Table 107. 

 VISCOSITY. 



125 



The coefficient of viscosity is the tangential force per unit area of one face of a plate of the 

 fluid which is required to keep up unit distortion between the faces. Viscosity is thus measured 

 in terms of the temporary rigidity which it gives to the fluid. Solids may be included in this 

 definition when only that part of the rigidity which is due to varying distortion is considered. 

 One of the most satisfactory methods of measuring the viscosity of fluids is by the observation of 

 the rate of flow of the fluid through a capillary tube, the length of which is great in comparison 

 with its diameter. Poiseuille* gave the following formula for calculating the viscosity coefiicient 



in this case : n ^= -0-7-1 where h is the pressure height, r the radius of the tube, s the density of 



the fluid, V the quantity flowing per unit time, and / the length of the capillary part of the tube. 

 The liquid is supposed to flow from an upper to a lower reservoir joined by the tube, hence h 

 and / are different. The product hs is the pressure under which the flow takes place. Hagen- 

 bach t pointed out that this formula is in error if the velocity of flow is sensible, and suggested a 

 correction which was used in the calculation of his results. The amount to be subtracted from 



h, according to Hagenbach, is -f= — , where g is the acceleration due to gravity. Gartenmeister J 



S2 . g 



points out an error in this to which his attention had been called by Finkener, and states that the 



quantity to be subtracted from h should be simply — ; and this formula is used in the reduction 



of his observations. Gartenmeister's formula is the most accurate, but all of them nearly agree 

 if the tube be long enough to make the rate of flow very small. None of the formulae take into 

 account irregularities in the distortion of the fluid near the ends of the tube, but this is probably 

 negligible in all cases here quoted from, although it probably renders the results obtained by the 

 " viscosimeter " commonly used for testing oils useless for our purpose. 



The term "specific viscosity" is sometimes used in the headings of the tables; it means the 

 ratio of the viscosity of the fluid under consideration to the viscosity of water at a specified tem- 

 perature. 



The friction of a fluid is proportional to the size of the rubbing surface, to -^, where v is the 



velocity of motion in a direction perpendicular to the rubbing surface, and to a constant known 

 as the viscosity. 



Variation of Viscosity of Water, wltli Temperature. Dynes per sq. cm. 



* " Comptes rendus," vol. 15, 1842; " Mdm. Serv. Etr." 1846. 



t " Pogg. Ann." vol. 109, i860. 



X " Zeitschr. Phys. Chem." vol. 6, 1890. 



§ Thorpe and Rogers, «' Philos. Trans." i8sA, 1894; " Proc. Roy. See' 



SS. '894. 



Smithsonian Tables. 



