352 Canon Moseley on the steady Flow of a Liquid. 



r*r rr r* r 



.'.I (2irrdr)p+\ (2-7rrxfjb)dr= \ (2 t nrdr)p l ; 



Jo Jo Jo 



.'. p-t-fjux^p^p' +w -v 2 (by equation 18); 



y ^9 



, h w a 

 .-. p=p> + w -- /J/ x-—v < * (19) 



Also, equation (13), v = v 6"' r , 



.'.p=p' + W LLX— °-€- 2 V r (20) 



7 2g K ' 



At the orifice of the pipe by which the water escapes, p =p' and 

 % = l; 



, , . wh wv\ _ 



y 2g 



or 



„ wh 7 wvl 



0= id— — 2. e -2y»- (21) 



7 r 2g { } 



And if we neglect t>J, which is equivalent to neglecting \J l9 



wh wi 



which is the value assigned to y in equation (13), where Ui is 

 also neglected. By equation (19) it appears that the pressure 

 on a point at a given distance x from the entrance of the pipe is 

 less as its distance r from the axis is greater. 



This fact is illustrated in the following instructive experi- 

 ment of Professor Ludwig, of Leipsic*. In the accompanying 

 diagram A B is the section of a pipe filled with water which flows 

 through it. C D E is a continuous glass tube whose straight 

 part C D passes through the pipe in a direction perpendicular 

 to its axis, enters it by stuffing-boxes at c, d, and is capable 

 of being moved in the direction G D without leakage, a and 

 b are small apertures in this tube. The pipe being filled with 

 water, the tube also fills with it. But the water in the pipe 

 being in motion and the aperture a nearer to the axis than b y 

 the pressure at a is by equation (20) less than that on b. The 

 water from the pipe therefore llows along the tube through b in 



* I do not know whether this Experiment has been published ; it was 

 communicated to me by my son H. N. Moseley, to whom it was shown by 

 Professor Ludwig. 



