﻿of an Imperfect Fluid. 371 



curved surface) represent the mass of fluid which passes through 

 the section A a b B in a unit of time. 



Representing by %u the work of any system of forces other 

 than the weight of the fluid which tends (with its weight) to 

 cause it to descend, and adopting in other respects the same 

 symbols as in the last article and the same reasoning, we have 

 by equation (1'), observing that in this casef—O, 



M U i + U 2 + U 3 )=:U sin i + 2,u • 

 where 



/ju= the unit of shear. 

 Usint= the work of the weight of the fluid which passes 

 through the transverse section AabB in a unit of 

 time. 

 Uj//, = the internal work of the shear of the same fluid. 

 V q /ub = the work of the shear of the same fluid ou the bot- 

 tom of its channel. 

 U 3/ c6= the work of the shear of the same fluid on the 

 sides of its channel. 

 By equation (2'), 



U = -| w \ \ mn 2 dx dy = \w \ \ z 2 dx dy ; 

 by equations (3', 4/), 



^u-Uj = /jl \ 1 mn —r- dx dy -\- fjb\ \ mn — — dx dy, 





2 i+*IW> 



where z } is any value of z for which t/ = 0, or which is measured 

 on the bottom of the channel 



#*U. 



;=i/"< y\ d y> 



where z 2 is any value of z for which x=0, or which is measured 

 on the sides of the channel ; 



= \w sine I I z 2 dx dy + 'Zu. 

 2B2 



