210 Prof. Potter on Hydrodynamics. 



Let fig. 2 represent the circular plate 

 attached to the pipe ; let OAPBB'P'A' be 

 a circular sector^ of which the arc BB' is 

 on the edge of the plate, AA' is on the 

 edge of the apertui-e where the air enters, 

 and PP' any other concentric arc. 



Let 



0A=«, 0P=5, OB=R. 



Then the fluid issuing uniformly from the 

 pipe, the motion soon becomes steady ; and the mass (M) issuing 

 in the indefinitely small time [U) from the pipe, is the same in 

 amount which escapes from the edge in the same time, and the 

 same also which passes over every concentric arc. 



At A, let Pi be the density, p^ the pressui'c, and v^ the velocity 

 At P, ... p ... p ... V 



At B, ... p' ... y ... v' 



Let h be the height of the disc GH above the plate EF, fig. 1, 

 then we have 



M = 27r«/i.Z7j/3,.S^ 



=^2'irsh.vp .ht 

 =27r'Rh. v'p'.Bt; 

 -.p'v'R, 



and 



. pvs=.pflVi- 



p-Kp 

 _ KpfLVi 



KpyR 



To form 8p for application in the general equation, we note 

 that V being taken the velocity of the nucleus of an atom, Bp is 

 to be taken only in respect of the variation of s from {s—Ss) to 

 (s + Bs), and 



and the equation becomes, since there is no impressed accelera- 

 ting force, 



if' 



Bp 



Bs\ds-^=0, 





ds 



