2 CoLOKADO* College Studies. 



— or do dz rf7*=efifective force in same direction due to 



an acceleration in the velocity u. The velocity v through 

 centrifugal force contributes to the effective force in this 



direction ^ ■> in i 7 * 



—Vf> vdo dz dr.* 



The velocity to can have no influence upon the forces in 



the direction of r. 



dn 



rdo dz dr 



dr 



is the difference in pressure on the two faces C K and D 31. 

 Equating by D 'Alenibert's Principle, we have 



Xp rde dz dr -rdO dz dr -p rdO dz dr-^-v'p r\le dz dr=0. 



dr 'U 



Dividing by p rdO dz dr and transposing, this equation be- 

 comes 



^ dp on 2 



X — = y r. 



pdr 'H 



Similarly for the forces acting in the direction of 6 



Yp rdo dz d?*= impressed force, 



1 p rdo dz d?'= effective force 



contributed by acceleration in v. 



— i—rdo dz dr=d\fieYence in the pressures on 

 rdo 



the opposite faces. But there is still another resulting force 



acting in this direction due to the fact that while a particle 



* If there were no motion in the direction of j', a force directed 

 toward the center would be necessary to maintain the configuration of 

 the element. This force would be 



dp 

 v'p r'^do dz dr— -y rdo dz dr. 

 dr 



Since motion along r is in a straight line, it follows from Newton's sec- 

 ond law that, if the velocity in that direction is uniform, the above 

 relation still holds. 



If the motion in this direction is accelerated, 



— P rdo dz dr=Xp rdo dz dr-\-v'p rhlo dz dr—^-^ rdO dz dr, 

 vt dr 



Su ^ , J dp 

 or —=X-\-v^r- 



3t rdr 



