Wastewater and Stormwater Collection Systems (FE Civil)

NCEES FE Civil spec: Water Resources and Environmental Engineering, G. Collection systems (e.g., wastewater, stormwater). FE Reference Handbook: Civil Engineering chapter, Hydrology/Water Resources section (Manning, sewage flow ratio curves, partial flow graph).

What the FE Civil Spec Covers

Section G of the Water Resources and Environmental Engineering area is about collection systems: the gravity pipes, manholes, lift stations and force mains that carry wastewater to a treatment plant and stormwater to a receiving water. Expect short calculation problems on design flow, pipe capacity with the Manning equation, slope from invert elevations, self-cleansing velocity and partially full pipes, plus a few conceptual questions about separate versus combined systems and infiltration and inflow.

Key Concepts

Sanitary, storm and combined sewers. Sanitary sewers carry domestic and industrial wastewater. Storm sewers carry runoff. Combined sewers carry both and can overflow (CSOs) during storms, which is why new systems are built separate.
Infiltration and inflow (I/I). Infiltration is groundwater leaking in through joints and cracks. Inflow is direct entry of stormwater from roof leaders, cross connections or manhole covers. Both add to the design flow of a sanitary sewer.
Design flow. Sanitary sewers are sized for peak flow: average per capita flow times population times a peaking factor, plus I/I. Storm sewers are usually sized with the rational method.
Velocity limits. A minimum of about 0.6 m/s (2 ft/s) keeps solids moving; a maximum of roughly 3 m/s (10 ft/s) limits scour of the pipe.
Layout. Gravity pipes follow the ground slope where possible. Manholes go at every change in grade, direction or pipe size and at regular spacing for cleaning. Where gravity flow is not possible, a lift station pumps flow through a pressurized force main.

Core Formulas

Manning equation (SI, then US customary with Q in cfs):

Q = \frac{1}{n} A R^{2/3} S^{1/2} Q = \frac{1.486}{n} A R^{2/3} S^{1/2}

For a circular pipe flowing full, $A = π D^{2} /4$ and the hydraulic radius is $R = A / P = D /4$ . At exactly half full, R is also D/4, so the velocity equals the full-flow velocity and the discharge is half the full-flow discharge.

Pipe slope from invert elevations over a horizontal length L:

S = \frac{invert _{u p} - invert _{d o w n}}{L}

Harmon peaking factor, with P the population in thousands:

P F = \frac{Q _{p e ak}}{Q _{a v g}} = 1 + \frac{14}{4 + P}

Rational method for storm sewer inlets (US units: Q in cfs, i in in/hr, A in acres):

Q = C i A

Where It Is in the FE Reference Handbook

Search the Civil Engineering chapter, Hydrology/Water Resources section. It has the Manning equation, the sewage flow ratio curves (peak to average flow versus population), the hydraulic element graph for partially full circular sewers, and the rational formula. Manning n values are tabulated in the Fluid Mechanics chapter.

Worked Example: Sizing a Sanitary Sewer

A subdivision of 8,000 people produces an average of 400 L per person per day. Ignore I/I. Use the Harmon peaking factor, n = 0.013 and a slope of 0.004. Choose the smallest of 300, 375 or 450 mm that carries the peak flow flowing full, and check the self-cleansing velocity.

Step 1: Average flow.

Q_{a v g} = \frac{8000 \times 400 L/d}{1000 \times 86 , 400 s/d} = 0.0370 m^{3} / s

Step 2: Peak flow. P = 8 (thousand people).

P F = 1 + \frac{14}{4 + 8} = 3.05 Q_{p e ak} = 3.05 \times 0.0370 = 0.113 m^{3} / s

Step 3: Full-flow capacity of 375 mm. A = 0.1104 m², R = 0.375/4 = 0.0938 m.

Q_{f u l l} = \frac{1}{0.013} (0.1104) (0.0938)^{2/3} (0.004)^{1/2} = 0.111 m^{3} / s < 0.113

The 375 mm pipe is just short, so try 450 mm: A = 0.1590 m², R = 0.1125 m.

Q_{f u l l} = \frac{1}{0.013} (0.1590) (0.1125)^{2/3} (0.004)^{1/2} = 0.180 m^{3} / s > 0.113 ✓

Step 4: Velocity check.

V_{f u l l} = \frac{Q _{f u l l}}{A} = \frac{0.180}{0.1590} = 1.13 m/s \geq 0.6 m/s ✓

Use a 450 mm sewer. At peak flow it runs at Q/Q_full = 0.113/0.180 = 0.63, and the hydraulic element graph would give the actual depth and velocity at that ratio.

Common Mistakes

Sizing for average flow instead of peak flow plus I/I.
Using R = D/2 for a full pipe. The hydraulic radius of a full circular pipe is D/4.
Using 1.486 with SI units or 1.0 with US units in the Manning equation.
Entering P in the Harmon formula as the full population instead of thousands.
Computing slope with station distance in stations (100 ft) instead of feet.

Practice Problems

Try these from the free PolyCalc FE Civil problem bank. Each one has a full worked solution.

A 400 mm diameter circular sanitary sewer with Manning roughness n = 0.013 flows half full. To maintain a self-cleansing velocity of 0.9 m/s, the minimum slope is most nearly: See the worked solution or practice the Fluids & Hydraulics deck
A 300 mm concrete sewer (n = 0.013) is laid at a slope of 0.005 and flows full. Using Manning's equation, its capacity is most nearly: See the worked solution or practice the Environmental & Water Quality deck
A sewer profile shows an invert of 102.50 ft at station 10+00 and 101.50 ft at station 12+00. The pipe slope is: See the worked solution or practice the Construction & Scheduling deck
At a pipe junction, 0.30 m³/s and 0.20 m³/s flow in from two pipes and 0.15 m³/s flows out in a third. The flow in the fourth pipe, which leaves the junction, is: See the worked solution or practice the Fluids & Hydraulics deck
Using the rational method Q = 0.278CIA, estimate peak runoff for C = 0.60, rainfall intensity I = 50 mm/hr, and drainage area A = 2 km². See the worked solution or practice the Hydrology & Stormwater deck

Related Calculators and Examples

Frequently Asked Questions

What is the minimum velocity in a sanitary sewer?

Gravity sanitary sewers are normally designed for a self-cleansing velocity of at least about 0.6 m/s (2 ft/s) so that solids do not settle out. Because a circular pipe flowing half full has the same hydraulic radius as one flowing full, its velocity is the same in both cases.

Why do sanitary sewers use a peaking factor?

Wastewater flow varies through the day, so pipes are sized for the peak flow, not the average. The peak is found by multiplying the average flow by a peaking factor that gets smaller as the population served gets larger, for example from the Harmon formula or a flow ratio curve.

Is a sewer sized to flow full on the FE exam?

Most FE problems compare the design peak flow with the full-flow capacity from Manning, then use the partial flow graph if they ask for the actual depth or velocity. Read the problem: some state a maximum depth ratio such as half full.

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