68
2 Basic Components
Formula (2.12) then becomes:
The power transferred to the fluid becomes
The power per mass flow rate unit, i.e. the work per mass unit, becomes
This is Euler’s formula, applied to an axial machine (  u 1 = u 2 ).
It is informative to remark that the work also may be found from
. m
L v
−
as
.
.
.
.
m
m
L v
L u L w
L u
−
= −
−
= −
. So, the work done on the flow by an active force,
indeed, is the force multiplied with the displacement, as applied in Chap. 1. This
seems to be evident at a first glance. But that is not the case, as we analyse below,
for a flow with losses.
2.2.6 Flow in Cascades with Loss: Force Components
Loss results in a total pressure drop (Eq. 2.8), which we may express by
being a positive quantity. For further analysis, we assume equal loss on all streamlines. A loss coefficient, based on inlet dynamic pressure, is then
With F the force of the flow onto the profile, then
u
a 1u
2u
L
s v ( v
v ).
r
=
−
u
a
2u
1u
P
L u
s v ( v
v )u.
r
= −
=
−
u
2u
1u
a
L u
W
u( v
v ).
s v
D
r
−
=
=
−
,
2
2
1
2
01r
02r
1
2
w
w
p
p
( p
) ( p
)
2
2
r
r
−
=
+
−
+
01r
02r
1
1
p
p .
q
x
−
=
,
,
2
u
a
1u
2u
a
1
2
2
2
2
a
1
2
a
2
1
01r
02r
2
a
m
2
1
01r
02r
F
sw ( w
w )
s w ( tg
tg )
s
F s( p p )
w ( tg
tg
) s( p
p )
2
s w tg ( tg
tg ) s( p
p )
r
r
b
b
r
b
b
r
b
b
b
=
−
=
−
=
−
=
−
+
−
=
−
+
−