Section- III, 1921 [117] Trans. R.S.C. 



The Coefficient of Viscosity of a Gas. An Elementary Laboratory 



Experiment 



By John Satterly, M.A., D.Sc, A.R.C.Sc, F.R.S.C. 



(Read May Meeting, 1920) 



The \olume of a liquid which flows per second through a 

 horizontal uniform capillary tube is given by the formula 



tzl^ . ^-^ (1) 



/ Sr? 



where pi =the pressure at the inlet end of the tube, 

 ^o^the pressure at the outlet end. 

 a — the radius of the bore of the tube. 

 / = the length of the tube. 

 77 =the coefficient of viscosity of the liquid. 

 This statement is known as Poiseuille's Law. 

 If instead of a liquid a gas is flowing through the tube (the 

 conditions being isothermal and the gas one that obeys Boyle's 

 Law) the formula is 



P^V.=P,V,.= ^^^-- (2) 



where pi, po, a, 1, r? have the meanings described above and T'l is the 

 \olume of gas (at pressure pi) entering the tube and Fo is the volume 

 of gas (at pressure p^) leaving the tube. If pi is only slightly greater 

 than p2, say p2 = pi—p where p is small, we may write 



ipl-\-p2) (Pl-p2) TTfl^ 



Pr Vi = (Pi -P)V2= ■ — 



from which 



Vi = p7ra\,Sh (3) 



or 77 = pira^/SlV (4) 



the same formula that was used in the case of liquids. Hence we 

 see that in order that Poiseuille's formula may be applied to the flow 

 of gases through a capillary tube the difi^erence of the pressures must 

 be small in comparison with either the inlet or outlet pressures. 

 The volume may then be measured indifferently at either of these 

 pressures. 



If for example we have /^i = atmospheric pressure = , say, 1,030 

 cms. of water and ^2 = say, 1,025 cms. of water, we make an error of 

 only 2| in 1,030, which is negligible in an elementary experiment. 



