Stormwater and Urban Flood Resilience Exercises

These exercises practise first-pass calculations used in stormwater and urban flood resilience engineering. They connect rainfall, runoff, storage, infiltration, pipe hydraulics, flood barriers, pump reliability, pollutant load, freeboard, and maintenance risk.

Assume simplified nominal values unless an exercise states otherwise. Real stormwater design requires local rainfall data, catchment surveys, hydraulic modelling, asset condition, maintenance assumptions, downstream tailwater, water-quality criteria, public-safety requirements, and regulatory approval.

How to Use These Exercises

For each problem:

1. define the catchment, storm event, and system boundary;
2. state whether the calculation concerns frequent drainage service or exceedance routing;
3. keep units consistent between millimetres, hectares, square metres, seconds, and cubic metres;
4. distinguish hydraulic capacity from operational condition;
5. state the engineering action when capacity, freeboard, or evidence is insufficient.

The most common mistake is designing only the underground drainage network. When pipes surcharge or inlets block, water still moves. Flood resilience asks whether that movement is controlled.

For each result, state whether it supports minor-system capacity, major-system routing, storage sizing, infiltration feasibility, critical-asset protection, pump reliability, water-quality treatment, or maintenance trigger response. Stormwater calculations should identify where water goes when the nominal system is exceeded.

Exercise 1: Runoff Volume from a Design Storm

A commercial catchment has area A=12\ \text{ha}. A design storm has rainfall depth P_d=45\ \text{mm}. Use runoff coefficient C_r=0.72.

Estimate the runoff volume.

Solution

Convert area:

Convert rainfall depth:

Runoff volume:

Engineering Comment

The runoff coefficient compresses many physical details into one number: imperviousness, slope, soil condition, depression storage, antecedent moisture, and drainage connection. The result is useful for screening, not for final basin design by itself.

Exercise 2: Rational-Method Peak Flow

A small urban catchment has area A=18\ \text{ha}, runoff coefficient C_r=0.65, and design rainfall intensity i=75\ \text{mm/h}.

Using the metric rational-method form:

estimate peak runoff in \text{m}^3/\text{s}.

Solution

Peak flow:

Engineering Comment

This unit coefficient assumes i in \text{mm/h} and A in hectares. The rational method also assumes the rainfall duration is at least the time of concentration and that the catchment is small enough for the approximation to be meaningful.

Exercise 3: Detention Storage from a Discrete Hydrograph

A detention basin has one-minute-level telemetry summarized into five 15-minute intervals. The average inflow values are:

The controlled outflow is 1.0\ \text{m}^3/\text{s}. Use \Delta t=900\ \text{s}. Estimate the required storage as the maximum cumulative positive volume.

Solution

Storage increment:

For the five intervals:

Cumulative storage:

Required storage:

Engineering Comment

The storage calculation does not include freeboard, sediment storage, outlet blockage, emergency spillway, tailwater, or public-safety requirements. Those items can control the final geometry even when the hydraulic storage volume is known.

Exercise 4: Infiltration Drawdown

An infiltration basin has effective infiltration area A=1500\ \text{m}^2 and field-estimated infiltration rate f=8\ \text{mm/h}. After a storm, stored water volume is 420\ \text{m}^3.

Estimate how much volume can infiltrate in 24 hours and the remaining stored volume.

Solution

Convert infiltration rate:

Infiltration volume:

Remaining volume:

Engineering Comment

If the design requires drawdown within 24 hours, this basin does not meet the target under the assumed rate. Field tests, clogging allowance, groundwater separation, underdrain condition, and overflow routing should be reviewed.

Exercise 5: Pipe Velocity and Reynolds Number

A storm sewer pipe has diameter D=0.75\ \text{m} and carries Q=0.90\ \text{m}^3/\text{s} when flowing full. Use water density \rho=1000\ \text{kg/m}^3 and dynamic viscosity \mu=0.001\ \text{Pa s}.

Find average velocity and Reynolds number.

Solution

Pipe area:

Velocity:

Reynolds number:

Engineering Comment

The flow is strongly turbulent. Velocity should also be checked against sediment transport, erosion risk, outlet protection, noise, air entrainment, manhole losses, and downstream capacity.

Exercise 6: Hydrostatic Force on a Flood Barrier

A temporary flood barrier protects an underground station entrance. The design water depth against the barrier is H=0.80\ \text{m} and the barrier width is b=2.0\ \text{m}. Use \gamma_w=9.81\ \text{kN/m}^3.

Estimate the hydrostatic force on the barrier.

Solution

Resultant force on a vertical rectangular barrier with triangular pressure:

The resultant acts at:

above the base.

Engineering Comment

The barrier check must include anchorage, leakage, impact, debris, installation tolerance, door-frame capacity, emergency access, and the possibility that water depth exceeds the assumed value.

Exercise 7: Redundant Pump Availability

A stormwater pump station has two independent pumps in parallel. Each pump has estimated availability A=0.96 during the design operating window.

Estimate the simplified parallel availability.

Solution

For two independent parallel components:

Engineering Comment

This result excludes common-cause failures. A flood can disable both pumps if they share power, controls, wet-well blockage, access, maintenance error, or telemetry failure. Resilience review should check backup power and physical separation.

Exercise 8: Pollutant Load During First Flush

During a first-flush period, flow is Q=0.35\ \text{m}^3/\text{s} and pollutant concentration is C=80\ \text{mg/L} for 20 minutes.

Estimate total pollutant load.

Solution

Convert concentration:

Convert time:

Pollutant load:

Engineering Comment

Concentration without flow does not define load. Water-quality decisions should use flow-weighted sampling, event timing, sediment fraction, receiving-water sensitivity, and treatment-system bypass conditions.

Exercise 9: Freeboard with Uncertainty

An overland flow route is predicted to reach water level 0.38\ \text{m} above street grade at a critical doorway. The doorway sill is 0.45\ \text{m} above street grade. Model uncertainty is estimated as \pm0.10\ \text{m}.

Find the nominal freeboard and state whether the uncertainty range includes doorway flooding.

Solution

Nominal freeboard:

Upper water-level estimate:

Since:

the uncertainty range includes possible doorway flooding.

Engineering Comment

The nominal result looks acceptable, but uncertainty changes the decision. The design may need more freeboard, a local threshold, modified grading, a flood barrier, or a verified overflow route away from the opening.

Exercise 10: Blocked-Inlet Risk Priority

A flood-risk review scores the failure mode “critical inlet blocked before storm peak” as:

A maintenance and monitoring plan reduces the occurrence ranking to O=3 and detection ranking to D=2.

Find the initial and revised risk priority numbers.

Solution

Initial:

Revised:

Reduction:

Engineering Comment

The reduction is credible only if inspection, cleaning, telemetry, and response authority are actually in place before storms. Blockage risk is operational as much as hydraulic.

Review Checklist

Before accepting a stormwater screening calculation, check:

• whether the catchment boundary and design event are defined;
• whether runoff, storage, infiltration, and outlet control use consistent units;
• whether pipe capacity is separated from inlet, blockage, and tailwater performance;
• whether water quality is evaluated as load, not concentration alone;
• whether pump redundancy includes common-cause failures;
• whether freeboard accounts for model uncertainty and critical openings;
• whether overland flow routes remain safe when the minor drainage system is exceeded;
• whether inlet blockage, debris, sediment, tailwater, power loss, access, and common-cause pump failure are included in resilience claims;
• whether post-storm telemetry, inspection, high-water marks, and maintenance records are used to update the model;
• whether maintenance and monitoring are connected to named actions.

Good flood resilience does not claim that flooding will never occur. It gives excess water a controlled path, protects critical assets, and preserves evidence so the model improves after real storms.