10 



Colorado College Studies. 



/■I \ ''''<' 1 - I/, 7 



(1) — — normal to rdfl dz, 

 flr 



c. ~[ (2) uormal to r/r ch, 



rclB 



j (o) normal iordO <lr. 



All of the above surfaces, except c (1 ), are to be considered 

 constant for the rates have been reduced to those of a uni- 

 form clement. In the case of r (1), if w is constant there is 

 no loss within the element, but if w varies along r the total 

 loss is increased by the increasing area of the opposite face. 

 Finding the difference in displacement of oijposite sides and 

 multiplying by ;j. we get, 



{1) // \ )nlO(1rdz, 



\dr rdr r ) 



(2) //.[ \rdOdrdz, 



\rdo' rdo 



b. 



(3) ."■(^\ rdo dr dz. 



\ dr (()• I 



(2) Jl^^'^ydO dr dz, 

 ^ \rd0' rdo) 



(B) //. r — ]rd0 dr dz. 

 . ' V dz'J 



\(l)r.('^ + ^)rdodrdz, 

 \dr rdr/ 



c. .; (2) ,,( ^\do dr dz, 



L 



(3) i>.(—^)rd0drdz. 



If these expressions are subtracted from the effective 

 forces ill the corresponding equations for a perfect liciuid the 

 resulting equations are 



