Canon Moseley on the steady Flow of a Liquid. 361 

 Substituting for V its value from equation (27), 



2w(2g)tw\ l lWhi r42 v 



fe)( e3vR '- 37R ~ 1 ) +4/XiR 



Also, by equation (6), 



wi 



But fM= — ; and (equation 13) v = v €~v r ; 

 7 



TT O lC* wi t -vrW 27TWhv r R _ • 



,\ U 4 = — 27rZ I — (-7« e v)flfr= u I ye v*dr ; 



Jo *y y Jo 



U 4 = 2lTOfe O (l-e-y»). 



Substituting for v its value from equation (29), 



_ / 2tt^ \ tp3(2g)*R3A*ey R (l -e--y R ) 



%7 



[9^(^ B -3 7 E~1) + 4R^] 



reducing, 



8ir«4(2y)»B«A*(tf«-l) 



7i[<g(^ B -3 7 R-i)+47 r %]*' 



The work lost per second in traversing the pipe being repre- 

 sented by U 3 + U 4 , equations in which the unit of work is the 

 French kilogram-metre, and 75 of these units per second being 

 a horse-power, it follows that the 



horse-power lost = 3 — -. . . . (44) 



The rise of temperature in water flowing through a pipe. 



It results from the experiments of Mr. Joule, that every 424 

 French units of work or kilogram-metres which are expended on 

 the friction of water raise the temperature of every kilogramme 

 of it by 1° of the Centigrade thermometer. Now, if we suppose 

 the motion of the water to have become steady, as also its tem- 

 perature, and the material of the pipe to be perfectly non-con- 

 ducting, so that no heat escapes from the water so long as it is 

 in the pipe, then the whole work converted into heat per second 

 is carried off by the water that escapes per second. Let t° be 

 the number of degrees Centigrade by which it raises the tempe- 

 rature of that water. Now Q cubic metres or 1000 Q kilogrammes 



