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122
HARBOUR ENGINEERING.
Accordingly, if it be possible to determine the velocity of impact, the
pressure momentarily exerted may be deduced from the above relationship.
Now, the velocity of a wave in shallow water has been found to be nearly
the same as that which would be acquired by a heavy body falling freely
from rest under the influence of gravitation through a height equal to the
semi-depth of the water plus three-fourths of the height of the wave. In
symbols,
When the depth of water exceeds the length of the wave, the speed of the
latter is practically independent of the depth, and is almost exactly equal to
the velocity acquired by a body falling freely through a height equal to one-
half the radius of the circle, the circumference of which constitutes the
length of the wave. That is: —
Reverting to the first, (a), of the foregoing equations, we may recall the
fact that if the velocity of a falling body be expressed in terms of the height
(Ä), or perhaps, more correctly, the depth below the position of rest, we have
v2 = 2gh;
and, substituting this value for V2 in (a),
p= 2wh ..... (8)
which leads us to the conclusion that the pressure intensity of a water-jet is
equal to the weight of a column of water twice as high as the amount of free
fall required to generate the specified velocity in a heavy particle.
We see, however, that the numerical coefficient in this last expression is
not applicable to wave pressures, owing to the modifications in the value of v
given above in (/I) and (y). As a matter of fact, the value of the coefficient
is very variously stated by different aùthorities, so that all that is justifiable
is to write in general terms,
p= kwh ..... (e)
where k has a fairly wide range of values.
Thus, Dubuat gives £=1’85
Rayleigh „ Æ=1‘96
Mariotte ,, Zc=l'25
Gaillard ,, £=1'31
Jæssel ,, 4=162
Thibault ,, Zr=l'85,
the average value being 1’6.
It is to be noted, however, that Gaillard considers the velocity of the
crest of the wave, while breaking, to exceed the velocity of the body of the