Page 535 - Fair, Geyer, and Okun's Water and wastewater engineering : water supply and wastewater removal

JWCL344_ch13_457-499.qxd 8/7/10 8:49 PM Page 493

Problems/Questions 493

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grate inlet in Example 13.16 (4 ft in area or 0.37 m ): four times bigger and intercepts
only 92% of the gutter flow.
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2. Assume C w 3.0 and W g 1 ft. (0.3 m) For 100% interception in sag, Q iw 1 ft /s (28.3 L/s),
and W g 1 ft (0.3 m). From Example 13.14, d 2.2 in 0.18 ft (55 mm). From
Eq. 13.41,
Q iw = f C w Pd 1.5
1 (1)(3.0) P (0.18) 1.5
1 0.23 P
P 1/0.23 4.35 ft (1.33 m)
Since,
P L 2W g (the perimeter does not include the length along the curb)
4.35 L 2 1
L 2.35 ft (0.72 m)
The required inlet length is 2 ft 6 in (750 mm).
Solution 2 (SI System):
1. From Eq. 13.43,
Q io = C o A(2 gd 0 ) 0.5
0.0283 = 0.60 A(2 * 9.81 * 0.055) 0.5
A = 0.045 m 2
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Assuming the open area in the grate is 50%, total grate area 2 0.045 0.09 m .
Using a 0.3-m wide grate inlet, the required inlet length will be 0.3 m. Read the note of
Solution 1 concerning the efficiency of submerged grate inlets in sag.
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2. Assume C w 3.0 and W g 0.3 m. For 100% interception in sag, Q iw 0.0283 m /s, C o
3.0, and W g 0.3 m.
From Example 13.14, d 55 mm 0.055 m
From Eq. 13.41,

Q iw = f C w Pd 1.5
0.0283 = 0.55 (3.0) P (0.055) 1.5
P = 1.33 m
Since P = L + 2W g
1.33 = L + 2 * 0.3
L = 0.72 m
The required inlet length is 750 mm.

PROBLEMS/QUESTIONS
13.1 Using the U.S. Customary System nomogram of Fig. 13.1a: 13.2 Using the SI System nomogram of Fig. 13.1b:
a. Given a 10-in. sewer, N 0.013, laid on a grade of a. Given a 250-mm sewer, N 0.013, laid on a grade of
3.0‰ (ft per 1,000 ft), find its velocity of flow and 3.0% (m per 1,000 m), find its velocity of flow and
rate. rate of discharge.
b. Given a velocity of 3.3 ft/s for this sewer, find its b. Given a velocity of 1 m/s for this sewer, find its (min-
(minimum) gradient for flow at full depth. imum) gradient for flow at full depth.