512 VISCOSITY. [CHAP, xi 



The definition of p adopted in Art. 283 implies the relation 



3X + 2/Lt = 0, 

 whence, finally, introducing the values of a, b, c, /, g y h, from 



f du dv dw\ . du ^ 



Art. 31, 



Pyy = ~P ~lA fc j~ + j~ + ^7~+ 2 A t ^"' 

 \dae dy dzj dy 



, dw 



dw dv 



dw 



.(5). 



dw 



The constant yu, is called the 'coefficient of viscosity.' Its physi- 

 cal meaning may be illustrated by reference to the case of a fluid 

 in what is called 'laminar' motion (Art. 31); i.e. the fluid moves 

 in a system of parallel planes, the velocity being in direction 

 everywhere the same, and in magnitude proportional to the 

 distance from some fixed plane of the system. Each stratum of 

 fluid will then exert on the one next to it a tangential traction, 

 opposing the relative motion, whose amount per unit area is /* 

 times the variation of velocity per unit distance perpendicular to 

 the planes. In symbols, if u = ay, v = 0, w = 0, we have 



If [M], [L], [T] denote the units of mass, length, and time, the 

 dimensions of the ps are [ML~ l T~*], and those of the rates of 

 distortion (a, b, c, ...) are [T~ l l, so that the dimensions of /* are 

 [ML- 1 T- 1 ]. 



The stresses in different fluids, under similar circumstances of 

 motion, will be proportional to the corresponding values of /j, ; but 

 if we wish to compare their effects in modifying the existing 

 motion we have to take account of the ratio of these stresses to 

 the inertia of the fluid. From this point of view, the determining 



