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484 Chapter 13 Hydraulics of Sewer Systems

EXAMPLE 13.14 WATER SPREAD AND DEPTH OF FLOW IN THE GUTTER
3
3
For a flow of 1.0 ft /s (0.0283 m /s), a longitudinal street grade of 2.0%, a mean crosswise street
grade of 5.6%, and an n coefficient of roughness of 0.015, find:
1. The total width of spread, and
2. The maximum depth of flow in the gutter.

Solution 1 (U.S. Customary System):
1. From Eq. 13.31:
K c 1.67 0.5 2.67
Q = S x S L T
n
0.5
1 = (0.56>0.015)(0.056) 1.67 (0.02) (T 2.67 )
T 2.67 = 1>(37.3 * 0.0081 * 0.14) = 23.8
T 23.8 0.37 3.23 ft (0.98 m) water spread
2. From Fig. 13.12:
d>T S x
d TS x 3.23 0.056 0.18 ft
2.2 in. (56 mm) maximum depth of flow in the gutter
Solution 2 (SI System):

K c 1.67 0.5 2.67
1. Q = S x S L T
n
0.376 0.5 2.67
0.0283 = (0.056) 1.67 (0.02) T
0.015
0.376 * 0.0081 * 0.1417 2.67
0.0283 = T
0.015
T 2.67 = 0.98
T = 0.985 m
2. From Fig. 13.12:

d>T S x
d TS x (0.985 m) (0.056) 0.055 m
55 mm

EXAMPLE 13.15 GRATE INLET
If a 2-ft-wide (0.61-m) grate inlet is introduced in the gutter of Example 13.14, what will be the
flow contained in the width of the grate?

Solution 1 (U.S. Customary System):
3
From Example 13.11, we get T 3.23 ft (0.98 m) and Q 1 ft /s (28.3 L/s). From Eq. 13.32:
E 0 = 1 - (1 - W g >T) 2.67
E 0 = 1 - (1 - 2>3.23) 2.67