He  found  that  the  pressure  in  the  orifice,  taken  by  means  of
a  small  side  orifice,  was  0.5767  of  the  absolute  pressure  in  the
reservoir  so  long  as  that  pressure  was  more  than  twice  the  atmos-
pheric pressure;  under  such  conditions  the  pressure  in  the  orifice
is  independent  of  the  pressure  of  the  atmosphere.
If  the  ratio  ^'  is  replaced  by  the  number  0.5767  and  if  «  is
Pi
replaced  by  its  value  1.405  in  equation  (264)  we  shall  have  for
the  equation  foi  the  flow  of  a  gas


it;  =  0.4822a  ^^-^ (265)

*  Der  CtvUingenieur,  voL  zx,  p.  14, 1874.
FLIEGNER'S   EQUATIONS   FOR  FLOW   OF  AIR  429

For  the  flow  into  the  atmosphere  from  a  reservou-  having  a
pressure  less  than  twice  the  atmospheric  pressure  Fliegner  found
the  empirical  equation


«;  =  0.9644a  y/^-    V/-^^— ^,    .     .    .(266)

where  pa  is  the  pressure  of  the  atmosphere.
These  equations  were  found  to  be  justified  by  a  comparison
with  experiments  on  the  flow  of  air,  made  by  Fliegner  himself,
by  Zeuner,  and  by  Weisbach,

Although  these  equations  were  deduced  from  experiments
made  on  the  flow  of  air  into  the  atmosphere,  it  is  probable  that
they  may  be  used  for  the  flow  of  air  from  one  reservoir  into
another  reservoir  having  a  pressure  differing  from  the  pressure
of  the  atmosphere.
Fliegner's  Equations  for  Flow  of  Air.  —  Introducing  the
values  for  g  and  R  in  the  equations  deduced  by  Fliegner,  we  have
the  following  equations  for  the  French  and  English  systems  of
units:

French  units.
Pi>  2Pa,    'M'- 0.395a  ^;


Pi  <   2Pa,      W  -  0.790a  V^"    ^\      f^K


T,


English  units.
Px  >  2pa,    ^  =  o.S3oa  -^  ;


Px  <  2paj    w  =  i.o6oa  y  ^2A^^_^.
