6.2 Fans
213
Internal
friction losses
( i)
Q ∆PL
Volumetric
losses
( v)
Qf (∆P+∆PL)
Organic
losses
( o)
Useful power
received by the fan
impeller
(Q+Qf) (∆P+∆PL)
Power received
by air
Q (∆P+∆PL)
Power
supplied to the
fan shaft
(Pwshaft)
Useful
power
received by
air (Pwv)
Q ∆P
Fig. 6.13 Sankey diagram for a fan. Modified from ATECYR (2012)
η t =
Q
Pw shaft
(6.6)
Multiplying by the following unit factors:
Q + Q f
( + L )
Q + Q f
( + L )
;
Q ( + L )
Q ( + L )
We obtain, after rearranging terms, Eq. 6.7, which is also deductible from the
Sankey diagram in Fig. 6.12:
η t =
Q + Q f
( + L )
Pw shaft
Q( + L )
Q + Q f
( + L )
Q
Q( + L )
(6.7)
In other words, the total efficiency (η t ) is equal to the product of the organic (η o ),
volumetric (η v ) and friction (η f ) efficiencies (Eq. 6.8) corresponding to the three
respective parentheses of the above equation.
η t = η o η v η f
(6.8)
6.2.7 Electric Motor Losses
The efficiency of an electric motor (η m ) is the quotient between the useful power the
motor provides (also called shaft power, Pw shaft ) and the power it absorbs (Pw) from
the electrical grid (Eq. 6.9). Figure 6.14 schematizes this concept.