356 On the Measurement of Absolute Viscosity. 



Let AYYiD represent a section of the capillary and 

 ABCD the volume which passes in unit time. Then if AY 

 is made equal to 2 AB the paraboloid of revolution AOD 

 (which is equal in volume to ABCD) represents the actual 

 flow of the liquid which passes in unit time. 



Y 



Y, C D 



and radius OY = ?% we have : apparent 



Then if OX = A 

 kinetic energy of volume AYYjD is equal to 



irr 2 dh d 



(1) 



Actual kinetic energy of volume AYYiD at any instant of 

 time in the tube is equal to 



irr*dC r , Q „L irr*dh* 



6ia0o y( '"" 



f)Hy 



(2) 



Kinetic energy of volume equal to AYYjD which leaves 

 the tube, is twice the kinetic energy possessed by the volume 

 AOD, namely, 



ird 

 64(X 3 



Jo 



xffdy = 



ITT 



] dlv 



(3) 



The value of (3) is exactly double that of (1). Hence if 

 a liquid flows through a eapillary with a mean velocity of v r 

 the work done in giving it its kinetic energy is 2 X ±mv 2 if 

 m is the mass which has left the tube. 



If then we take this value and integrate between the 

 initial and final heads, H and F respectively, we get for the 

 total work expended on kinetic energy, 



(H=F)(H + F)0* 



Wi 



(H + F) J 



1 



%(H + F) 



