220
6 Fans and Flow Control Devices
Q 2 = 1.25 · 100
m
3
s
= 125
m
3
s
Applying the appropriated affinity law, we have:
N 2 = N 1
Q 2
Q 1
= 500 min
−1
125
m
3
s
100
m 3
s
N 2 = 625 min
−1
(b) Similarly, using the corresponding affinity law:
P 2 = P 1
N 2
N 1
2
; P 2 = 1000 Pa ·
625 min
−1
500 min
−1
2
P 2 = 1562.5 Pa
(c) The useful energy supplied to the fluid (Pw v ) is:
Pw v = P T Q = 1000 Pa · 100
m
3
s
= 100 kW
The power received in the fan shaft (P shaft ) is 200 kW.
Therefore, the total efficiency of the fan is:
η t =
Pw v
Pw shaft
=
100 kW
200 kW
= 0.5
6.2.9 Fan Characteristic Curves
The fan characteristic curves are the graphical representation of the interrelation
between a number of parameters, namely, airflow rate, static or total pressure, fan
speed, efficiency, and power requirements of a fan. Of them, the curves that represent
the airflow rate provided by fan at a given total or static pressure are the most basic.
In order to obtain these curves, airflow rates and pressures are analysed for a fan in
a test rig, whose outlet orifice is progressively blocked (Fig. 6.19). In other words,
the differential pressure to be overcome by the fan is increased and the flow rate it
provides is measured. Thus, the fan curve represents the airflow rate provided by the
fan at different system resistances.
It should be noted that when the system is in free delivery, the fan provides its
maximum airflow. At this point, the static pressure is zero, and therefore, the total and
dynamic pressures coincide. Conversely, when the fan outlet is completely sealed,
6 Fans and Flow Control Devices
Q 2 = 1.25 · 100
m
3
s
= 125
m
3
s
Applying the appropriated affinity law, we have:
N 2 = N 1
Q 2
Q 1
= 500 min
−1
125
m
3
s
100
m 3
s
N 2 = 625 min
−1
(b) Similarly, using the corresponding affinity law:
P 2 = P 1
N 2
N 1
2
; P 2 = 1000 Pa ·
625 min
−1
500 min
−1
2
P 2 = 1562.5 Pa
(c) The useful energy supplied to the fluid (Pw v ) is:
Pw v = P T Q = 1000 Pa · 100
m
3
s
= 100 kW
The power received in the fan shaft (P shaft ) is 200 kW.
Therefore, the total efficiency of the fan is:
η t =
Pw v
Pw shaft
=
100 kW
200 kW
= 0.5
6.2.9 Fan Characteristic Curves
The fan characteristic curves are the graphical representation of the interrelation
between a number of parameters, namely, airflow rate, static or total pressure, fan
speed, efficiency, and power requirements of a fan. Of them, the curves that represent
the airflow rate provided by fan at a given total or static pressure are the most basic.
In order to obtain these curves, airflow rates and pressures are analysed for a fan in
a test rig, whose outlet orifice is progressively blocked (Fig. 6.19). In other words,
the differential pressure to be overcome by the fan is increased and the flow rate it
provides is measured. Thus, the fan curve represents the airflow rate provided by the
fan at different system resistances.
It should be noted that when the system is in free delivery, the fan provides its
maximum airflow. At this point, the static pressure is zero, and therefore, the total and
dynamic pressures coincide. Conversely, when the fan outlet is completely sealed,