Calculation Procedure:
- Compute the flow rate in the half-full sewer
A flow of 1 million gal/day = 1.55 ft
3
/s (0.04 m
3
/s). Hence, a flow of 5 million gal/day =
5(1.55) = 7.75 fWs (219.1 LIs) in a half-full sewer.
- Compute the full-sewer flow rate
In a full sewer, the flow rate is twice that in a half-full sewer, or 2(7.75) = 15.50 ft
3
/s (0.44
m
3
/s) for this sewer. This is equivalent to 15.50/1.55 = 10 million gal/day (438.1 L/s).
Full-sewer flow rates are used because pipes are sized on the basis of being full of liquid.
- Compute the sewer-pipe slope
The pipe slope S ft/ft = (E 1 - EQ)/L 9 where E 1 = inlet elevation, ft above the site datum; E 0
= outlet elevation, ft above site datum; L = pipe length between inlet and outlet, ft. Substi-
tuting gives S = 5/1000 = 0.005 ft/ft (0.005 in/in).
- Determine the pipe size to use
The Manning formula v = (1.486/W)^
273
S
172
is often used for sizing sewer pipes. In this
formula, v = flow velocity, ft/s; « = a factor that is a function of the pipe roughness; R
= pipe hydraulic radius = 0.25 pipe diameter, ft; S = pipe slope, ft/ft. Table 14 lists val-
ues of n for various types of sewer pipe. In sewer design, the value n = 0.013 for pipes
flowing full.
Since the Manning formula is complex, numerous charts have been designed to sim-
plify its solution. Figure 12 is one such typical chart designed specifically for sewers.
Enter Fig. 12 at 15.5 ft^3 /s (0.44 m^3 /s) on the left, and project through the slope ratio of
0.005. On the central scale between the flow rate and slope scales, read the next larger
standard sewer-pipe diameter as 24 in (610 mm). When using this chart, always read the
next larger pipe size.
- Determine the fluid flow velocity
Continue the solution line of step 4 to read the fluid flow velocity as 5 ft/s (1.5 m/s) on the
extreme right-hand scale of Fig. 12. This is for a sewer flowing}w//.
TABLE 14. Values of n for the Manning Formula
Type of surface of pipe n
Ditches and rivers, rough bottoms with much 0.040
vegetation
Ditches and rivers in good condition with some 0.030
stones and weeds
Smooth earth or firm gravel 0.020
Rough brick; tuberculated iron pipe 0.017
Vitrified tile and concrete pipe poorly j ointed and 0.015
unevenly settled; average brickwork
Good concrete; riveted steel pipe; well-laid 0.013 *
vitrified tile or brickwork
Cast-iron pipe of ordinary roughness; unplaned 0.012
timber
Smoothest pipes; neat cement 0.010
Well-planed timber evenly laid 0.009
*Probably the most frequently used value.
