Page 405 - Civil Engineering Formulas

332 CHAPTER TWELVE

PREDICTION OF SEDIMENT-DELIVERY RATE

Two methods of approach are available for predicting the rate of sediment accu-
mulation in a reservoir; both involve predicting the rate of sediment delivery.
One approach depends on historical records of the silting rate for existing
reservoirs and is purely empirical. The second general method of calculating the
sediment-delivery rate involves determining the rate of sediment transport
as a function of stream discharge and density of suspended silt.
The quantity of bed load is considered a constant function of the discharge
because the sediment supply for the bed-load forces is always available in all
but lined channels. An accepted formula for the quantity of sediment transported
as bed load is the Schoklitsch formula:
86.7
3/2
G b S (Q i bq o ) (12.128)
1/2
D g
where G total bed load, lb/s (kg/s)
b
D effective grain diameter, in (mm)
g
S slope of energy gradient
3
3
Q total instantaneous discharge, ft /s (m /s)
i
b width of river, ft (m)
3
3
q critical discharge, ft /s (m /s) per ft (m), of river width
o
4/3
(0.00532/S )D g
An approximate solution for bed load by the Schoklitsch formula can be
made by determining or assuming mean values of slope, discharge, and single
grain size representative of the bed-load sediment. A mean grain size of 0.04 in
(about 1 mm) in diameter is reasonable for a river with a slope of about 1.0 ft/mi
(0.189 m/km).
EVAPORATION AND TRANSPIRATION
The Meyer equation, developed from Dalton’s law, is one of many evaporation
formulas and is popular for making evaporation-rate calculations:
E C (e w e a )# (12.129)
# 1 0.1w (12.130)

where E evaporation rate, in 30-day month
C empirical coefficient, equal to 15 for small, shallow pools and 11 for
large, deep reservoirs
e saturation vapor pressure, in (mm), of mercury, corresponding to
w
monthly mean air temperature observed at nearby stations for small
bodies of shallow water or corresponding to water temperature
instead of air temperature for large bodies of deep water