Chapter X — 181 — Loss and Retention 



in the more general use of the term meaning net loss, evaporation would be 

 considered as having a value of zero. Because of the ease of measuring 

 net water loss, the term is more conveniently used in this sense. 



Evaporation from a Free Water Surface: — Dalton in 1801 made 

 several important observations on evaporation ; he has been credited with a 

 formula for calculating the rate of evaporation from extensive areas of 

 water. Humphreys (1940) doubts the authenticity of the formula at- 

 tributed to Dalton. The following statements by Dalton indicate the 

 state of knowledge of the subject up to Dalton's time. 



"Some fluids evaporate more quickly than others. The quantity evapo- 

 rated is in direct proportion to the surface exposed, all other circumstances 

 alike. An increase of temperature in the liquid is attended with an increase 

 of evaporation, not directly proportional. Evaporation is greater where 

 there is a stream of air than where the air is stagnant. Evaporation from 

 water is greater the less the humidity previously existing in the atmosphere, 

 all other circumstances the same." 



Dalton's observations lead him to conclude that " . . . . the evaporat- 

 ing force must be universally equal to that of the temperature of the water 

 [vapor pressure of water at saturation at surface temperature] diminished 

 by that already existing in the atmosphere [vapor pressure of water in 

 air]." He further concluded that, "The quantity of any liquid evaporated 

 in the open air is directly as the force of steam from such liquid [vapor 

 pressure] at its temperature, all other circumstances being the same." 



Since, in studying transpiration, we are dealing with evaporation from 

 relatively small areas, Stefan's (1881) analysis of the rate of evaporation 

 from flush circular areas is of interest. Stefan found that such evapora- 

 tion into still air could be expressed mathematically by the formula 



P — oo 



V = 4 a k log ^ , where (i) 



ir — p^ 



V = amount of water evaporated per unit area, 

 a = radius of the evaporational area. 



k =z the diflfusion coefficient. 



P = atmospheric pressure. 



pO z= the vapor pressure of the liquid in air. 



pi = the vapor pressure of the liquid at saturation at the surface temperature. 



The coefficient of diffusion of water vapor into air has the dimensions of 

 mass diffused per unit area per unit time for a unit vapor-pressure gradient. 



H pO and p^ are small in comparison with P, the equation becomes ap- 

 proximately 



V = 4 a k AP PJ (2) 



P 



The importance of Stefan's relation is that evaporation from small 

 areas is shown to be proportional to the linear dimensions of the evaporating 

 surface and not to the area as is suggested by Dalton for large areas. 



Evaporation from Tubes: — When water evaporates from a surface 

 that is not flush with the edge of the container molecules escaping near the 

 periphery of the liquid cannot diffuse laterally but are confined to the tube 

 immediately above the fluid and hence contribute to the total vapor pressure 

 above the liquid. Evaporation under these conditions is reduced. Stefan 

 (1873) calculated the rate of evaporation in this case to be 



