"36 Canon Moseley on the steady Flow of a Liquid. 



The Velocity [at any point) of the Flow of a Liquid through a 

 straight pipe of any shape. 



Let it be supposed that the liquid fills the pipe, and that it 

 arranges itself in films geometrically similar to the internal sur- 

 face of the pipe, the molecules in each film moving with the same 

 velocity, but those in diff'erent films with diff'erent velocities. 

 The sections of these films made by a plane perpendicular to the 

 axis being geometrically similar, let straight lines be supposed 

 to be similarly placed in them, one in each section, and let the 

 length of any one of these lines be represented by r. Let -v/r re- 

 present the area of that section for which r=l, and 2^/^^ the 

 perimeter of that section. The area of any other section will 

 then be represented by r^-^/r, and its perimeter by 2r'\/r,. 



Adopting the same notation and reasoning in the same way 

 as before (p. 186, Phil. Mag. Sept. 1871), 



\} = h{\v{%^rdr), U,= r ^y^^% ^ 

 Jo Jo ^9 



•^ 



.\2yifwh^\rdr^'^^''i^rdr^^^^-'X<f,l^\{^rdr. . (49) 



Differentiating and considering U^ constant^ 



2'\lrwhvr= -^ v^r — 2'\lr^lfM ( "7- ) ^« 



_,.2 _.1±._- 



Taking 2gh = v'^, and ■j—='^, and reducing, 



...^K->=-Mfe), 



/dv_ 



dr J '{v'^-v^)v ~ 2glil ' 



\dr/ \.v 2\v—v v + v/J 



2gliL 



Ifl fJL 



Integrating between the limits and r, 



