Page 433 - Civil Engineering Formulas

HYDRAULICS AND WATERWORKS FORMULAS 359

economically by provided against the erosion which would occur if the dam were
overtopped. A major cause of earth-dam failures has been overtopping; therefore,
care must be exercised that freeboard and spillway capacity are ample to prevent it.

Wave Action. The height and velocity of waves are functions of fetch and wind
velocity. Fetch is the clear-water distance form the dam to the opposite shore.
Generally the straight-line distance is used. However, where slight bends in the
measured line will lengthen the fetch, such bends may be incorporated according
to judgment. The Molitor-Stevenson equation for the height of waves, h , is
w
For a fetch greater than 20 miles,
h w 0.17(VF) 0.5 (12.214)

For a fetch less than 20 miles,
h w 0.17(VF) 0.5 2.5 (F) 0.25 (12.215)
where h height of wave from trough to crest, ft
w
V wind velocity, mph
F fetch, statute miles
For wave heights between 1 and 7 ft, the velocity, v, in feet per second is
given approximately by the formula
(12.216)
v 7 2h w
is in feet.
where h w

Freeboard. Freeboard (sometimes termed net freeboard) is the vertical
distance between the maximum water surface of the spillway design flood and
the crown of the dam. This vertical distance should be ample to prevent
overtopping of the dam due to wind setup and wave action.
Wind setup may be computed by the Zuider Zee formula
2
V F
S cos A (12.217)
1,400D
where S setup above pool level, ft
V wind velocity, mph
F fetch, miles
D average depth of water, ft
A angle of incidence of waves
The height of waves above pool level plus the run-up of waves on the face
of the dam may be computed by the formula
V 2
Height of wave action 0.75h w 1.5h w (12.218)
2g