6.2 Fans
215
Fig. 6.15 Mechanical
analogy for the electric
power triangle
S
Pw
Q
Φ
It is measured in volt-amperes reactive (var).
Aparent power (S) is the total power which includes both the power consumed,
which is then transformed into heat and work (P), and the consumed and then returned
(Q). It is calculated for a three-phase system by means of (Eq. 6.12):
S =
√
3U I
(6.12)
It is measured in volt-amperes (VA).
Exercise 6.5 The asynchronous motor of a mine fan has the following motor
nameplate:
• Power = 3.2 kW,
• Voltage = 6 kV,
• Frequency = 50 Hz,
• Efficiency = 86%, and
• Cos ϕ = 0.85.
Determine:
(a) Power developed by the motor on its shaft,
(b) Power absorbed,
(c) Intensity absorbed, and
(d) Losses of power in the motor.
Solution
(a) The power developed in the shaft can be approximated by means of the nominal
power, whose value is 3.2 kW.
(b) The actual or absorbed power (Pw) is calculated from the efficiency:
Pw =
Pw shaft
η
=
3200 W
0.86
= 3720.93 W
215
Fig. 6.15 Mechanical
analogy for the electric
power triangle
S
Pw
Q
Φ
It is measured in volt-amperes reactive (var).
Aparent power (S) is the total power which includes both the power consumed,
which is then transformed into heat and work (P), and the consumed and then returned
(Q). It is calculated for a three-phase system by means of (Eq. 6.12):
S =
√
3U I
(6.12)
It is measured in volt-amperes (VA).
Exercise 6.5 The asynchronous motor of a mine fan has the following motor
nameplate:
• Power = 3.2 kW,
• Voltage = 6 kV,
• Frequency = 50 Hz,
• Efficiency = 86%, and
• Cos ϕ = 0.85.
Determine:
(a) Power developed by the motor on its shaft,
(b) Power absorbed,
(c) Intensity absorbed, and
(d) Losses of power in the motor.
Solution
(a) The power developed in the shaft can be approximated by means of the nominal
power, whose value is 3.2 kW.
(b) The actual or absorbed power (Pw) is calculated from the efficiency:
Pw =
Pw shaft
η
=
3200 W
0.86
= 3720.93 W