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462 Chapter 13 Hydraulics of Sewer Systems

EXAMPLE 13.2 DETERMINATION OF FLOW RATE AND VELOCITY IN SEWER USING NOMOGRAMS
1. Given a 12-in. (304.8 mm) sewer, N 0.013, laid on a grade of 4.05% (4.05 ft per 1,000 ft
or 4.05 m/1,000 m), find its velocity of flow and rate of discharge from (a) the table in
Appendix 7 and (b) from the nomogram in Fig. 13.1a.
2. Given a velocity of 3 ft/s (0.9 m/s) for this sewer, find its (minimum) gradient for flow at
full depth (a) from Appendix 7 and (b) from the nomogram in Fig. 13.1a.

Solution 1 (U.S. Customary System):
3 1/2
1/2
1. (a) s >N (4.05 10 ) >1.3 10 2 4.90
From the table in Appendix 7:
V 4.90 0.5897 2.89 ft/s
3
Q 4.90 0.4632 2.27 ft /s
(b) Given diameter 12 in., n 0.013, and s 0.00405, from the nomogram of Fig. 13.1a:
V 2.9 ft/s
3
Q 2.3 ft /s
2. (a) NV 3 0.013 3.9 10 2
2
s (3.9 10 2 1.6958) 4.37%. This is shown also in Appendix 8.
(b) Given diameter 12 in., n 0.013, and v 3 ft/s, find S from the nomogram of
Fig. 13.1a:

s 4.4 %

Solution 2 (SI System):
1. Given diameter 304.8 mm, n 0.013, and s 0.00405, from the nomogram of Fig. 13.1b:
Q 60 L/s
v 0.86 m/s

2. Given diameter 304.8 mm, n 0.013, and V 0.9 m/s, from the nomogram of Fig. 13.1b:
s 0.0045 4.5%

13.3 LIMITING VELOCITIES OF FLOW
Wastes from bathrooms, toilets, laundries, and kitchens are flushed into sanitary sewers
through house or building sewers. Sand, gravel, and debris of many kinds enter storm
drains through curb and yard inlets. Combined sewers carry mixtures of the two. Heavy
solids are swept down sewer inverts like the bed load of streams. Light materials float on
the water surface. When velocities fall, heavy solids are left behind as bottom deposits,
while light materials strand at the water’s edge. When velocities rise again, gritty sub-
stances and the flotsam of the sewer are picked up once more and carried along in heavy
concentration. There may be erosion. Within reason, all of these happenings should be
avoided, insofar as this can be done. Each is a function of the tractive force of the carrying
water that should be better known than it commonly is.