MEASURING OF AIR. 429 



The theory generally given for measuring air through an 

 orfice is to equate the change in kinetic energy through the 

 orifice to the work done by the expansion of the gas from the 

 pressure p.^ existing on the upstream side of the orifice to the 

 pressure p., on the downstream side. If c is the coefficient of 

 contraction of the stream, this leads to the equation known as 

 the formula of Saint Venant 



/c— 1 K— 1 



^ R.r /c-i \pj ^^pj \ 



Avhere IV is the weight delivered per second. 

 a is the area of the orifice. 

 p^, p.^ are the up and downstream pressures. 

 g is the acceleration of gravity. . < 



RT is the equivalent of pi' in the gas equation and '"1 



K is the ratio of the specific heats. 



The above equation is only correct, if the velocit)' of ap- 

 proach of the gas to the orifice is zero or can 1)e assumed to be 

 approximately zero. As the velocity in the discharge pipe 

 of a compressor cannot be neglected, the correct ec|uation has to 

 be deducted as follows : — 



The equation of continuity is: ( W'eiglit ])er second) x 

 specific volume) = ( area of channel) x (velocity). 



// u indicates velocity ' ■ 



jr zccight per second 

 a area of channel and orifice 

 2' 7'olnme 

 p pressure 

 K ratio of specific heats 



and I and 2 are suffixes indicating respectively the upstream and 

 downstream side of the orifice, then the change in kinetic energy 



is - — (ir — ii\ ) and the work of expansion is /^' v . dp. 



In order to integrate this expression we assume an adiajjatic 

 expansion with the relation between p and 7- of 



p . v'^ —- constant. 

 Hence 



1 ^ , 1 



2e V ■-• ' ' J p. 



dp 



or with W =1 



l(„:-„;)-^^-;^l/>.^~'-*/«'} 



