﻿38 
  Steadfj 
  Floio 
  of 
  cm 
  Incompressible 
  Viscous 
  Fluid. 
  

   while 
  

  

  11 
  

  

  = 
  

  

  A 
  . 
  r,~ 
  

  

  

  

  = 
  

  

  7ra%2 
  ■ 
  

  

  

  1 
  

  

  (92 
  

  

  2Q 
  

  

  2Q 
  

  

  (C) 
  

  

  Substituting 
  this 
  value 
  in 
  (5) 
  we 
  get 
  

  

  'Gi'^ 
  2g~ 
  '^'^ 
  2g 
  tj7 
  l" 
  V<ro 
  ^/ 
  37ra'^ 
  V-t'o' 
  '<-•' 
  / 
  J 
  ^ 
  ^ 
  

   At 
  the 
  boundaries 
  Uq 
  — 
  u 
  = 
  {), 
  so 
  that 
  here 
  

  

  -57 
  -CT 
  -GT 
  ' 
  37ra* 
  La'o^ 
  X" 
  S 
  ' 
  * 
  * 
  • 
  V 
  / 
  

  

  _ 
  8/^Q 
  r 
  f;o^ 
  _ 
  '^^ 
  1 
  

  

  giving 
  the 
  difference 
  of 
  head 
  (expressed 
  as 
  the 
  langth 
  of 
  a 
  

   column 
  of 
  the 
  fluid) 
  as 
  measured 
  by 
  piezometers 
  opening 
  

   flush 
  with 
  the 
  sides 
  of 
  the 
  tube 
  at 
  points 
  distant 
  respectively 
  

   .I'o 
  and 
  X 
  from 
  the 
  point 
  of 
  convergence, 
  and 
  where 
  the 
  radii 
  

   are 
  respectively 
  ^o 
  and 
  a. 
  

  

  From 
  (6) 
  we 
  have, 
  at 
  the 
  centre 
  where 
  ^=0, 
  

  

  Q 
  

  

  

  

  

  ""-7r«V 
  

  

  

  Liile 
  the 
  

  

  mean 
  

  

  velocity 
  

  

  over 
  the 
  whole 
  

  

  Q 
  

  

  section 
  

  

  

  /. 
  

  

  Maximum 
  velocitv 
  

  

  9 
  

  

  Mean 
  velocity 
  

  

  