FLUID MACHINERY
ME 406
Pumps
Compressors
FANS
Sample Problems
1. What horsepower is supplied to air moving at 20 fpm through a 2 ft by 3 ft duct under a pressure of 3 in. water
gage?
2. Air is flowing in a duct with velocity of 7.62 m/s and a static pressure of 2.16 cm water gage. The duct diameter
is 1.22 m, the barometric pressure is 99.4 kPa and the gauge fluid temperature and air temperature are 30°C.
What is the total pressure of air against which the fan will operate in cm of water?
3. A ventilation system includes a fan of 750 m per minute. A capacity discharging thru a 122 cm x 91 cm air duct
against 30 mm.WG static pressure. Air temperature is at 21°C and the barometer pressure is 97 kPa. What input
horsepower will be required to give fan an efficiency of 44.3%? Specific volume of water is 1.00416x10 m /kg
Solutions to
Sample Problems
Sample Problem No.1
What horsepower is supplied to air moving at 20 fpm
through a 2 ft by 3 ft duct under a pressure of 3 in.
water gage?
Given:
Solution:
v = 20 fpm
A = 2 x 3 = 6 ft
h = 3 in
Using the equation below,
=γ
Where
will be solved using the continuity equation,
Also, γ and
must be in terms of air,
=
Required:
GP in Hp
ℎ =
ℎ
Thus;
=ℎ =ℎ
=
Sample Problem No.1
What horsepower is supplied to air moving at 20 fpm
through a 2 ft by 3 ft duct under a pressure of 3 in.
water gage?
Given:
Solution:
v = 20 fpm
A = 2 x 3 = 6 ft
h = 3 in
Using the equation below,
=γ
Where
will be solved using the continuity equation,
Also, γ and
=
must be in terms of air,
=
Required:
GP in Hp
ℎ =
Substituting the values;
62.4
ℎ =
3
1
12
ℎ
→
ℎ =
ℎ
Sample Problem No.1
What horsepower is supplied to air moving at 20 fpm
through a 2 ft by 3 ft duct under a pressure of 3 in.
water gage?
Given:
Solution:
v = 20 fpm
A = 2 x 3 = 6 ft
h = 3 in
Using the equation below,
=γ
Where
will be solved using the continuity equation,
Also, γ and
=
must be in terms of air,
=
Required:
GP in Hp
ℎ =
ℎ
→
ℎ =
Substituting the values;
62.4
ℎ =
2
3
1
12
15.6
ℎ =
ℎ
Sample Problem No.1
What horsepower is supplied to air moving at 20 fpm
through a 2 ft by 3 ft duct under a pressure of 3 in.
water gage?
Given:
Solution:
v = 20 fpm
A = 2 x 3 = 6 ft
h = 3 in
Using the equation below,
=γ
15.6
ℎ
=
ℎ =
Substituting the values;
Required:
GP in Hp
15.6
=
6
20
1
33,000
−
Sample Problem No.1
What horsepower is supplied to air moving at 20 fpm
through a 2 ft by 3 ft duct under a pressure of 3 in.
water gage?
Given:
Solution:
v = 20 fpm
A = 2 x 3 = 6 ft
h = 3 in
Using the equation below,
=γ
15.6
ℎ
=
ℎ =
Substituting the values;
Required:
GP in Hp
15.6
=
6
20
= .
1
33,000
−
Sample Problem No.2
Given:
v = 7.62 m/s
h = 2.16 cm. WG
Air is flowing in a duct with velocity of 7.62 m/s and a static
pressure of 2.16 cm water gage. The duct diameter is 1.22 m, the
barometric pressure is 99.4 kPa and the gauge fluid temperature
and air temperature are 30°C. What is the total pressure of air
against which the fan will operate in cm of water?
Solution:
For the total fan head,
=ℎ +ℎ
D = 1.22 m
P = 99.4 kPa
t = 30°C
Required:
H in cm.WG
Total fan head must be in terms of cm.WG as a requirement unit of the
problem. ℎ is already in cm.WG. So, we need to solve for the velocity
head
ℎ =
(7.62)
2
ℎ =
2 9.8066
Sample Problem No.2
Given:
v = 7.62 m/s
h = 2.16 cm. WG
Air is flowing in a duct with velocity of 7.62 m/s and a static
pressure of 2.16 cm water gage. The duct diameter is 1.22 m, the
barometric pressure is 99.4 kPa and the gauge fluid temperature
and air temperature are 30°C. What is the total pressure of air
against which the fan will operate in cm of water?
Solution:
For the total fan head,
=ℎ +ℎ
D = 1.22 m
P = 99.4 kPa
t = 30°C
Required:
H in cm.WG
Total fan head must be in terms of cm.WG as a requirement unit of the
problem. ℎ is already in cm.WG. So, we need to solve for the velocity
head
ℎ =
(7.62)
2
ℎ =
ℎ = 2.9605
2 9.8066
Note: when using the velocity head equation, unit is always in terms of
air.
Sample Problem No.2
Given:
v = 7.62 m/s
h = 2.16 cm. WG
Air is flowing in a duct with velocity of 7.62 m/s and a static
pressure of 2.16 cm water gage. The duct diameter is 1.22 m, the
barometric pressure is 99.4 kPa and the gauge fluid temperature
and air temperature are 30°C. What is the total pressure of air
against which the fan will operate in cm of water?
Solution:
For the total fan head,
=ℎ +ℎ
D = 1.22 m
P = 99.4 kPa
Since ℎ is in meters of air, we will convert it to cm.WG
t = 30°C
Required:
ℎ =
ℎ
Solving for the density of air using the given conditions;
H in cm.WG
99.4
=
=
0.28708
−
−
30 + 273
Sample Problem No.2
Given:
v = 7.62 m/s
h = 2.16 cm. WG
Air is flowing in a duct with velocity of 7.62 m/s and a static
pressure of 2.16 cm water gage. The duct diameter is 1.22 m, the
barometric pressure is 99.4 kPa and the gauge fluid temperature
and air temperature are 30°C. What is the total pressure of air
against which the fan will operate in cm of water?
Solution:
For the total fan head,
=ℎ +ℎ
D = 1.22 m
P = 99.4 kPa
Since ℎ is in meters of air, we will convert it to cm.WG
t = 30°C
Required:
ℎ =
ℎ
Solving for the density of air using the given conditions;
H in cm.WG
99.4
=
=
0.28708
−
−
= 1.1427
30 + 273
Sample Problem No.2
Given:
v = 7.62 m/s
h = 2.16 cm. WG
Air is flowing in a duct with velocity of 7.62 m/s and a static
pressure of 2.16 cm water gage. The duct diameter is 1.22 m, the
barometric pressure is 99.4 kPa and the gauge fluid temperature
and air temperature are 30°C. What is the total pressure of air
against which the fan will operate in cm of water?
Solution:
For the total fan head,
=ℎ +ℎ
D = 1.22 m
P = 99.4 kPa
t = 30°C
Since ℎ is in meters of air, we will convert it to cm.WG
ℎ
ℎ = ℎ
→ ℎ =
= 1.1427
ℎ = ℎ = 2.9605
Required:
H in cm.WG
1.1427
(296.05
)
ℎ = 0.338296
ℎ =
1000
=ℎ
Sample Problem No.2
Given:
v = 7.62 m/s
h = 2.16 cm. WG
D = 1.22 m
Air is flowing in a duct with velocity of 7.62 m/s and a static
pressure of 2.16 cm water gage. The duct diameter is 1.22 m, the
barometric pressure is 99.4 kPa and the gauge fluid temperature
and air temperature are 30°C. What is the total pressure of air
against which the fan will operate in cm of water?
Solution:
For the total fan head,
=ℎ +ℎ
ℎ = 0.338296
P = 99.4 kPa
t = 30°C
Required:
H in cm.WG
= 0.338296 + 2.16
= .
.
.
=ℎ
Sample Problem No.3
Given:
Q = 750 m /min
A = 122 cm x 91 cm
A ventilation system includes a fan of 750 m per minute. A capacity
discharging thru a 122 cm x 91 cm air duct against 30 mm.WG static
pressure. Air temperature is at 21°C and the barometer pressure is 97
kPa. What input horsepower will be required to give fan an efficiency
of 44.3%? Specific volume of water is 1.00416x10 m /kg
Solution:
Using total fan efficiency equation,
h = 30 mm. WG
=
ℎ
ℎ
.
=
,
t = 21°C
P = 97 kPa
e = 44.3%
Required:
BP in Hp
Solving for GP,
=ℎ +ℎ
=γ
Using continuity equation to solve for velocity;
=
=
=
750
1.22
(0.91
1
) 60
Sample Problem No.3
Given:
Q = 750 m /min
A = 122 cm x 91 cm
A ventilation system includes a fan of 750 m per minute. A capacity
discharging thru a 122 cm x 91 cm air duct against 30 mm.WG static
pressure. Air temperature is at 21°C and the barometer pressure is 97
kPa. What input horsepower will be required to give fan an efficiency
of 44.3%? Specific volume of water is 1.00416x10 m /kg
Solution:
Using total fan efficiency equation,
h = 30 mm. WG
=
ℎ
ℎ
.
=
,
t = 21°C
P = 97 kPa
e = 44.3%
Required:
BP in Hp
Solving for GP,
=ℎ +ℎ
=γ
Using continuity equation to solve for velocity;
=
=
=
750
1.22
(0.91
= 11.2592
1
) 60
Sample Problem No.3
Given:
Q = 750 m /min
A = 122 cm x 91 cm
A ventilation system includes a fan of 750 m per minute. A capacity
discharging thru a 122 cm x 91 cm air duct against 30 mm.WG static
pressure. Air temperature is at 21°C and the barometer pressure is 97
kPa. What input horsepower will be required to give fan an efficiency
of 44.3%? Specific volume of water is 1.00416x10 m /kg
Solution:
Using total fan efficiency equation,
h = 30 mm. WG
=
ℎ
ℎ
.
,
=
t = 21°C
P = 97 kPa
e = 44.3%
Solving for GP,
For velocity head;
Required:
BP in Hp
=ℎ +ℎ
=γ
ℎ =
= 11.2592
(11.2592)
2
ℎ =
2 9.8066
ℎ = 6.4635
Sample Problem No.3
Given:
Q = 750 m /min
A = 122 cm x 91 cm
h = 30 mm. WG
A ventilation system includes a fan of 750 m per minute. A capacity
discharging thru a 122 cm x 91 cm air duct against 30 mm.WG static
pressure. Air temperature is at 21°C and the barometer pressure is 97
kPa. What input horsepower will be required to give fan an efficiency
of 44.3%? Specific volume of water is 1.00416x10 m /kg
Solution:
Using total fan efficiency equation,
=
ℎ
ℎ
.
,
=
t = 21°C
P = 97 kPa
e = 44.3%
Required:
BP in Hp
Solving for GP,
=γ
=ℎ +ℎ
Since the static pressure head is given, we just need to convert the unit in
terms of air;
ℎ
ℎ = ℎ
→ ℎ =
We will be using the given conditions to determine the density of air and
water
Sample Problem No.3
Given:
Q = 750 m /min
A = 122 cm x 91 cm
A ventilation system includes a fan of 750 m per minute. A capacity
discharging thru a 122 cm x 91 cm air duct against 30 mm.WG static
pressure. Air temperature is at 21°C and the barometer pressure is 97
kPa. What input horsepower will be required to give fan an efficiency
of 44.3%? Specific volume of water is 1.00416x10 m /kg
Solution:
Density of water using the given specific volume,
h = 30 mm. WG
=
t = 21°C
1
1
=
= 995.8572
0.00100416
P = 97 kPa
e = 44.3%
Density of air using the given air conditions,
97
Required:
BP in Hp
=
=
0.28708
−
−
= 1.1493
21 + 273
A ventilation system includes a fan of 750 m per minute. A capacity
discharging thru a 122 cm x 91 cm air duct against 30 mm.WG static
pressure. Air temperature is at 21°C and the barometer pressure is 97
kPa. What input horsepower will be required to give fan an efficiency
of 44.3%? Specific volume of water is 1.00416x10 m /kg
Sample Problem No.3
Given:
Q = 750 m /min
A = 122 cm x 91 cm
h = 30 mm. WG
Solution:
Using total fan efficiency equation,
=
ℎ
ℎ
.
=
,
t = 21°C
P = 97 kPa
e = 44.3%
Required:
Solving for GP,
=ℎ +ℎ
=γ
Since the static pressure head is given, we just need to convert the unit in
terms of air;
ℎ
= 1.1493
ℎ = ℎ
→ ℎ =
BP in Hp
995.8572
ℎ =
1.1493
(0.03
)
ℎ = 25.9947
=ℎ
= 995.8572
Sample Problem No.3
Given:
Q = 750 m /min
A = 122 cm x 91 cm
A ventilation system includes a fan of 750 m per minute. A capacity
discharging thru a 122 cm x 91 cm air duct against 30 mm.WG static
pressure. Air temperature is at 21°C and the barometer pressure is 97
kPa. What input horsepower will be required to give fan an efficiency
of 44.3%? Specific volume of water is 1.00416x10 m /kg
Solution:
Using total fan efficiency equation,
h = 30 mm. WG
=
ℎ
ℎ
.
,
=
t = 21°C
P = 97 kPa
Solving for GP,
e = 44.3%
=
Required:
BP in Hp
=ℎ +ℎ
=γ
ℎ +ℎ
= 1.1493
where,
1.1493
=
=
1000
9.8066
−
−
= 0.011271
Sample Problem No.3
Given:
Q = 750 m /min
A = 122 cm x 91 cm
h = 30 mm. WG
A ventilation system includes a fan of 750 m per minute. A capacity
discharging thru a 122 cm x 91 cm air duct against 30 mm.WG static
pressure. Air temperature is at 21°C and the barometer pressure is 97
kPa. What input horsepower will be required to give fan an efficiency
of 44.3%? Specific volume of water is 1.00416x10 m /kg
Solution:
Using total fan efficiency equation,
=
ℎ
ℎ
.
,
=
t = 21°C
P = 97 kPa
Solving for GP,
e = 44.3%
=
Required:
BP in Hp
=ℎ +ℎ
=γ
ℎ +ℎ
Substituting the given values,
= 0.011271
750
6.4635 + 25.9947
ℎ = 6.4635
ℎ = 25.9947
=ℎ
= 0.011271
Sample Problem No.3
Given:
Q = 750 m /min
A = 122 cm x 91 cm
h = 30 mm. WG
A ventilation system includes a fan of 750 m per minute. A capacity
discharging thru a 122 cm x 91 cm air duct against 30 mm.WG static
pressure. Air temperature is at 21°C and the barometer pressure is 97
kPa. What input horsepower will be required to give fan an efficiency
of 44.3%? Specific volume of water is 1.00416x10 m /kg
Solution:
Using total fan efficiency equation,
=
ℎ
ℎ
.
=
,
t = 21°C
P = 97 kPa
Solving for GP,
e = 44.3%
=
Required:
BP in Hp
=ℎ +ℎ
=γ
ℎ +ℎ
Substituting the given values,
= 0.011271
750
6.4635 + 25.9947
= 6.13
1
60
1
0.746
−
Sample Problem No.3
Given:
Q = 750 m /min
A = 122 cm x 91 cm
h = 30 mm. WG
A ventilation system includes a fan of 750 m per minute. A capacity
discharging thru a 122 cm x 91 cm air duct against 30 mm.WG static
pressure. Air temperature is at 21°C and the barometer pressure is 97
kPa. What input horsepower will be required to give fan an efficiency
of 44.3%? Specific volume of water is 1.00416x10 m /kg
Solution:
Using total fan efficiency equation,
=
ℎ
ℎ
.
,
=
t = 21°C
P = 97 kPa
e = 44.3%
Solving for power input,
Required:
BP in Hp
= 6.13
=
=
6.13
0.443
=
.
BP = 13.8375 Hp