178 



THE ROYAL SOCIETY OF CANADA 



Let Vi, Vi and pi, pi be the volumes and pressures in the two vessels 

 at any instant. Let the density of the gas under the standard pressure 



pQ, be po; at any other pressure, p, \t'\B p = p 



Po 



^0 



Now the rate of flow 



v ^0 / dt \ po y 



of gas leaving the first and entering the second vessel is, supposing 

 pi> pi, 



dM _ _ d 

 dt dt 



The rate of flow through a capillary tube whose length is /, and radius 

 r, is, 



dt I ' 8n 



where P is the difference in pressure between the ends, and /j. is the 

 coefficient of viscosity.^ 



™ . 1 , . dM dl , 



Ihe rate oi change ot mass is— — = — p — so that 



dt dt 



whence 



( 



Thus 



dM 

 dt 



dM\ 7rr^ Po 



"~r ) dx= — —— . — 



dt / 8m Po 



irr' Po p\-p^ 



rp2 



pdp. 



8nl po 2 



Combining this with equation (1) we get 



dt 2fx 



(2) 



^^^~ - ^ iP'^ -p^) = o 



dt 2fx 



(3) 



in which K = 



TrrVo 

 8lpo 



These equations give, on simplifying, 



p2dpT—pidp2 ^ p\V\-\-piV-> Jf^Q 



P'2 



2fx ViVi 



'Lamb, H., Hydrodynamics, Cambridge 1916, p. 578ff. 



