420 HYDRAULICS AND ITS APPLICATIONS 



water. In large waves this is sensibly true, but in small waves, the 

 curvature of whose surface is comparatively great, the modifying effect of 

 the forces called into play by surface tension becomes appreciable, and in 

 very small waves becomes the predominating factor. The effect of surface 

 tension is to increase the sub-surface pressure under the crests and 

 to reduce that under the troughs of the waves. If T be the surface 

 tension in Ibs. per linear foot of surface, and if p be the radius of 

 curvature at any point, the resultant increase or diminution of pressure 



T 



in feet of water is given by ~p feet. 



Assuming the wave to be of trochoidal form, the horizontal and vertical 

 displacements of a particle since leaving the crest are given by 

 x = RB (approx.) : y = r (I cos 6). 

 1 d? y , r 



" 7 := T& toP*-) == -& cos e - 



If the pressures at the crest and at any other point Q (Fig. 184D) are 

 not equal, but are respectively p e and p Ibs. per square foot, we have : 



= Z /! _ 

 " w\ Po p 



T r 



= W W (1 ~ COS ^ 



But ~ +rcos0-^-r=( E - l] r (1 - cos 0) (1) p. 419. 

 ^ 9 * 9 \ 9 I 



For water at 60 F, T = '005 Ibs. per foot (approx.), and on 

 substituting this value, the quadratic becomes 



I = -0975 F 2 V -0095 F 4 - '00324. 



For this to have real roots V* must be not less than '342, and V not less 

 than '765 f.s., or 9'2 inches per second. When V has this value, I = 

 67 inches. 



For higher values of V, I has two values, one less and one greater 

 '67, The greater vatoe represents the length of the ordinary wave 



