VISCOMETRY 



view is that of Couette (6). Here, the liquid is placed between two 

 concentric cylinders, one of which is rotated while the other remains 

 stationary. The viscosity is usually determined by measuring the 

 moment due to viscous resistance, M, acting upon the inner cylinder, 

 when the outer one is rotated at a constant velocity. If R\ is the radius 

 of the inner cylinder, Ri the radius and fi the angular velocity of the outer 

 cylinder, and L the depth of liquid of viscosity t] between the cylinders: 



R\ Rl \ Rl- R\ M 



If the dimensions of the apparatus and the depth of the liquid layer 

 are known exactly, absolute viscosity can be evaluated from the ratios 

 of the moment to the angular velocity. Relative viscosity can be 

 obtained without knowing the dimensions exactly, for tj/tjo = (M/A/o) 

 (Oo/^)(Z-o/L). In practice, the best method is to measure M and Afo 

 at the same depth of liquid and the same angular velocity. Then 

 ^/t^o = Af/A/o- There are numerous possible methods of measuring 

 the moment due to viscous resistance. The most common is to suspend 

 the inner cylinder by a wire of known restoring force, N. In this case, 

 the inner cylinder will turn through an angle 0, equal to M/N, and this 

 angle can be measured. Also, the inner cylinder could be mounted 

 on a mechanism similar to that of a galvanometer, and the moment 

 could thus be estimated in terms of the current through the galvan- 

 ometer which just prevents the cylinder from turning. Another possi- 

 bility would be to measure the rate of energy consumption with a 

 wattmeter, for this rate should be proportional to the moment due to 

 viscous resistance. 



The velocity gradient at every point within the liquid enclosed 

 between the two cylinders is directly proportional to the angular 

 velocity of the outer cylinder and inversely proportional to the square 

 of the radius at the point in question. In a viscometer in which the 

 distance between the inner and outer cylinders is small compared with 

 the radius of the inner cylinder, the velocity gradient is essentially 

 constant everywhere throughout the enclosed liquid. Even in a vis- 

 cometer in which the distance between cylinders is one-tenth the radius 

 of the inner cylinder, the velocity gradient will not vary much more 

 than 10% from the mean. This essential constancy of velocity gradient 

 makes the rotating cylinder apparatus the most useful from a theoretical 



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