In most cases, the water-surface elevation leaving the manhole is only slightly lower than the water-surface elevation entering the manhole. However, a pipe may enter the manhole much higher than the outlet (or any other pipe), as shown in Figure 3.6. This is referred to as a drop manhole or, more generally, a drop structure.
In this situation, flow at the inlet to the manhole passes through critical depth, which will serve as an internal boundary condition for the inflowing pipe. Problems occur when the manhole floods because of high flows, high tailwater, or a downstream restriction. In this case, the incoming pipe has a tailwater depth that must be accounted for in hydraulic routing. Models must switch between the two downstream boundary conditions for the incoming pipe, which is sometimes the cause of instability.
In hydrologic routing, the flows are forced through the manhole regardless of depth.
Figure 3.6 Example of drop manholes.
References
Abbott, M. B. 1979. Computational Hydraulics: Elements of the theory of free surface flows.
London: Pitman.
Chaudhry, M. H. 1987. Applied Hydraulic Transients. New York: Van Nostrand Reinhold.
Chow, V. T. 1973. Open Channel Hydraulics. New York: McGraw Hill.
Cunge, J. A. 1969. On the subject of a flood propagation computation method (Muskingum method). Journal of Hydraulic Research 7, no. 2: 205–230.
Cunge, J. A., F. M. Holley, and A. Verwey. 1980. Practical Aspects of Computational River Hydraulics. London: Pitman.
Fread, D. L. 1993. Flow routing. In Handbook of Hydrology, edited by D. Maidment.
New York: McGraw-Hill.
French, R. H. 1985. Open Channel Hydraulics. New York: McGraw-Hill.
Haestad Methods, T. M. Walski, D. V. Chase, D. A. Savic, W. Grayman, S. Beckwith, and E. Koelle. 2003. Advanced Water Distribution Modeling and Management.
Waterbury, CT: Haestad Press.
Haestad Methods, G. Dyhouse, J. Hatchett, and J. Benn. 2003. Floodplain Modeling Using HEC-RAS. Waterbury, CT: Haestad Press.
Hydrologic Engineering Center (HEC). 1990. HEC-1 Flood Hydrograph Package. Davis, CA: US Army Corps of Engineers, Hydrologic Engineering Center.
Linsley, R. K., M. A. Kohler, and J. L. H. Paulhus. 1982. Hydrology for Engineers. New York: McGraw-Hill.
National Oceanic and Atmospheric Agency, National Weather Service. 2000.
FLDWAV Computer Program, Version 2-0-0.
Ponce, V. M. 1986. Diffusion wave modeling of catchment dynamics. Journal of the Hydraulics Division, ASCE 112, no. 8: 716–727.
Ponce, V. M., R. M. Li, and D. B. Simons. 1978. Applicability of kinematic and diffusion models.” Journal of the Hydraulic Division, ASCE 104, no. HY12: 1663.
Preissmann, A. 1960. Propogation des intumescenes dans les canaue et rivieres. Grenoble:
First Congress de L’Association Francaise de Calcul.
Price R. K. 1973. A comparison of four numerical methods for flood routing. Journal of the Hydraulics Division, ASCE 100, no. 7: 879–899.
Roesner, L. A., J. A. Aldrich, and R. E. Dickinson. 1989. Storm Water Management Model User’s Manual Version 4: Extra Addendum. EPA 600/3-88/001b. US Environmental Protection Agency.
Samani, H. M. V. and S. Jebelifard. 2003. Design of circular urban storm sewer systems using multilinear Muskingum flow routing methods. Journal of Hydraulic Engineering 129, vol. 11: 832.
US Soil Conservation Service. 1972. National Engineering Handbook. Section 4,
“Hydrology.” SCS/ENGNEH-4.
Weinmann, D. E., and E. M. Laurenson. 1979. Approximate flood routing methods: A review. Journal of the Hydraulics Division, ASCE 105, no. HY12: 1521.
Wylie, B. E., and V. L. Streeter. 1993. Fluid Transients in Systems. Englewood Cliffs, NJ:
Prentice-Hall.
Yen, B. C. 1996. Hydraulics for excess water management. In Water Resources Handbook, edited by L. W. Mays. New York: McGraw-Hill.
Yen, B.C. 2001. Hydraulics of sewer systems. In Stormwater Collection Systems Design Handbook, edited by L. W. Mays. New York: McGraw-Hill.
Problems
3.1 Match the equation with the proper description.
3.2 Even though Muskingum routing is not considered the most appropriate rout-ing method for sewers, it is amenable to manual calculations and spreadsheets.
For this problem, route the storm with the following hydrograph through a reach of sewer with the following properties:
K = 2000 s
∆t = 1200 s x = 0.3
In addition to the inflow hydrograph, there is a dry weather flow of 2 ft3/s.
Equation Description
1 St. Venant a Slide wave downstream 2 Muskingum b Full hydrodynamic equations 3 Kinematic wave c Storage routing
4 Translation d Based on normal depth 5 Preissmann e Simple storage approximation 6 Modified Puls f Slot for surcharged flow
a. Calculate the three Muskingum coefficients and verify that they sum to 1.0.
b. Calculate the inflow (add dry and wet flow) and outflow hydrographs for the reach and plot them on the same graph.
3.3 In this problem, route the flow through a gravity sewer just beyond the crest of a hill that receives water from a force main and a pump station. The gravity flow reach is shown schematically. There are numerous manholes along the way, but you are only monitoring at MH-2 and O-1. When the pump station is running, the inflow at manhole MH-1 is 20 ft3/s; when it is off, the flow is 0. There is neg-ligible additional inflow along the pipe. The gravity pipe is circular 24-in. PVC with Manning’s n = 0.010. At time = 0, the gravity pipe is empty (Q = 0 ft3/s) and the pump station starts.
During dry weather, the constant-speed pump runs for shorter times than in wet weather, but the discharge rate is essentially the same whenever the pump is running.
Given the inflow patterns in the following table, develop the hydrographs at the monitoring manhole (MH-2) and the outlet (O-1) for both the dry weather and wet weather conditions. Plot the dry and wet weather hydrographs on separate graphs; that is, three curves (MH-1, MH-2, and O-1) on each of two graphs. Also determine the average flow out of the reach during a 2-hour period for each condition.
Hint: There are two ways to approach this problem; one is to solve with an extended period simulation model like SewerCAD, the other is to manually cal-culate with a spreadsheet. With the model approach, it’s safe to ignore any man-hole losses. Set the outlet depth to equal the pipe crown and use a stepwise pattern for the inflow. It’s suggested that a hydraulic routing time step of 0.1 hr be used with a hydrologic routing time step of 0.01 hr. With a spreadsheet, use convex routing with c = 0.15 for P-1 and c = 0.06 for P-2. Calculate flow every 0.01 hr.
Dry Weather Pattern Wet Weather Pattern
Time, hr
Flow at MH-1,
ft3/s Time, hr
Flow at MH-1, ft3/s
0.00 20 0.00 20
0.20 0 0.30 0
0.55 20 0.45 20
0.65 0 0.60 0
0.81 20 070 20
0.90 0 0.95 0
1.15 20 1.00 20
1.22 0 1.20 0
1.45 20 1.30 20
1.50 0 1.60 0
1.72 20 1.65 20
1.80 0 1.90 0
2.00 20 2.00 20
P-1 L = 2000 ft MH-1
Rim = 410 ft Invert = 400 ft
MH-2 Rim = 390 ft Invert = 380 ft
0-1 Rim = 330 ft Invert = 320 ft P-2
L = 6000 ft
Recall from Chapter 1 that there are four situations in which pressure flow occurs in sewer collection systems:
• Force mains – sewage is pumped along stretches where gravity flow is not feasible.
• Pressure sewers – each customer has a pump that discharges to the pressure sewer.
• Vacuum sewers – flow is pulled through the system by vacuum pumps.
• Surcharged gravity sewers – The depth of flow in a gravity pipe is above the crown because of downstream control.
Although gravity flow is generally the first choice in sewer networks, pressure flow is frequently encountered and models must be able to simulate pumping systems and the flow in pressure systems. Closed-conduit flow is governed by the continuity, energy, and momentum equations, as described in Chapter 2. With closed-conduit flow, pressure terms in the energy equations must be considered. Head losses are caused by pipe friction and also occur at pipe fixtures. Energy is added to the system by pumps.
This chapter reviews the basic principles of pressure hydraulics and pumping, which are frequently employed in sewer models.
4.1 Friction Losses
In pipe flow, shear stresses develop between the liquid and the pipe wall. The magni-tude of this shear stress is dependent upon the properties of the fluid, its velocity, the internal roughness of the pipe, and the length and diameter of the pipe.