5.2. RUBBLE-MOUND STRUCTURES
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the best length scale at which to conduct this second model study. (Assume both
prototype and model
= 9.79 kN/m3.)
Solution. Ideally, we would want to satisfy Eqn. 5.30, but for this example
and
28 kN/m3
9.79 kN/m3
29.22 kN/m3
9.79 kN/m3
2.985
Because (ya/7w)p 0 (7a/?w)m r we should choose the length scale that satisfies
either Hudson’s stability number criterion (Eqn. 5.25) or Sharp and Khader's criterion
(Eqn. 5.29).
The given scale ratios are found as
N _ (t«)p _ 28 kN/m3
_
70 (7a)m
29.22 kN/m3
tr
_ (7a/7w ~ l)p
2.860 — 1
(7«/7w-l) -
- 2 985 _ !
0.937
and
_ (Wa)p _ 120 kN
Wa ~
~ 2.8 N
42 857
The length scale solved from Hudson’s scaling criterion (Eqn. 5.25) is
0.937
42 857X 1/3
0.958 )
33.3
Alternately, the length scale solved using Sharp and Khader's criterion (Eqn. 5.29)
gives
(H" ■ <°' 937),/1
Therefore, damage-inducing model wave heights scaled up using Sharp and Khader's
criterion would be about 4% higher (with 2% longer periods) than model waves
scaled up using Hudson’s criterion. It should be noted that ignoring altogether the
difference in fluid density between model and prototype (i.e.,
— 1) would
have produced a length scale of Nl = 35.5, which is the least conservative of the
three.