THEORY OF SIMPLE WAVES 



319 



Table 3 Properties of Simple Waves. From Robert L. Wiegel (1-K) 



apg 



co.sh k(ij + h) 



cos k(.v — ci) 



co.sh kh 

 and for deep water, on the basis of equation (15) 



P 



apgc'"' cos 



Hx - ct) 



(28) 



The pressiu'es indicated h.v c(|uations (27) and (28) are 

 tho.se due to wave formation oidy; i.e., the pressures 

 which act over and above the hydrostatic pressure po 

 = — pf/.// in still water. 



When the dinien.sions of a body arc small as compared 

 to the wave length, the total force exerted on it by waves 

 can be represented in term.s of the body \-ohimi' and pres- 

 sure gradient existing instantaneously at a particular 

 point under the surface wave. This will often prf)ve to 

 be much less laborious than integration of pi-essures o\-er 

 the body surface, particularly for a complicated bodv 

 form. The pressure gradients are obtained by partial 

 differentiation of <>f|ua1ions (27) and (2S) with resj^cct to 



