﻿Problems 
  of 
  Evaporation. 
  273 
  

  

  Steady 
  wind 
  blowing 
  over 
  a 
  flat 
  surface 
  of 
  water. 
  

  

  Take 
  the 
  plane 
  of 
  the 
  surface 
  for 
  that 
  of 
  2 
  = 
  0. 
  Let 
  u 
  be 
  

   the 
  velocity 
  of 
  the 
  wind 
  in 
  the 
  direction 
  of 
  the 
  x 
  axis. 
  

   There 
  is 
  no 
  wind 
  in 
  the 
  directions 
  of 
  the 
  other 
  two 
  axes. 
  

   Then 
  outside 
  of 
  the 
  layer 
  of 
  rapid 
  shearing 
  the 
  equation 
  of 
  

   diffusion 
  when 
  a 
  steady 
  state 
  has 
  been 
  attained 
  is 
  

  

  u 
  ^= 
  k 
  w 
  (5) 
  

  

  provided 
  the 
  distance 
  from 
  the 
  margin 
  is 
  great 
  enough 
  for 
  

  

  ^— 
  j- 
  and 
  ^— 
  g 
  to 
  be 
  neglected 
  in 
  comparison 
  with 
  ^— 
  -^ 
  . 
  

  

  The 
  velocity 
  wis 
  a 
  function 
  of 
  z 
  only, 
  and 
  kju 
  is 
  supposed 
  

   constant, 
  equal 
  to 
  A 
  2 
  , 
  say. 
  The 
  value 
  of 
  V 
  over 
  the 
  surface 
  

   when 
  x 
  is 
  positive 
  is 
  V 
  . 
  Then 
  all 
  the 
  conditions 
  are 
  

  

  satisfied 
  if 
  

  

  (_ 
  i 
  

   zx 
  2 
  \ 
  

   1 
  — 
  Erf 
  -^y- 
  J 
  when 
  x 
  is 
  positive. 
  . 
  (6) 
  

  

  V 
  = 
  when 
  x 
  is 
  negative. 
  

  

  This 
  makes 
  ^r— 
  = 
  -= 
  — 
  —^ 
  — 
  r 
  over 
  the 
  wet 
  surface. 
  

   Oz 
  li 
  v 
  (ttx) 
  

  

  Hence 
  the 
  rate 
  of 
  evaporation 
  is 
  

  

  ^•/jy 
  =YojO'W 
  — 
  per 
  unit 
  area. 
  . 
  . 
  . 
  (7) 
  

  

  Then 
  the 
  amount 
  evaporated 
  between 
  and 
  x 
  over 
  a 
  strip 
  

   dy 
  in 
  diameter 
  is 
  by 
  integration 
  

  

  2pY 
  {kuxl7r)My. 
  

  

  Finally, 
  if 
  the 
  length 
  of 
  the 
  strip 
  from 
  one 
  margin 
  to 
  the 
  

   other 
  be 
  I, 
  and 
  parts 
  near 
  enough 
  to 
  the 
  edges 
  for 
  the 
  end 
  

   corrections 
  at 
  both 
  ends 
  to 
  be 
  important 
  be 
  neglected, 
  the 
  

   amount 
  'evaporated 
  can 
  be 
  found 
  at 
  once 
  to 
  be 
  

  

  2pVo(^/J;% 
  (8) 
  

  

  taken 
  over 
  the 
  whole 
  area. 
  

  

  Hence 
  for 
  areas 
  of 
  the 
  same 
  shape 
  and 
  linear 
  dimensions 
  

   proportional 
  to 
  a 
  the 
  rate 
  of 
  evaporation 
  would 
  be 
  proportional 
  

   to 
  a 
  1 
  ' 
  5 
  . 
  In 
  particular, 
  for 
  a 
  circular 
  area 
  of 
  radius 
  a 
  it 
  

   would 
  be 
  

  

  3-95pV 
  (foia 
  8 
  )*. 
  ..... 
  (9) 
  

  

  