Page 509 - 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 467

13.4 Flow in Partially Filled Sewers 467
and

2/3
v >V (N>n)(r>R) (s >S) 1/4 (N>n)(r>R) 1/6 (13.14)
s
s
or
q >Q (N>n)(a>A)(r>R) 1/6 (13.15)
s
What these equations imply is illustrated in Appendix 11 and in Example 13.3.

EXAMPLE 13.4 DETERMINATION OF FLOW IN PARTIALLY FILLED SEWERS USING DESIGN
DIAGRAMS

An 8-in. (200-mm) sewer is to flow at 0.3 depth on a grade ensuring a degree of self-cleaning
equivalent to that obtained at full depth at a velocity of 2.5 ft/s (0.75 m/s). Find the required grades
and associated velocities and rates of discharge at full depth and 0.3 depth. Assume that N 0.013 at
full depth.
Solution:
1. From Appendix 8 find for full depth of flow and V 2.5 ft/s (0.61 m/s),
3
Q 0.873 ft /s (0.762 m/s)
s 5.20‰
2. From Appendix 10 or Appendix 9, find for 0.3 depth,

a>A 0.252
r>R 0.684 (or R>r 1.46)
v>V 0.776
q>Q 0.196
N>n 0.78
and from Appendix 9, find
(r>R) 1/6 0.939
Hence, at 0.3 depth and a grade of 5.20‰,

v 0.776 2.5 1.94 ft/s (0.59 m/s) for n N, or 1.51 ft/s (0.46 m/s) for N/n 0.78 and
3
3
q 0.196 0.873 0.171 ft /s (4.84 L/s) for n N, or 0.133 ft /s (3.77 L/s) for N/n 0.78
For self-cleaning flow, however,
s 1.46 5.20 7.6‰ by Eq. 13.13
v s 0.939 2.5 2.35 ft/s (0.72 m/s) for n N,
or 0.78 2.35 1.83 ft/s (0.56 m/s) for N/n 0.78, by Eq. 13.14
and
3
q s 0.252 0.939 0.873 0.207 ft /s (5.86 L/s) for n N,
3
or 0.78 0.207 0.161 ft /s (4.56 L/s) for N/n 0.78, by Eq. 13.15.