Page 538 - 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 496

496 Chapter 13 Hydraulics of Sewer Systems
2 1.333
n coefficient of roughness H f 6.31725 L (vn) D
D inside diameter of pipe (m) 10.24557 L (Qn) D
2 5.3334
S slope, or rate of grade (dimensionless).
where
Given a 0.3048-m sewer, n 0.013, laid on a grade of 4.05% Q flow (m /s)
3
(m per 1,000 m), find (a) its minimum hydraulic gradient for A cross-sectional area of pipe (m )
2
flow at full depth using the equations in Problems 13.13 and v velocity of flow (m/s)
13.14, (b) its head loss through 304.8 m of sewer, and (c) its n coefficient of roughness
head loss through 152.4 m of sewer.
D inside diameter of pipe (m)
13.18 Given a square sewer (W W 0.3048 m 0.3048 m), s slope, or rate of grade (dimensionless)
n 0.013, laid on a grade of 4.05% (m per 1,000 m), find its H f hydraulic head loss (m)
velocity of flow (v) and rate of discharge (Q) using the SI L length of the pipe (m).
System design equations from Problem 13.3.
13.19 Given a rectangular sewer (L W 0.6096 m Determine the required velocity (v), the required grade (s), and
0.3048 m), n 0.013, laid on a grade of 4.05‰ (m per 1,000 m), the total head loss (H f ) of a 1.2192-m (or 48–in.) circular pipe
3
find its velocity of flow (v) and rate of discharge (Q) using the when it is flowing full at a discharge rate (Q) of 2.832 m /s (or
3
SI System design equations from Problem 13.4. 100 ft /s). The coefficient of roughness (n) is 0.015 and the
length of the pipe (L) is 304.8 m (or 1,000 ft).
13.20 A SI System formula for the required diameter of a cir-
cular sewer flowing full, expressed in terms of the required ca- 13.22 For any partially filled circular sewer laid on any grade,
pacity and the planned slope, can be derived by substituting val- the cross-sectional area of the water, the velocity of flow and
2
ues for A 0.785 D , r 0.25 D, and V in the formula Q A the water flow rate is laborious, and a chart for partially full cir-
V, and solving the resulting equation for the diameter D. The cular sewers (Appendix 10) is normally used. For any ratio of
following are the derived SI System equations based on SI depth of flow to diameter of sewer, the curves in Appendix 9
System Manning formula: give the ratios of the area, velocity, and flow for that depth to
the corresponding values for the circular sewer flowing full.
1.5
D 3.9849 (vn) (s) 0.75 The capacity of a circular sewer flowing full is 7.08 m /s (or
3
3
1.5475 (Qn) 0.375 (s) 0.1875 250 ft /s). Determine:
where (a) The depth of flow, in terms of the diameter of the sewer
v velocity of flow (m/s) (b) The relative velocity when the discharge is 2.832
3
n coefficient of roughness m /s (or 100 ft /s).
3
s slope, or rate of grade (dimensionless)
3
Q flow (m /s) 13.23 A trunk sewer, 1,200 mm in diameter (n 0.013), is
D inside diameter of pipe (m). placed on a slope of 0.003 between two manholes 120 m apart.
The average design flow in the line is 667 L/s and the minimum
The preceding SI System equation is derived assuming the
and peak flows are 0.5 and 2.5 of the average flow, respectively.
sewer is flowing full. If the sewer is flowing only half full, the Q
value must be adjusted to full flow before the preceding SI (a) What would be the depth of flow in the pipe at aver-
System equation can be applied. age flow?
3
3
A sewer pipe is to discharge 0.11328 m /s (or 4 ft /s) when laid (b) Would the pipe need flushing at regular short inter-
on a grade of 0.0016 and flowing only half full. Determine the vals? Show your supporting computations.
required diameter (D) if the velocity (v) is to be determined by (c) If the depth of flow is 900 mm, what is the discharge?
the Manning equation.
(d) What would be the difference in elevation between
13.21 The SI System Manning formula can be rearranged for the inverts at both ends of the pipe?
solving the sewer pipe’s slope or rate of grade as follows:
(e) Compute the maximum population that can be
2/3 2
s [v n >(r )] served by this line. Assume that the average per
capita contribution is 380 L/day.
s H f >L
(f) Suppose that at the downstream end manhole, this
Q Av
sewer joins with a branch sewer that is 600 mm in di-
When a circular pipe is used, that is, when r 0.25 D, the fol- ameter, has a slope of 0.005, and a peak flow of 250 L/s.
lowing working equations can be derived: At what height above the invert of the trunk sewer
should the invert of the branch sewer be located, so
2 1.333
s 6.31725 (vn) D
that at design peak flows, there will be no backing up
2 5.3334
10.24557 (Qn) D of sewage into the branch sewer?