Page 511 - 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 469

13.5 Flow in Sewer Transitions 469

Solution:
From Appendix 9 “Hydraulic Elements of Circular Conduits,” a>A 0.949, r>R 1.192, when
d>D 0.9.
2
Area of the partially filled sewer 0.949(D 0.785) 0.7442D 2
Hydraulic radius of the partially filled sewer 1.192 (D>4) 0.298D
The remaining will be similar to the solution of Example 13.5.

Appendix 11 confirms that minimum grades are enough as long as circular sewers
flow more than half full. However, for granular particles, when flows drop to 0.2 depth,
grades must be doubled for equal self-cleansing; at 0.1 depth they must be quadrupled.
Expressed in terms of the Weisbach-Darcy friction factor ƒ, Eqs. 13.14 and 13.15 become,
respectively,
v >V (F/ƒ) 1/2 (13.16)
s
and
q >Q (a>A)(F>ƒ) 1/2 (13.17)
s

EXAMPLE 13.7 SELF-CLEANING FLOW IN SEWERS
3
An 8-in. (200-mm) sewer is to discharge 0.161 ft /s (4.56 L/s) at a velocity as self-cleaning as a
sewer flowing full at 2.5 ft/s (0.75 m/s). Find the depth and velocity of flow and the required slope.
Solution:
3
1. From Example 13.4, Q 0.873 ft /s and S 5.20‰.
Hence, q s >Q 0.161>0.873 0.185
2. From Appendix 11, for N n and q s /Q 0.185, d s /D 0.25, v s /V 0.91, and s/S 1.70.
Hence, v s 0.91 2.5 2.28 ft/s (0.69 m/s)
s s 1.70 5.20 8.8‰
3. From Appendix 11, for N/n variable and q s /Q 0.185, d s /D 0.30, v s /V 0.732, and
s/S 1.46
Hence, v s 0.732 2.5 1.83 ft/s (0.56 m/s)
s s 1.46 5.20 7.6‰

Egg-shaped sewers and cunettes were introduced, principally in Europe, to provide
enough velocity for dry-weather flows in combined sewers. The hydraulic elements of
these sewers and of horseshoe-shaped and box sewers that can be charted in the same way
as circular sewers are in Appendixes 10 and 11.

13.5 FLOW IN SEWER TRANSITIONS
Although flow in sewers is both unsteady (changing in rate of discharge) and nonuniform
(changing in velocity and depth), these factors are normally taken into account only at
sewer transitions. This is so because it is not practicable to identify with needed accuracy