K

Again,  at  outflow,  which  is  axial — i.e.,  a^=o — if  h^  is  the
axial  component  of  discharge,  which  in  fig.  136  is  greater
than  6j,  then

Vm  =  \  cot  <f).
252  CENTRIFUGAL  FANS

The  work  done  per  pound  of  air  by  the  wheel  is-

a-^Vm  _  Vm  &t  cot  a

The  loss  by  friction  in  the  guides  is —

b  2
=  F, — i  cosec^  a,


Guide.    Vanes.
\


Fig.  136.
the  f fictional  loss  in  the  wheel-


F,


=  -^(^x  cosec'^  d  +  &2^  cosec^  ^),
and  the  leaving  losses  are —

where  63  =  velocity  of  discharge  from  the  fan  casing  to  the
left  of  D.
SCREW  FANS  253

Hence,  when  working  at  the  speed  at  which  shock  at  inflow
is  avoided,  the  general  equation  of  the  fan  is

H  =  ^•'»^^""^"  -  rIl  cose.c2  a
9  '^9

- 1  fJ  h_  cosec2  ^  +  ^-  cosec2  <f>     -  (1  +  F3)-^3.
Let  s^  and  s^  be  the  breadths  of  the  wheel  at  inflow  and
outflow,  and  s,  that  of  the  casing  to  the  left  of  D,  where
the  speed  is  h^ ;  then  it  follows  that

Q,  =  2  TT r-in  Sj  &!  =  2  TT ?-,rt s^h^  =  2iT r,n  Sg  63.
