Exercise set

Water and Wastewater Collection, Storage, and Wet-Weather Flow Exercises

Solved water and wastewater exercises for storage balance, I/I, peak flow, equalization, wet wells, overflow, sensor reconciliation and release gates.

Branch: Environmental Engineering
Content: Exercise set
Updated: Jul 03, 2026
Revision: v1.0.0 · reviewed

These exercises focus on collection-system flow, storage and wet-weather operating evidence. They cover storage balance, inflow and infiltration, peak-hour flow, equalization, basin drawdown, wet-well overflow, backup-power delay, overflow volume and sensor reconciliation.

Assume simplified screening calculations unless an exercise states otherwise. Field release should use calibrated flow meters, level sensors, rainfall data, pump status, overflow threshold, starting storage and downstream constraints.

Release Evidence Notes

Storage evidence must preserve the time basis. A tank can pass a one-hour event and fail a six-hour storm. The release package should state starting volume, usable volume, dead storage, outlet condition, overflow elevation and sensor uncertainty.

Wet-weather evidence should distinguish sanitary base flow from inflow, infiltration, stormwater cross-connection and groundwater response. A single peak number is weak unless the rainfall and monitoring boundary are clear.

Engineering Boundary Notes

These calculations do not replace hydraulic modeling, regulatory overflow reporting, collection-system inspection, pump-station commissioning or site-specific emergency response planning. They are screening exercises for release and operations decisions.

Scenario Map

Scenario	Exercises	Primary check	Engineering decision
Flow and wet weather	1, 2, 3, 9, 13	water balance, I/I, peaking and infiltration rate	Decide whether the collection system can pass the event.
Storage and overflow	4, 5, 6, 7, 10, 11, 12, 14	equalization, drawdown, wet-well time, first flush and overflow volume	Decide whether storage prevents release or surcharge.
Monitoring and release	8, 15, 16, 17, 18	level residual, sensor bias, reconciliation and gate evidence	Decide whether operating data support release.

Exercise 1: Storage Water Balance

A basin starts with $900\ \text{m}^3$ . Storm inflow is $0.18\ \text{m}^3/\text{s}$ and controlled outflow is $0.11\ \text{m}^3/\text{s}$ for $2$ hours. Compute final volume.

Solution

Net inflow:

Q_n=0.18-0.11=0.07\ \text{m}^3/\text{s}

Time:

t=2(3600)=7200\ \text{s}

Added volume:

\Delta V=0.07(7200)=504\ \text{m}^3

Final volume:

V_f=900+504=1404\ \text{m}^3

Engineering Comment

The starting volume is part of the evidence. A basin that is already partially full has less event capacity.

Plausibility Check

Seven hundredths of a cubic meter per second for two hours is about five hundred cubic meters.

Exercise 2: Wet-Weather Inflow and Infiltration

Dry-weather flow is $4200\ \text{m}^3/\text{d}$ . Wet-weather flow during a storm is $7600\ \text{m}^3/\text{d}$ . Estimate I/I flow and percentage of wet-weather flow.

Solution

Q_{II}=7600-4200=3400\ \text{m}^3/\text{d}

Percentage:

p=\dfrac{3400}{7600}=0.447=44.7\%

Engineering Comment

Nearly half the wet-weather flow is not base wastewater. That should trigger collection-system investigation or storage planning.

Plausibility Check

The storm adds a large flow compared with dry-weather conditions, so a high percentage is expected.

Exercise 3: Peak-Hour Sewer Flow

Average dry-weather flow is $95\ \text{L/s}$ . The peak-hour factor is $2.6$ . Estimate peak-hour flow.

Solution

Q_p=2.6(95)=247\ \text{L/s}

Engineering Comment

Peak factor should match the population, catchment and monitoring period. It should not be borrowed blindly from another system.

Plausibility Check

Multiplying about one hundred liters per second by about two and a half gives about two hundred fifty liters per second.

Exercise 4: Equalization Storage Requirement

Influent flow is $0.42\ \text{m}^3/\text{s}$ for $3$ hours while treatment can accept $0.30\ \text{m}^3/\text{s}$ . Find equalization volume required.

Solution

Q_n=0.42-0.30=0.12\ \text{m}^3/\text{s}

V=0.12(3)(3600)=1296\ \text{m}^3

Engineering Comment

This volume must be usable storage, not geometric volume hidden below pump cutoff or above overflow.

Plausibility Check

About one tenth of a cubic meter per second for several hours gives more than one thousand cubic meters.

Exercise 5: Basin Drawdown Time

A basin contains $1500\ \text{m}^3$ above normal level. Drawdown pump rate is $0.09\ \text{m}^3/\text{s}$ . Estimate drawdown time.

Solution

t=\dfrac{1500}{0.09}=16667\ \text{s}

Convert:

t=\dfrac{16667}{3600}=4.63\ \text{h}

Engineering Comment

Drawdown time matters if another storm can arrive before storage is recovered.

Plausibility Check

At less than one tenth cubic meter per second, removing fifteen hundred cubic meters takes several hours.

Exercise 6: Wet-Well Time to Overflow

A wet well has $42\ \text{m}^3$ volume between current level and overflow. Inflow is $0.035\ \text{m}^3/\text{s}$ and pumps are unavailable. Estimate time to overflow.

Solution

t=\dfrac{42}{0.035}=1200\ \text{s}=20\ \text{min}

Engineering Comment

Twenty minutes may be less than backup dispatch or power-transfer time. The alarm response should be checked.

Plausibility Check

At $0.035\ \text{m}^3/\text{s}$ , the wet well fills about two cubic meters per minute.

Exercise 7: Backup-Power Delay Storage Gate

Backup power starts after $8\ \text{min}$ . Inflow is $0.060\ \text{m}^3/\text{s}$ . Available wet-well storage is $35\ \text{m}^3$ . Check margin.

Solution

Volume accumulated:

V=0.060(8)(60)=28.8\ \text{m}^3

Margin:

M=35-28.8=6.2\ \text{m}^3

Engineering Comment

The gate passes, but only if starting level and inflow match the assumption.

Plausibility Check

Eight minutes at $0.06\ \text{m}^3/\text{s}$ is just under thirty cubic meters.

Exercise 8: Level-Sensor Balance Residual

A tank level change indicates storage increase of $260\ \text{m}^3$ . Flow meters report inflow $900\ \text{m}^3$ and outflow $620\ \text{m}^3$ . Compute residual.

Solution

Flow-based storage change:

\Delta V_f=900-620=280\ \text{m}^3

Residual:

R=280-260=20\ \text{m}^3

Engineering Comment

The residual may be acceptable or not depending on sensor uncertainty, bypasses and level-volume calibration.

Plausibility Check

The two independent estimates are close, differing by twenty cubic meters.

Exercise 9: I/I Rate per Sewer Length

Wet-weather I/I is $3400\ \text{m}^3/\text{d}$ over $28\ \text{km}$ of sewer. Compute I/I rate per kilometer.

Solution

r=\dfrac{3400}{28}=121.4\ \text{m}^3/(\text{d km})

Engineering Comment

Rate per length helps prioritize CCTV, smoke testing or rehabilitation areas, but local defects can dominate.

Plausibility Check

Dividing a few thousand cubic meters per day over a few dozen kilometers gives about one hundred per kilometer.

Exercise 10: First-Flush Capture Volume

A facility wants to capture the first $12\ \text{mm}$ of runoff from an impervious area of $2.5\ \text{ha}$ . Compute volume.

Solution

Area:

A=2.5\ \text{ha}=25000\ \text{m}^2

Depth:

d=12\ \text{mm}=0.012\ \text{m}

Volume:

V=Ad=25000(0.012)=300\ \text{m}^3

Engineering Comment

First-flush capture depends on runoff coefficient, bypass behavior and maintenance state.

Plausibility Check

One centimeter over twenty-five thousand square meters is a few hundred cubic meters.

Exercise 11: Overflow Volume

A wet well overflows for $18\ \text{min}$ at an estimated excess flow of $22\ \text{L/s}$ . Compute overflow volume.

Solution

Convert flow:

22\ \text{L/s}=0.022\ \text{m}^3/\text{s}

Time:

t=18(60)=1080\ \text{s}

Volume:

V=0.022(1080)=23.8\ \text{m}^3

Engineering Comment

Overflow reporting should document estimation method, duration, receiving water and uncertainty.

Plausibility Check

About one fiftieth cubic meter per second for about one thousand seconds gives about twenty cubic meters.

Exercise 12: Detention Volume from Hydrograph Excess

For a design storm, inflow exceeds outlet capacity by $0.05\ \text{m}^3/\text{s}$ for $70\ \text{min}$ . Estimate required detention volume.

Solution

t=70(60)=4200\ \text{s}

V=0.05(4200)=210\ \text{m}^3

Engineering Comment

This rectangular-excess approximation is only a screen. Detailed design should integrate the hydrograph.

Plausibility Check

Five hundredths of a cubic meter per second for a bit over an hour gives a few hundred cubic meters.

Exercise 13: Wet-Weather Peaking Ratio

Base flow is $0.12\ \text{m}^3/\text{s}$ and monitored wet-weather peak is $0.46\ \text{m}^3/\text{s}$ . Compute peaking ratio.

Solution

PF=\dfrac{0.46}{0.12}=3.83

Engineering Comment

A peaking ratio near four suggests strong wet-weather response or system inflow.

Plausibility Check

The peak is almost four times base flow.

Exercise 14: Dead Storage Allowance

A tank has geometric volume $1800\ \text{m}^3$ . Dead storage below outlet is $220\ \text{m}^3$ and freeboard reserve is $160\ \text{m}^3$ . Compute usable storage.

Solution

V_u=1800-220-160=1420\ \text{m}^3

Engineering Comment

Usable storage, not geometric volume, should be compared with storm or equalization demand.

Plausibility Check

Subtracting about four hundred cubic meters from eighteen hundred leaves about fourteen hundred.

Exercise 15: Sensor Bias Storage Error

A level sensor has bias $+25\ \text{mm}$ . Tank surface area is $900\ \text{m}^2$ . Estimate storage error.

Solution

\Delta h=25\ \text{mm}=0.025\ \text{m}

\Delta V=A\Delta h=900(0.025)=22.5\ \text{m}^3

Engineering Comment

Small level bias can create meaningful volume error in large tanks. Calibration evidence should be part of release.

Plausibility Check

One fortieth of a meter over nine hundred square meters gives a little over twenty cubic meters.

Exercise 16: Rainfall-Runoff Reconciliation

Rainfall over a $12\ \text{ha}$ catchment is $18\ \text{mm}$ . Runoff coefficient is $0.65$ . Estimate runoff volume and compare with measured inflow $1380\ \text{m}^3$ .

Solution

Area:

A=120000\ \text{m}^2

Depth:

d=0.018\ \text{m}

Runoff:

V=0.65(120000)(0.018)=1404\ \text{m}^3

Residual:

R=1404-1380=24\ \text{m}^3

Engineering Comment

The residual is small for storm monitoring, but calibration and catchment boundary should still be documented.

Plausibility Check

The measured inflow is close to the runoff estimate.

Exercise 17: Storage Evidence Completion

A storage release checklist requires $9$ records. Eight are accepted and one level calibration is conditional. The gate requires all accepted. Decide status.

Solution

Accepted percentage:

C=\dfrac{8}{9}=88.9\%

Because one record is conditional and all must be accepted, release is blocked.

Engineering Comment

Storage decisions depend directly on level calibration. Conditional calibration should not support release.

Plausibility Check

Any conditional item fails a one hundred percent acceptance rule.

Exercise 18: Collection and Storage Release Gate

A release gate requires I/I screen pass, storage pass, overflow screen pass, sensor reconciliation pass and evidence completion pass. Results are pass, pass, pass, fail and pass. Decide status.

Solution

The all-of gate fails because sensor reconciliation failed:

G=\text{blocked}

Engineering Comment

Hydraulic release should not proceed when the monitoring data do not reconcile with the storage claim.

Plausibility Check

One failed required gate blocks release.

Common Release Mistakes

Comparing storage demand with geometric volume instead of usable volume.
Ignoring starting tank level before a storm.
Treating I/I as constant without rainfall and groundwater context.
Reporting overflow volume without duration and uncertainty.
Accepting storage calculations with uncalibrated level sensors.
Mixing peak flow, average flow and event volume without time basis.

Validation Package Checklist

Flow, rainfall, level and pump-status data with calibration status.
Starting storage, usable storage, dead storage and overflow threshold.
I/I estimate with monitoring boundary and storm record.
Equalization, wet-well and backup-delay calculations with duration.
Sensor reconciliation and residual disposition.
Overflow estimate, receiving-water note and reporting basis.
Release authority and every checklist item accepted.

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