344. T. H. Havelock. 
Pressure Distribution. 
5. The wave resistance for a travelling distribution of pressure applied to 
the upper surface of the liquid has been worked out by various methods, but 
not by that used in the previous sections. It is convenient, for comparison, 
to have the general case set out in the same way and using the same principle 
for the calculation of the resistance. 
We begin by assuming a possible form for the velocity potential and finding 
the surface pressure to which it corresponds. 
We take 
fg ies) Ke+iKD 
= | sec 0d0 | Heh ts) Cats see K dk, (20) 
o K — Ky sec? 0 + iu sec 0 
with © = x cos 0 + ysin 0. 
From the kinematical condition at z = 0, the surface elevation is given by 
(a) KF (k) exe 
a 1 
=—.- 2 68d), ——~~—_____ 21 
c = |_see | K — Ky sec? 0 + insec 0 ay 
The pressure at the surface (zg = 0) is found from 
pe eON ' 99 
b= — of — Gt + wd. (22) 
Using (20) and (21), this reduces to 
p= ae) I d0 |" KE (i) etx (ecos@ + ysin @) dk 
—1 /0 
= = Free I KF (1c) Ty (er) dic, (23) 
0 
where 7? = 27+ y*. Since we may write 
plr) = [: Ty (ter) 1 dic | ~p@O)ip keodvendles (24) 
Jo 0 
we see that 
a 7 oo f (x) eke tee 
— XG} 7) AG) = i] 5 25 
$ 2mco [e ee | K — Ky Sec? 6 + iy sec Qieaan ee) 
represents the solution for a surface pressure (7), symmetrical round the moving 
origin, with 
Fe) = | (@) So (er) a de. (26) 
0 
To generalise this, we first suppose the pressure concentrated round the origin 
and of integrated amount P, so that f(«) in (25) is replaced by P/27. Then for 
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