Page 96 - Fair, Geyer, and Okun's Water and wastewater engineering : water supply and wastewater removal

JWCL344_ch02_029-060.qxd 8/2/10 9:14 PM Page 59

Problems/Questions 59

Solution 2 (SI System):
1. The size of the required rainfall collection cistern:
The minimum volume of the cistern required will be:
(454.2 L/d) 100 days 45,420 L 45.42 m 3
Say, a 3-m-deep, 4-m-square cistern (3 m 4 m 4 m).
2. The size of the required catchment area:
Because the mean annual rainfall is 114 cm, then the total design rainfall is:

(114 cm) 2>3 76.2 cm
The total year’s requirement (365 day)(454 L/d) 165,800 L.
Referring to Fig. 2.18, the catchment area required to produce 165,800 L (43,800 gal)
2
2
from a design storm of 76 cm (30 in.) is 307 m (3,300 ft ).
Say, a 31-m 10-m catchment area.

PROBLEMS/QUESTIONS

2.1 The response of a new water surface will establish new Determine the volume of silt accumulations for drainage area,
2
2
hydrologic equilibria. Determine the equivalent mean draft where A, c, and n are 40 mi (103.60 km ), 1.7, and 0.77,
under the following conditions: (a) areal rate of runoff of the respectively.
original watershed Q 27.5 in./year (69.85 cm/year); (b) areal 2.5 The volume of silt deposited annually can be approxi-
rate of evaporation E 40.5 in./year (102.87 cm/year); (c) areal mated by the following equation:
rate of rainfall R 47.5 in./year (120.65 cm/year); (d) reservoir 6 n
2
area a 1,500 acres (6.07 km ); (e) catchment area A 25,600 V s 1,233.5c[(A>(2.59 10 )]
2
acres (103.60 km ); and (f) mean annual water surface 90% where
of the reservoir area at spillway level. V s volume of silt deposited annually, m 3
2.2 Determine the revised mean annual runoff, Q r , assuming A the size of the drainage area, m 2
(a) the original mean annual runoff Q 27.5 in./year (69.85 c a coefficient with a value varying from 0.43 through 1.7 to
cm/year); and (b) the equivalent mean draft D e 1.08 in./year 4.8 for low, average, and high deposition, respectively
(2.74 cm/year).
n a coefficient to be determined specifically for a target
2.3 Determine the effective catchment area assuming (a) orig- drainage area.
2
inal catchment area A 25,600 acres (103.60 km ); (b) reser- Determine the volume of silts deposited annually V s in m , as-
3
2
voir area a 1,500 acres (6.07 km ); (c) mean annual water 6 2
suming it is known that c 1.7, n 0.77, and A 648 10 m
surface 90% of reservoir area at spillway level; (d) original
(160,119 acre).
watershed’s runoff rate Q 27.5 in./year (69.85 cm/year);
2.6 Using the same metric equation from Problem 2.5 of V s
(e) evaporation rate E 40.5 in./year (102.87 cm/year); and 6 n
1,233.5c[(A>(2.59 10 )] and assuming c 1.7, n 0.77,
(f) rainfall rate R 47.5 in./year (120.65 cm/year). 6 2
and drainage area 984 10 m (243,143 acre), determine
2.4 In some parts of the United States, the volume of silt V s in
the volume of silt deposited annually.
acre-ft deposited annually can be approximated by the follow-
2.7 A research team has investigated two drainage areas in
ing equation:
the southwestern region of the United States, and has meas-
V s c(A) n
ured the volumes of their annually deposited silts. The fol-
where lowing are the field data collected by the researchers using
A drainage area, mi 2 the metric units:
c 0.43 for low deposition; 1.7 for average deposition; 4.8 for For drainage area 1:
6
2
high deposition A 1 984 10 m 243,143 acre 379.8 mi 2
3
n 0.77 for southwestern streams. V s1 203,000 m 164.6 acre-ft