40 EFFECTS OF WINDS AND OF 



depth of the water and its surface slope is established. In this part of the 

 exposition, each of the various strips, each parallel to the wind direction, 

 across the lake from windward to leeward is assumed to act independently 

 of every other such strip. 



(2) It is recognized that the various strips across a lake do not act in- 

 dependently. The method of applying the relation derived in (1) to an 

 actual lake with its irregular bottom and shores is set forth. 



(3) A statement is made in regard to the manner in which the exponent 

 of h (2.4) has been derived. 



RELATION BETWEEN DEPTH AND SLOPE PRODUCED BY 



WIND. 



The Chezy formula for the flow of water in an open channel is the standard 

 formula usually given in the text-books on hydraulics. It is the fundamental 

 basis from which other more elaborate formulae have been built up. 



The Chezy formula is 



V = C(RS)* (52) 



In this formula, 



F = the mean velocity of flow in a cross-section of the channel. 



C = an empirical coefficient depending in the main upon the roughness 



of the solid surfaces of the channel, and also upon the velocity 



of flow, upon the hydraulic radius, and possibly upon the 



slope of the water surface. 

 R = the mean hydraulic radius = the area of the cross-section of the 



stream of water divided by its wetted perimeter. 

 S = the slope of the water surface. 



This Chezy formula is adopted as a part of the basis for the following 

 derivation of the relation between the wind and the slope of the water surface 

 ultimately produced by it. 



Consider the conditions on a lake during a period when a wind of uniform 

 constant velocity and direction is blowing over the surface of the lake. 

 Consider any strip of surface of the lake, of unit width, with the axis of the 

 strip parallel to the direction of the wind. So long as the wind remains 

 constant in velocity and direction it is evident that the rate at which the 

 surface water will be delivered to leeward along the strip by the action of 

 the wind will be approximately constant. Let the volume of water delivered 

 per unit of time past any line across the strip under the action of a wind of 

 fixed velocity be called Q. 



The velocity of this surface drift caused by the wind is evidently a maxi- 

 mum at the surface where the wind acts upon the water, diminishes gradually 

 with increase of depth below the surface, and becomes zero, or practically 

 so, at a moderate depth below the surface. This is illustrated by figure 3, 

 plate 4, in which the arrows are proportional to the velocities under con- 



