664 RICE ART. L 



and so 



dur = — g dz, 



or Hr -\- gz = constant throughout the film. However, if 

 there are two such components, r and s, a similar line of reason- 

 ing will show that 



Trdur + Tsdfx, = - g{Tr + T,)dz, 



which only necessitates that 



Trinr + gz) + Tsins + gz) = constant, 



but not two such independent conditions. 



In following up the arguments on pages 307-309 the reader 

 may possibly be familiar with Poiseuille's formula for the efflux 

 of liquid from a narrow tube, in viscous flow and under a pres- 

 sure gradient which is small enough to permit the motion to be 

 zero at the wall of the tube and not to cause turbulent motion. 

 It is 



Trpr^ dp^ 

 '^^ ~~^ ~dl 



where m is the mass crossing any section in unit time, p the 

 density, t? the coefficient of viscosity, and d-p/dl the pressure 

 gradient along the length I of the tube. This makes the 

 volume of flow per unit time, i.e., 7n/p, proportional to the fourth 

 power of the radius, other things being equal, and this would 

 require a mean velocity across a section equal to 



pD^ dp 

 32»7 dl 



(where D is the diameter), and so proportional to the square of 

 the diameter. The formula for the mean velocity of flow 

 between parallel plates at a distance apart equal to D (again 

 for non-turbulent slow motion) is also known to be 



pD^ dp, 

 12r, dl 



