and 



B/2 



f. 



2 



dy cos [k(y - y) sin 6] = sin (k B/2 sin 6) cos (k y sin 



k sin 



-B/2 

 it follows that 



i 



i> (*, y,- 



-h) = 



^ p r /2 



dd sec 2 (9 esc 



2 / 







77 P C J Q 





dk 



k- 1 



h sech M 



sin (k L/2 cos 



1 , 



kh - — sec^ 8 tanh kh 

 F 2 



sin (k B/2 sin 0) sin (k x cos (9) cos (ky sin 



4p / /2 J:,," 1 sech *„ A 

 / dd sec 2 0csc 6 



TT O C I 



F J 0. 



1 - — sec 2 6 sech 2 k Q h 



F 2 



sin (k Q L/2 cos 0) sin (k 6/2 sin 9) cos (k Q x cos 0) cos (k Q y sin 0) 



From Bernoulli's equation, neglecting the steady hydrostatic pressure and second-order 

 terms, the pressure on the bottom is given by p = p c cp . Thus the ratio of the bottom pres- 

 sure to that of the constant surface pressure p Q is given in nondimensional form by 



?- (£ ,) = —/! (£ i/) + — / 2 (£ t?) [2] 



?0 77 2 



where 



77/2 



ff sech A-// 



/ d(9sec d esc 9 4- dK 



1 

 AT/ - — sec 2 tanh KH 



F 2 



sin (A - cos 0) sin (^/3 sin #) cos {K £ cos #) cos (K rj sin 



77/2 sech K Q H 



dd sec esc 



1 9 , 



1 sec 2 <9sech 2 K n H 



F 2 



sin (K cos 0) sin (K Q /3 sin 0) sin (K Q £ cos 0) cos (K Q -q sin 



5 



