Canon Moseley on the steady Flow of a Liquid. 37 



••• (f )(4=1)*--^^ (50) 



.2_ 



{©'-'}' 



'S^wir 



(51) 



1+^ - -l^e- 



Wl 



Taking, as before, — =7, and neglecting, as before, the work 



accumulated in the liquid which escapes per unit of time (Phil. 

 Mag. Sept. 1871, p. 193), 



v-VQC-^y^- (52) 



The discharge from a closed straight channel of any given geometric 

 form in terms of the maximum velocity. 



Assuming R to be the value of r for that film which is in con- 

 tact with the interior of the channel, and Q to represent the 

 discharge per unit of time, and reasoning as before (Phil. Mag. 

 Sept. 1871, p. 195), 



Qr~ 1 (2'\/rr6?r)i; = 2'<|r j z;r6?r = 2'</ri;Q \ e~*yV£?r by equation (52), 



Jq Jo Jq 



f- 



^y^rdr= - ~ 6-*vv+ J- ( e-^y'dr= - -j^e-^v^j 



^y ^7 Jo ^r 



^ 6-*v + C, 



(^y) 



i 



'^,-*v>vrf,= _ i_ ,-*va R _ ^_ (e-rB _ 1 ) 



•••QB=t^.{l-(^% + l>"'*'''.^''o. . . . , . (53) 



in which expression 7 is dependent on the work Ug lost in the 

 descent of the water in the reservoir and in its passage into the 

 pipe, and on the amount of work Uj which it carries away with 

 it on leaving the pipe, but is approximately constant for the 

 same pipe and the same reservoir under different heads of water. 



Equation (53) may be put under another form. 



Let n = actual section of the pipe, % = actual perimeter. 

 Then 



n = RV^ ;^ = 2Rt„ 



a a R^ 1 



