTAL PRINCIPLES OF FANS AND BLOWERS
ANALYSIS OF FANS AND BLOWERS:
5. Power Output of Fan (Air Power), 𝑷𝒂
The power output of a fan or air power is
based on fan volume and the fan total
pressure.
𝑃 = 𝛾 𝑄𝐻
6. Power Output of the Fan (Brake Power), 𝑷𝑩
The power output of a fan, or brake power, is
the power delivered to the fan shaft.
𝑒 =
𝑃
𝑃
7. Power Input to the Fan (Input Power), π‘·π’Š
The power input to the fan, or input power, is
the power supplied to the fan motor.
𝑒 =
𝑃
𝑃
Source: Industrial Plant Engineering by Capote, R. and Mandawe, J.
20
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3/6/2024
FUNDAMENTAL PRINCIPLES OF FANS AND BLOWERS
ANALYSIS OF FANS AND BLOWERS:
8. Static Efficiency of Fan, 𝒆𝒔
The static efficiency of a fan is the product of the fan/blower efficiency
and the ratio of the static pressure to the total pressure.
𝑒 =𝑒
β„Ž
β„Ž
=
𝑃
,
𝑃
9. Overall Efficiency of Fan, 𝒆𝒐
The overall efficiency of a fan is the product of the fan/blower
efficiency and the mechanical/motor efficiency.
𝑒 =𝑒 𝑒
Source: Industrial Plant Engineering by Capote, R. and Mandawe, J.
21
FUNDAMENTAL PRINCIPLES OF FANS AND BLOWERS
ANALYSIS OF FANS AND BLOWERS:
10. Fan Affinity Laws
There are three (3) basic fan laws which encompass all fan functional
principles.
Variation in Fan Speed (Constant Diameter & Constant Density)
𝑄
𝑁
=
𝑄
𝑁
𝐻
𝑁
=
𝐻
𝑁
𝑃
𝑁
=
𝑃
𝑁
Variation in Fan Diameter (Constant Speed & Constant Density)
𝑄
𝐷
=
𝑄
𝐷
𝐻
𝐷
=
𝐻
𝐷
𝑃
𝐷
=
𝑃
𝐷
Source: Industrial Plant Engineering by Capote, R. and Mandawe, J.
22
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3/6/2024
FUNDAMENTAL PRINCIPLES OF FANS AND BLOWERS
ANALYSIS OF FANS AND BLOWERS:
10. Fan Affinity Laws
There are three (3) basic fan laws which encompass all fan functional
principles.
Variation in Gas Density (Constant Diameter & Constant Speed)
𝑄 =𝑄
𝐻
𝜌
=
𝐻
𝜌
𝑃
𝜌
=
𝑃
𝜌
Source: Industrial Plant Engineering by Capote, R. and Mandawe, J.
23
FUNDAMENTRAL PRINCIPLES OF PUMPS
ANALYSIS OF FANS AND BLOWERS:
Source: Industrial Plant Engineering by Capote, R. and Mandawe, J.
24
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FUNDAMENTRAL PRINCIPLES OF PUMPS
ANALYSIS OF FANS AND BLOWERS:
Source: Industrial Plant Engineering by Capote, R. and Mandawe, J.
25
FUNDAMENTRAL PRINCIPLES OF PUMPS
ANALYSIS OF FANS AND BLOWERS:
𝑄
𝑁
=
𝑄
𝑁
𝐻
𝑁
=
𝐻
𝑁
𝑃
𝑁
=
𝑃
𝑁
Source: Industrial Plant Engineering by Capote, R. and Mandawe, J.
26
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3/6/2024
FUNDAMENTRAL PRINCIPLES OF PUMPS
ANALYSIS OF FANS AND BLOWERS:
𝑄
𝐷
=
𝑄
𝐷
𝐻
𝐷
=
𝐻
𝐷
𝑃
𝐷
=
𝑃
𝐷
Source: Industrial Plant Engineering by Capote, R. and Mandawe, J.
27
PROBLEM SOLVING:
1. Determine the power required to move the air at 20 fpm through a 2’×3’ duct
under 3 𝑖𝑛𝐻 𝑂.
Given: A Fan used to move air in a duct
𝑉 = 20 𝑓𝑑/π‘šπ‘–π‘›
β„Ž = 2 𝑓𝑑, 𝑀 = 3𝑓𝑑
β„Ž = 3 𝑖𝑛
Required: Power supplied to the Air, 𝑃
Solution:
Solving for the power supplied to
the air,
Assumption,
𝑃 =𝑃
𝛾 β„Ž =𝛾 β„Ž
Note: β„Ž = β„Ž
For the static head,
𝛾 β„Ž
β„Ž =
𝛾
For the air power,
𝑃 = 𝛾 𝑄𝐻
Note:
𝐻 =β„Ž +β„Ž =β„Ž +
For more inquiries, message me at:
mfarnaldo@tsu.edu.ph
βˆ†π‘‰
2𝑔
28
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3/6/2024
PROBLEM SOLVING:
1. Determine the power required to move the air at 20 fpm through a 2’×3’ duct
under 3 𝑖𝑛𝐻 𝑂.
Solution:
For the fan capacity,
𝑄 = 𝐴𝑉
𝑄 = 2𝑓𝑑 3𝑓𝑑
20
𝑓𝑑
π‘šπ‘–π‘›
1 π‘šπ‘–π‘›
60 𝑠
𝑄 = 2 𝑓𝑑 /𝑠
For the static head,
𝛾 β„Ž
β„Ž =β„Ž =
𝛾
𝑙𝑏
62.40
𝑓𝑑
β„Ž =β„Ž =
𝛾
3 𝑖𝑛
For more inquiries, message me at:
mfarnaldo@tsu.edu.ph
29
PROBLEM SOLVING:
1. Determine the power required to move the air at 20 fpm through a 2’×3’ duct
under 3 𝑖𝑛𝐻 𝑂.
Solution:
Finally, solving for the power supplied to the air,
𝑃 = 𝛾 𝑄𝐻
62.40
𝑃 =𝛾 𝑄
𝑃 = 2
𝑓𝑑
𝑠
𝑙𝑏
𝑓𝑑
3 𝑖𝑛
𝛾
62.40
𝑙𝑏
𝑓𝑑
3 𝑖𝑛
1 𝑓𝑑
12 𝑖𝑛
1 𝐻𝑃 − 𝑠
550 𝑙𝑏 − 𝑓𝑑
𝑷𝒂 = 𝟎. πŸŽπŸ“πŸ”πŸ• 𝑯𝑷 (ans)
For more inquiries, message me at:
mfarnaldo@tsu.edu.ph
30
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3/6/2024
PROBLEM SOLVING:
2. A fan whose static efficiency is 40% has a capacity of 60,000 𝑓𝑑 /β„Žπ‘Ÿ @ 60℉ and
barometer of 30 inHg and gives a static pressure of 2 in𝐻 𝑂 on full delivery.
Determine the size of the motor required to operate the fan.
Given: A Fan
𝑒 = 40%
𝑄 = 60,000 𝑓𝑑 /𝑠
𝑃
= 30 𝑖𝑛𝐻𝑔
β„Ž , = 2 𝑖𝑛
Required: Size of the Motor required to operate the fan, 𝑃
Solution:
Solving for the brake power using the static efficiency,
𝑃 ,
𝑒 =
𝑃
For the static head,
𝛾 β„Ž
For the static air power,
β„Ž
=
𝑃 , = 𝛾 𝑄𝐻
𝛾
𝐻 =β„Ž +β„Ž
Note: β„Ž = β„Ž
For more inquiries, message me at:
mfarnaldo@tsu.edu.ph
31
PROBLEM SOLVING:
2. A fan whose static efficiency is 40% has a capacity of 60,000 𝑓𝑑 /β„Žπ‘Ÿ @ 60℉ and
barometer of 30 inHg and gives a static pressure of 2 in𝐻 𝑂 on full delivery.
Determine the size of the motor required to operate the fan.
Solution:
Hence, the static air power
𝑃 , = 𝛾 𝑄𝐻
𝛾 β„Ž
𝑃 , =𝛾 𝑄
𝛾
𝑃 , = 𝑄𝛾 β„Ž
𝑙𝑏
𝑓𝑑
𝑃 , = 60000
62.40
β„Žπ‘Ÿ
𝑓𝑑
𝑃 , = 0.3152 𝐻𝑃
2 𝑖𝑛
1 β„Žπ‘Ÿ
3600𝑠
1 𝑓𝑑
12 𝑖𝑛
1 𝐻𝑃 − 𝑠
550 𝑙𝑏 − 𝑓𝑑
For more inquiries, message me at:
mfarnaldo@tsu.edu.ph
32
16
3/6/2024
PROBLEM SOLVING:
2. A fan whose static efficiency is 40% has a capacity of 60,000 𝑓𝑑 /β„Žπ‘Ÿ @ 60℉ and
barometer of 30 inHg and gives a static pressure of 2 in𝐻 𝑂 on full delivery.
Determine the size of the motor required to operate the fan.
Solution:
Finally, solving for the size of the motor required to operate the fan
Using the static efficiency,
𝑃
𝑃 ,
𝑒 =
𝑒 =
𝑃
𝑃
𝑃
𝑃 ,
𝑃 =
𝑃 =
𝑒
𝑒
Assume: 𝑒 = 100%
0.3152 𝐻𝑃
𝑃 = 𝑃 = 0.7880 𝐻𝑃
𝑃 =
0.40
Use a motor that has the rating of
π‘·π’Š ≈ 𝟏. 𝟎𝟎 𝐇𝐏 (ans)
𝑃 = 0.7880 𝐻𝑃
For more inquiries, message me at:
mfarnaldo@tsu.edu.ph
33
PROBLEM SOLVING:
3. Air enters a fan through a duct at a velocity of 6.30 m/s and an inlet static
pressure of 2.50 cm of water lower than the atmospheric pressure. The air
leaves the fan through a duct at a velocity of 11.25 m/s and a discharge static
pressure of 7.62 cm of water above the atmospheric pressure. If the density of
the air is 1.20 π‘˜π‘”/π‘š and the fan delivers 9.45 π‘š /𝑠 of air. Determine the fan
efficiency when the power delivered to the fan is 13.75 kW.
Given: A Fan through a Duct
(Pressurized Air = Blower)
𝑉 = 6.30 π‘š/𝑠
β„Ž , = −2.50 π‘π‘šπ» 𝑂
𝑉 = 11.25 π‘š/𝑠
β„Ž , = 7.62 π‘π‘šπ» 𝑂
𝜌 = 1.20 π‘˜π‘”/π‘š
𝑄 = 9.45 π‘š /𝑠
𝑃 = 13.75 π‘˜π‘Š
Required: Fan Efficiency, 𝑒
For more inquiries, message me at:
mfarnaldo@tsu.edu.ph
34
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3/6/2024
PROBLEM SOLVING:
3. Air enters a fan through a duct at a velocity of 6.30 m/s and an inlet static pressure of 2.50
cm of water lower than the atmospheric pressure. The air leaves the fan through a duct at a
velocity of 11.25 m/s and a discharge static pressure of 7.62 cm of water above the
atmospheric pressure. If the density of the air is 1.20 π‘˜π‘”/π‘š and the fan delivers 9.45 π‘š /𝑠
of air. Determine the fan efficiency when the power delivered to the fan is 13.75 kW.
Solution
Solving for the fan efficiency,
𝑃
𝑒 =
𝑃
For the air power,
𝑃 = 𝛾 𝑄𝐻
For the total dynamic head,
𝐻 =β„Ž +β„Ž
βˆ†π‘ƒ βˆ†π‘‰
𝛾 βˆ†β„Ž
βˆ†π‘‰
𝐻=
+
=
+
𝛾
2𝑔
𝛾
2𝑔
𝛾 (β„Ž , − β„Ž , ) 𝑉 − 𝑉
𝐻=
+
𝛾
2𝑔
For more inquiries, message me at:
mfarnaldo@tsu.edu.ph
35
PROBLEM SOLVING:
3. Air enters a fan through a duct at a velocity of 6.30 m/s and an inlet static pressure of 2.50
cm of water lower than the atmospheric pressure. The air leaves the fan through a duct at a
velocity of 11.25 m/s and a discharge static pressure of 7.62 cm of water above the
atmospheric pressure. If the density of the air is 1.20 π‘˜π‘”/π‘š and the fan delivers 9.45 π‘š /𝑠
of air. Determine the fan efficiency when the power delivered to the fan is 13.75 kW.
Solution
Solving for the fan efficiency,
𝛾 (β„Ž , − β„Ž , ) 𝑉 − 𝑉
𝐻=
+
; 𝛾 = πœŒπ‘”
𝛾
2𝑔
π‘˜π‘”
1π‘š
1000
7.62π‘π‘š − −2.50π‘π‘š
11.25 − 6.30
100π‘π‘š
π‘š
𝐻=
+
π‘š
π‘˜π‘”
2 9.81
1.20
𝑠
π‘š
𝐻 = 88.76 π‘š
π‘š
𝑠
𝑃 = 𝛾 𝑄𝐻
For more inquiries, message me at:
mfarnaldo@tsu.edu.ph
36
18
3/6/2024
PROBLEM SOLVING:
3. Air enters a fan through a duct at a velocity of 6.30 m/s and an inlet static pressure of 2.50
cm of water lower than the atmospheric pressure. The air leaves the fan through a duct at a
velocity of 11.25 m/s and a discharge static pressure of 7.62 cm of water above the
atmospheric pressure. If the density of the air is 1.20 π‘˜π‘”/π‘š and the fan delivers 9.45 π‘š /𝑠
of air. Determine the fan efficiency when the power delivered to the fan is 13.75 kW.
Solution
𝑃 = 𝛾 𝑄𝐻
π‘˜π‘”
π‘š
𝑃 = 9.87 π‘˜π‘Š
𝑃 = 1.20
9.81
π‘š
𝑠
9.45
π‘š
𝑠
88.76 π‘š
1
𝑁−𝑠
π‘˜π‘” − π‘š
1 π‘˜π‘
1000 𝑁
1
π‘˜π‘Š − 𝑠
π‘˜π‘ − π‘š
Finally, solving for the fan efficiency
𝑃
𝑒 =
𝑃
9.87
𝑒 =
13.75
𝒆𝒇 = 𝟎. πŸ•πŸπŸ•πŸ– = πŸ•πŸ. πŸ•πŸ–% (ans)
For more inquiries, message me at:
mfarnaldo@tsu.edu.ph
37
PROBLEM SOLVING:
4. A fan delivers 4.70 π‘š /𝑠 of air at a static pressure of 5.08 cm of water when operating at a
speed of 400 rpm. The power required to operate the fan is 2.963 kW. If 7.05 π‘š /𝑠 of air are
desired using the same fan and installation, determine the pressure in cm of water.
Given: A Fan
Required: The Static Pressure from the New Fan
Solution:
Solving for the static pressure from the new fan,
Using the fans laws (@ Constand Fan Diameter)
𝑄
𝑁
=
𝑄
𝑁
𝐻
𝑁
=
𝐻
𝑁
𝑃
𝑁
=
𝑃
𝑁
Note: It is assumed that 𝐻 = β„Ž
/
𝑄
𝐻
=
→ π‘―πŸ = 𝟏𝟏. πŸ’πŸ‘ π’„π’Ž 𝒐𝒇 π’˜π’‚π’•π’†π’“ (𝒂𝒏𝒔)
𝑄
𝐻
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3/6/2024
PROBLEM SOLVING:
5. A fan running at 2000 rpm delivers 16,000 𝑓𝑑 /π‘šπ‘–π‘› against 3in of water static
pressure, thereby consuming 15 BHP. If the fan speed is increased to 2200 rpm
so that the pressure ratio is 1:1.10, determine the new capacity of the fan.
Given: A Fan
𝑁 = 2000 π‘Ÿπ‘π‘š,
𝑄 = 16,000
𝑓𝑑
π‘šπ‘–π‘›
β„Ž , = 3 𝑖𝑛
𝑃 , = 15 𝐻𝑃
𝑁 = 2200 π‘Ÿπ‘π‘š
Required: New Capacity, 𝑄
Solution:
Solving for the new capacity of the fan,
Using the fans laws (@ Constant Fan Diameter)
𝑄
𝑁
=
𝑄
𝑁
π‘ΈπŸ = πŸπŸ•, πŸ”πŸŽπŸŽ π’‡π’•πŸ‘ /π’Žπ’Šπ’ (ans)
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PROBLEM SOLVING:
6. A blower draws 3000 𝑓𝑑 /π‘šπ‘–π‘› of air through a duct 12in in diameter with a
suction of 3in of water. The air is discharged through a duct 10in in diameter
against a pressure of 2in of water. The air is measured at 70°F and 30.20 inHg.
Determine the amount of air horsepower produced. Use 62.34 𝑙𝑏 /𝑓𝑑 for water.
Given: A Blower
𝑄 = 3000 𝑓𝑑 /π‘šπ‘–π‘›
𝐷 = 12 𝑖𝑛 = 1 𝑓𝑑
β„Ž , = −3𝑖𝑛
𝐷 = 10 𝑖𝑛
β„Ž , = 2𝑖𝑛
𝑇
= 70°πΉ; 𝑃
= 30.20 𝑖𝑛𝐻𝑔
𝜌 = 62.34 𝑙𝑏 /𝑓𝑑
Required: Amount of Air Horsepower, 𝑃
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3/6/2024
PROBLEM SOLVING:
6. A blower draws 3000 𝑓𝑑 /π‘šπ‘–π‘› of air through a duct 12in in diameter with a suction of 3in of
water. The air is discharged through a duct 10in in diameter against a pressure of 2in of
water. The air is measured at 70°F and 30.20 inHg. Determine the amount of air horsepower
produced. Use 62.34 𝑙𝑏 /𝑓𝑑 for water.
Solution:
Solving for the amount of
air horsepower produced,
𝑃 = 𝛾 𝑄𝐻
For the total dynamic head,
𝐻 =β„Ž +β„Ž
𝐻=
𝐻=
𝛾 βˆ†β„Ž
βˆ†π‘‰
+
𝛾
2𝑔
𝛾 (β„Ž
−β„Ž
,
,
)
𝛾
+
𝑉 −𝑉
2𝑔
For the air velocities,
4𝑄
𝑄 = 𝐴𝑉 → 𝑉 =
πœ‹π·
𝑉 = 63.66 𝑓𝑑/𝑠
𝑉 = 91.67 𝑓𝑑/𝑠
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41
PROBLEM SOLVING:
6. A blower draws 3000 𝑓𝑑 /π‘šπ‘–π‘› of air through a duct 12in in diameter with a suction of 3in of
water. The air is discharged through a duct 10in in diameter against a pressure of 2in of
water. The air is measured at 70°F and 30.20 inHg. Determine the amount of air horsepower
produced. Use 62.34 𝑙𝑏 /𝑓𝑑 for water.
Solution:
For the total dynamic head,
𝐻=
𝛾 (β„Ž
−β„Ž
,
,
)
,
)
𝛾
+
𝑉 −𝑉
2𝑔
+
𝑉 −𝑉
2𝑔
Note: 𝛾 = πœŒπ‘”
𝐻=
𝜌 (β„Ž
,
𝜌
−β„Ž
Using the ideal gas equation,
𝑃 = 𝜌 𝑅𝑇
14.70 𝑙𝑏
𝑖𝑛
30.20 𝑖𝑛𝐻𝑔
144
29.92 𝑖𝑛𝐻𝑔 − 𝑖𝑛
𝑓𝑑
𝑃
𝑙𝑏
𝜌 =
=
= 0.0756
𝑅𝑇
𝑓𝑑
𝑙𝑏 − 𝑓𝑑
53.34
70℉inquiries,
+ 460
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𝑙𝑏 − 𝑅 For more
mfarnaldo@tsu.edu.ph
42
21
3/6/2024
PROBLEM SOLVING:
6. A blower draws 3000 𝑓𝑑 /π‘šπ‘–π‘› of air through a duct 12in in diameter with a suction of 3in of
water. The air is discharged through a duct 10in in diameter against a pressure of 2in of
water. The air is measured at 70°F and 30.20 inHg. Determine the amount of air horsepower
produced. Use 62.34 𝑙𝑏 /𝑓𝑑 for water.
Solution:
For the total dynamic head,
𝐻=
𝐻=
𝛾 (β„Ž
,
−β„Ž
𝛾
𝑙𝑏
62.34
𝑓𝑑
,
)
+
𝑉 −𝑉
2𝑔
2𝑖𝑛 − −3𝑖𝑛
0.0756
1 𝑓𝑑
12 𝑖𝑛
𝑙𝑏
𝑓𝑑
91.67 − 63.66
+
2 32.20
𝑓𝑑
𝑠
𝑓𝑑
𝑠
𝐻 = 411.14 𝑓𝑑
Solving for the amount of air horsepower produced,
𝑃 = 𝛾 𝑄𝐻
𝑙𝑏
𝑓𝑑
𝑓𝑑
𝑃 = 0.0756
32.20
3000
411.14 𝑓𝑑
𝑓𝑑
𝑠
π‘šπ‘–π‘›
𝑷𝒂 = 𝟐. πŸ–πŸ‘ 𝑯𝑷 (ans)
1 𝑙𝑏 − 𝑠
32.20 𝑙𝑏 − 𝑓𝑑
1 𝐻𝑃 −
33000 𝑙𝑏 − 𝑓𝑑
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43
PROBLEM SOLVING:
7. A fan delivers 12,000 𝑓𝑑 /π‘šπ‘–π‘› at a static pressure of 1in of water gauge at a
speed of 400 rpm and requires and input of 4 HP. If the same installation 15,000
𝑓𝑑 /π‘šπ‘–π‘› are desired, determine the new fan speed and the new power input.
Given: A Blower
𝑄 = 12, 000 𝑓𝑑 /π‘šπ‘–π‘›
β„Ž , = 1𝑖𝑛
𝑁 = 400 π‘Ÿπ‘π‘š
𝑃 , = 4 𝐻𝑃
𝑄 = 15,000 𝑓𝑑 /π‘šπ‘–π‘›
Required: New Fan Speed, N and
New Power Input, 𝑃 ,
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22
3/6/2024
PROBLEM SOLVING:
7. A fan delivers 12,000 𝑓𝑑 /π‘šπ‘–π‘› at a static pressure of 1in of water gauge at a
speed of 400 rpm and requires and input of 4 HP. If the same installation 15,000
𝑓𝑑 /π‘šπ‘–π‘› are desired, determine the new fan speed and the new power input.
Solution:
Solving for the new fan speed,
Using the fan affinity laws
𝑄
𝑁
=
𝑄
𝑁
𝑁 =𝑁
𝑄
𝑄
π‘΅πŸ = πŸ“πŸŽπŸŽ π’“π’‘π’Ž (ans)
Solving for the new input power,
Using the fan affinity laws
𝑃
𝑁
=
𝑃
𝑁
𝑃, = 𝑃,
𝑁
𝑁
𝑃 , = 7.81 𝐻𝑃
π‘·π’Š,𝟐 ≈ πŸ–. 𝟎 𝑯𝑷 (ans)
Standard Motor Size
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45
46
23
3/6/2024
Questions?
Clarifications?
Pleasefeelfree to contactme,
Engr.MarcFlorenzArnaldo,throughemail or MS Teams.
Email Address
MS Teams
Consultation Hours
mfarnaldo@tsu.edu.ph
Marc Florenz Arnaldo
Tuesday - Friday 1 PM to 4 PM
49
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25
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