Outflow Routing Calculator

This sample inflow series demonstrates a short storm pulse.

The routing core applies the level‑pool continuity equation over each time step:

• Continuity: S₂ = S₁ + ((I₁ + I₂)/2)·Δt − ((O₁ + O₂)/2)·Δt
• Linear storage model: S = K·O
• Power storage model: S = K·O^m

For the linear model, O₂ is solved algebraically. For the power model, O₂ is solved using a safe bisection search on the implicit equation.

1. Choose a time step that matches your hydrograph spacing.
2. Paste inflow data as time,inflow or one inflow per line.
3. Select a reservoir model and set K, plus m if needed.
4. Enter initial outflow and choose automatic or manual initial storage.
5. Click Calculate to view the routed table above the form.
6. Download CSV for spreadsheets or PDF for quick field reporting.

Use this practical article to interpret routed hydrographs and document design decisions.

Outflow routing is a core step in stormwater and temporary works design, especially where construction activities change runoff rates and surface roughness. A routing model converts an inflow hydrograph (the runoff entering a basin, manhole, pipe reach, or channel control) into an outflow hydrograph that reflects storage, throttling, and controlled release. This supports safer sizing of detention, sediment controls, cofferdams, and pump systems, and it provides traceable calculations for submittals.

The calculator applies level‑pool routing, which assumes the storage element has a single representative water surface for each time step. The continuity equation tracks how storage changes from one step to the next, while an assumed storage–outflow relationship links discharge to stored volume. In the linear option, storage is proportional to outflow through parameter K. In the power option, the exponent m shapes the response so outflow accelerates as storage rises. These relationships approximate outlet controls, weirs, or system constraints when a detailed stage–discharge curve is not available.

Good routing practice starts with a sensible time step. Use a spacing that captures the rise and recession of the inflow pulse; overly large steps can smear peak values and underestimate maximum storage. Next, calibrate K (and m when used) to match expected drainage behavior. For example, a longer K produces slower outflow response and typically increases peak storage. If the project has a hard capacity limit—such as a pump maximum, pipe surcharge threshold, or regulated release rate—enter a maximum outflow cap so the storage update follows continuity.

Always validate results with basic checks. Confirm that outflow lags inflow for detention behavior and that total outflow volume is close to total inflow volume when initial and ending storage are similar. If the mass balance is poor, reduce the time step, review initial conditions, or confirm that inflow values align with the chosen Δt. Document the final inputs and export the table to support review and field communication.

Example data (time index, inflow)

The series below represents a short storm pulse. Try Δt = 1 hour, Linear model, K = 3600, and O₀ = 0.

After routing, compare peak inflow versus peak outflow and record the maximum storage. Those two values typically drive outlet selection, freeboard checks, and temporary bypass planning during construction.

1) What is outflow routing used for on sites?

It predicts how runoff is delayed and released by basins, tanks, manholes, or controlled outlets. This helps size storage, set discharge limits, and document drainage compliance during construction.

2) When should I use the linear model?

Use it when you want a stable, quick approximation or when storage behaves roughly proportional to outflow. It is commonly applied for preliminary sizing and sensitivity checks.

3) When is the power model better?

Choose it when outflow increases nonlinearly with storage, such as orifice–weir combinations or systems that drain faster at higher heads. It provides added flexibility through exponent m.

4) How do I pick a time step Δt?

Match Δt to your inflow spacing and storm dynamics. Smaller steps capture sharper peaks and improve mass balance. If results look jagged or peak storage seems low, reduce Δt.

5) Why does outflow sometimes exceed inflow?

During the recession, stored water continues draining, so outflow can be higher than current inflow. If it happens during the rising limb, review K, Δt, and initial storage.

6) What does the maximum outflow cap represent?

It represents a physical or regulatory discharge limit, like pump capacity, outlet rating, or permitted release. When capped, the calculator updates storage directly from continuity to preserve mass balance.

7) How should I report results to reviewers?

Export the table, highlight peak inflow, peak outflow, peak reduction, and maximum storage. Include Δt, model choice, K and m values, and initial conditions so the routing is fully reproducible.