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JWCL344_ch13_457-499.qxd 8/7/10 8:49 PM Page 486

486 Chapter 13 Hydraulics of Sewer Systems
As shown in Fig. 13.12, the total gutter flow is composed of frontal flow, Q (the flow
w
in the depressed gutter or over the grate width), and side flow, Q . The total efficiency of
s
the grate inlet is determined by calculating the grate’s ability to capture frontal flow and
side flow. The term R represents the ratio of intercepted frontal flow to the total frontal
f
flow, and is expressed as follows:
R l K (V V ) (13.34)
cf
0
f
where
K cf 0.295 (0.090 in U.S. units)
V average velocity in the gutter at the location of the inlet (m/s, ft/s)
V 0 splash-over velocity of the inlet (m/s, ft/s).
The splash-over velocity is the minimum velocity of the gutter flow capable of induc-
ing enough momentum for some of the flow to skip over the grate opening and be carried
over and downstream. The splash-over velocity is a function of the grate type and the grate
length and can be found in the HEC-22 manual (FHWA, 1996) or obtained from the grate
manufacturer. If the gutter velocity is less than the splash-over velocity, all frontal flow is
intercepted and R equals 1.0.
f
The ratio, R , of side flow intercepted to total side flow is expressed as follows:
s
K V 1.8 -1
cs
R = a1 + 2.3 b (13.35)
s
S L
x
where K is 0.0828 (0.15 in U.S. units) and L is the grate length (m, ft).
cs
The total intercepted flow is expressed as
Q Q R Q R (13.36)
i
s s
w f
The total efficiency of the grate inlet on grade is expressed as
E R E R (1 E ) (13.37)
f 0
0
s
EXAMPLE 13.16 INTERCEPTED FLOW BY GRATE INLET
What will be the flow intercepted by the grate inlet in the gutter of Examples 13.14 and 13.15?
Assume the grate inlet length is 2 ft (0.61 m) and its splash-over velocity, V 0 , is 3 ft/s (0.91 m/s).
Solution 1 (U.S. Customary System):
From Examples 13.14 and 13.15:
3
Q g 1 ft /s (28.3 L/s)
T 3.23 ft (0.98 m)
W g 2 ft (0.61 m)
L 2ft (0.61 m)
d 2.2 in 0.18 ft (55 mm)
S L 2%
S x 5.6 %
3
Q w 0.92 ft /s (26 L/s)
V Q g /A g
2
2
A g triangular area of gutter flow Td/2 3.23 0.18>2 0.29 ft (0.027 m )
2
3
V Q g >A g 1ft >s>0.29 ft 3.45 ft/s (1.05 m/s)