Stormwater for the FE Civil Exam: Detention Storage, Routing and Water Quality

NCEES FE Civil spec: Water Resources and Environmental Engineering, F. Stormwater (e.g., detention, routing, quality). FE Reference Handbook: Civil Engineering chapter, Hydrology/Water Resources section (rational formula, NRCS runoff, weirs).

What the FE Civil Spec Covers

Section F is stormwater: detention, routing and quality. The common exam problem asks how much storage a basin needs so that post-development peak flow does not exceed an allowable release, usually the pre-development peak. You may also see a mass balance on a basin over a time step, outlet sizing with weir or orifice equations, and qualitative questions about best management practices.

Key Concepts

Continuity (storage equation): inflow minus outflow equals the rate of change of storage. Integrated over time, storage gained equals inflow volume minus outflow volume.
Maximum storage occurs when outflow equals inflow, which happens on the falling limb of the inflow hydrograph.
Outlet structures: orifices control small frequent storms; weirs or risers pass larger ones. Release rates follow $Q = C_{d} A 2 g h$ for an orifice and $Q = C L H^{3/2}$ for a weir.
Water quality: first-flush capture, extended detention, wet ponds, bioretention, swales and infiltration trenches remove sediment and attached pollutants.

Core Formulas

I - O = \frac{d S}{d t} Δ S = \frac{I _{1} + I _{2}}{2} Δ t - \frac{O _{1} + O _{2}}{2} Δ t

Triangular hydrograph method: inflow peak $Q_{i}$ , base time $t_{b}$ , outflow rising linearly to its peak $Q_{o}$ where it meets the inflow falling limb:

V_{s} = \frac{1}{2} t_{b} (Q_{i} - Q_{o})

Constant release rate (flat outflow line):

V_{s} = \frac{1}{2} t_{b} (1 - \frac{Q _{o}}{Q _{i}}) (Q_{i} - Q_{o})

Where It Is in the FE Reference Handbook

The handbook has no detention storage formula, so you build it from continuity and geometry. The inflow side comes from the rational formula or NRCS runoff and the outlet side from the weir and orifice equations, all in the Civil Engineering chapter, Hydrology/Water Resources section and the Fluid Mechanics chapter (orifice discharge).

Worked Example

A post-development triangular inflow hydrograph peaks at 40 cfs at 30 min and ends at 90 min. The allowable release (pre-development peak) is 15 cfs. Outflow rises linearly from zero and peaks when it meets the falling limb of the inflow. Find the required storage.

Step 1, apply the triangular method with $t_{b} = 90$ min = 5,400 s:

V_{s} = \frac{1}{2} (5400 s) (40 - 15) cfs = 67, 500 ft^{3}

Step 2, check by geometry. The falling limb is $I = 40 (90 - t) /60$ , which equals 15 cfs at t = 67.5 min. Inflow volume to that time is the total triangle minus the tail:

\frac{1}{2} (90) (40) - \frac{1}{2} (22.5) (15) = 1800 - 168.75 = 1631.25 cfs-min

Outflow volume to 67.5 min is a triangle:

\frac{1}{2} (67.5) (15) = 506.25 cfs-min

V_{s} = (1631.25 - 506.25) (60 s/min) = 67, 500 ft^{3} \approx 1.55 ac-ft

Answer: about 67,500 ft³ of detention storage. Both methods agree.

How FE Questions Are Framed

Read the outflow assumption carefully, because it changes the answer. If the basin releases at a constant permitted rate, the storage is the part of the inflow triangle above a horizontal line. If the outflow rises gradually from zero (an uncontrolled orifice or weir), use the triangular method above. If the problem gives tabulated inflow and outflow at even time steps, apply the mass balance step by step with average rates over each interval and add the storage changes.

Some problems start one step earlier and ask you to build the inflow peak with the rational method, or the runoff volume with the curve number method, for both pre- and post-development conditions. The allowable release is then the pre-development peak and the inflow is the post-development hydrograph. After the volume is known, the outlet is sized so that the orifice or weir passes the allowable release at the maximum stage in the basin.

Common Mistakes

Using the total inflow volume as the storage. The basin is releasing water the whole time.
Forgetting to convert minutes to seconds when multiplying by cfs or m³/s.
Taking the storage at the inflow peak instead of at the time outflow equals inflow.
Using instantaneous rates instead of averages over the time step in a basin mass balance.
Comparing the post-development peak with the wrong allowable release, such as a peak for a different return period.
Ignoring freeboard. The basin must hold the required volume below the emergency spillway crest.

Practice Problems

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

Runoff from a development produces a triangular inflow hydrograph with a peak of 6 m³/s and a total base time of 90 minutes. The downstream permit allows a constant release of 2 m³/s. The detention storage required is most nearly: See the worked solution or practice the Hydrology & Stormwater deck
Inflow to a basin exceeds outflow by a constant 1 m³/s for 30 minutes. What additional storage volume is required? See the worked solution or practice the Hydrology & Stormwater deck
A basin starts with 1,000 m³ of storage at t = 0. Measured inflows at t = 0, 300 and 600 s are 1, 3 and 2 m³/s; measured outflows at the same times are 0.5, 1.0 and 1.5 m³/s. Using trapezoidal integration of net flow, what is the maximum storage among the three tabulated times? See the worked solution or practice the Hydrology & Stormwater deck
Modified Puls routing uses Δt = 600 s and 2S₂/Δt + O₂ = 2S₁/Δt − O₁ + I₁ + I₂. At the start of the step S₁ = 300 m³, O₁ = 0.5 m³/s, I₁ = 0.5 m³/s and I₂ = 1.5 m³/s. The storage-outflow rating pairs (S in m³, O in m³/s) are (300, 0.50), (450, 0.75), (600, 1.00), (750, 1.25); interpolate linearly. Find S₂. See the worked solution or practice the Hydrology & Stormwater 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

How is required detention storage found on the FE exam?

Storage is the area between the inflow hydrograph and the outflow hydrograph up to the time they cross. With triangular hydrographs this is a simple triangle area, so most FE problems reduce to geometry.

What is the difference between detention and retention?

A detention basin stores runoff temporarily and releases it through an outlet at a controlled rate, then drains dry. A retention basin holds a permanent pool and loses water mainly by infiltration and evaporation.

How do stormwater ponds improve water quality?

Holding runoff long enough lets suspended solids and the pollutants attached to them settle out. Longer detention times, a permanent pool and vegetated outlets increase removal of sediment, phosphorus and metals.

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