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2.6 Area and Volume of Reservoirs 43
A the size of the drainage area, m 2
c a coefficient with a value varying from 0.43 to 1.7 to 4.8 for low, average, and high depo-
sition, respectively
n a coefficient to be determined specifically for a target drainage area 0.77 for southwest-
ern steams in the U.S.
A plot of trap efficiency against the proportion of the mean annual flow stored in a reser-
voir traces curves quite similar to curves for the expected performance of settling basins of
varying effectiveness. Close to 100% of the sediment transported by influent streams may be
retained in reservoirs storing a full year’s tributary flow. Trap efficiency drops to a point be-
tween 65% and 85% when the storage ratio is reduced to 0.5 (half a year’s inflow) and to
30% to 60% when the storage ratio is lowered to 0.1 (5 weeks’ inflow). Silting is often fast
when reservoirs are first placed in service and may be expected to drop off and reach a steady
state as delta building goes on and shores become stabilized. An annual silting rate of
2
2
3
2
2
1.0 acre-ft/mi (note: 1 acre-ft/mi 476.25 m /km 0.47625 ML/km ) of watershed
2
2
corresponds roughly to a yearly reduction in storage of 0.32585 MG/mi (0.476 ML/km )
because an acre 3 ft (0.91 m) deep is about 1 MG (3.785 ML).
EXAMPLE 2.4 VOLUME OF SILTING
Determine the volume of silt accumulations for a drainage area having the following characteristics:
2
8
2
2
Area 100 mi 259 km 2.59 10 m 259,000,000 m 2
Average deposition of silt: c 1.7
Area located in the Southwestern United States: n 0.77
Solution 1 (U.S. Customary System):
V s cA n (2.7)
where
V s volume of silt deposited annually, acre-ft
A the size of the drainage area, mi 2
V s 1.7 (100) 0.77
1.7 34.7
59 acre-ft

Solution 2 (SI System):
6 n
V s 1,233.5c[A>(2.59 10 )] (2.7a)
where
V s volume of silt deposited annually, m 3
A the size of the drainage area in m 2
6 n
V s 1,233.5c[A>(2.59 10 )]
8
6 0.77
V s 1,233.5(1.7)[(2.59 10 )>(2.59 10 )]
1,233.5(1.7)(34.6737)
3
72,708.98 m
2.6 AREA AND VOLUME OF RESERVOIRS
The surface areas and volumes of water at given horizons are found from a contour map of
the reservoir site. Areas enclosed by each contour line are planimetered, and volumes
between contour lines are calculated. The average-end-area method is generally good
enough for the attainable precision of measurements.