FREEBOARD 199
A modification of equation (4.10) includes a provision for wind
speed:
H0.032 (UF)1/20.76 0.24(F)1/4. (4.11)In the case of medium-sized reservoirs and preliminary design stages of
large reservoirs, wave freeboard, fw, is usually taken as 0.75Hc^2 /2g,
wherecis the wave propagation velocity (m s^1 ) which, in turn, is approxi-
mately given by c1.5 2 H; thus
fw0.75H(1.5 2 H)^2 /2g. (4.12)(Equation (4.12) assumes that the height of the wave crest above the
reservoir level is approximately 0.75H.) For a more detailed treatment of
the subject see, for example, Saville, Clendon and Cochran (1962), US
Corps of Engineers (1962), Falvey (1974), Zipparo and Hasen (1993) and
Sentürk (1994).
Using the concept of significant wave height, Hs(the mean height of
the highest third of the waves in a train with about 14% of waves higher
thanHs(see also Sections 14.9 and 14.10 for further details), e.g. ICE
(1996) recommends the use for the design wave height, Hd, of a multiple of
Hsranging from 0.75Hsfor concrete dams to 1.3Hsfor earth dams with a
grassed crest and downstream slope and 1.67Hsfor dams with no water
carryover permitted. Hs(m) can be determined quickly from Fig. 4.1 as a
function of the wind velocity (m s^1 ) and fetch (m) based on the simplified
Donelan/JONSWAP equation HsUF0.5/1760.
Required wind speed, U (m/s)3025201510
200 300400500 700 1000 2000 3000400050007000 10,00015,000
Fetch, F (metres)100(^0) .2
(^0). 3
(^0). 4
(^0). 5
(^0). 6
(^0). 7
(^0). 1
0.8
0.9
1.0
1.2
1.4
1.6
Significant W
ave Height H
s: (m)
Fig. 4.1 Relationship between fetch, windspeed and significant wave
height (ICE, 1996)