686 Prof. Wilmer Duff on Poiseuille's Law 



being sheared varies from in the axis of the tube to a 

 maximum of pr/2lrj at the surface of contact of tube and 

 liquid, I and r being the length and radius respectively of 

 the tube, p the difference of pressure at the ends of the tube, 

 and 7) the coefficient of viscosity. In Poiseuille's experiments 

 the maximum rate of shear varied with different tubes and 

 different pressures between 5000 and 500,000 radians per 

 second; and all subsequent measurements of viscosity by 

 Poiseuille's method have, I believe, been made within these 

 limits. 



A number of considerations, relating to the discrepancies 

 between different methods of measuring viscosity, the contra- 

 dictory results obtained by myself * and others in testing the 

 effect of electrostatic stress on viscosity, and Poisson and 

 Maxwell's | view of a liquid as differing from a solid only in 

 the magnitude of its elastic constants and rate of relaxation 

 under stress, suggested the desirability of a test of Poiseuille's 

 law at much lower rates of shear than those stated above. 



Method and Apparatus. 



The rate of outflow from a capillary tube varies, according 

 to Poiseuille's law, as the product of the pressure and the 

 fourth power of the radius, while the maximum rate of shear 

 varies as the product of the pressure and the radius. Hence, 

 to get a low rate of shear together with a measurable rate of 

 outflow, it is necessary to use small pressures and a tube of 

 large radius, the dimensions being such that the flow shall 

 be rectilinear. 



Two large beakers were connected by the tube which 

 passed into the vessels through rubber stoppers. Differences 

 of level of the liquid in the beakers were measured by means 

 of optical levers. Two legs of each lever rested on an outside 

 support, while the third leg was borne by a small vessel, or 

 float, that floated on the surface of the liquid. When the 

 liquid had come to the same level in the two vessels, as 

 indicated by the readings of the scales becoming stationary, 

 a slight initial difference of level was produced by opening 

 for a moment a siphon that connected a third vessel to one 

 of the other two. Or the initial difference of level was 

 produced by lowering a body of known volume into one of 

 the vessels: in this case one of the levers might be dispensed 

 with, since the subsequent changes of level in one vessel 

 could be deduced from that of the other and the known 



* Physical Review, vol. iv. no. 19 (1896). 



* Phil. Mag. [4] vol. xxxv. pp. 133, 210 (1868). 



