Calculator Inputs
Example Data Table
Use this sample inflow hydrograph to verify the calculator quickly.
| Time (hours) | Inflow (m3/s) |
|---|---|
| 0 | 10 |
| 1 | 25 |
| 2 | 45 |
| 3 | 60 |
| 4 | 40 |
| 5 | 25 |
| 6 | 15 |
Formula Used
Muskingum (channel routing)
Storage is approximated as S = K [X·I + (1−X)·O]. The routed outflow uses:
C0 = (Delta t − 2KX) / (2K(1−X) + Delta t)
C1 = (Delta t + 2KX) / (2K(1−X) + Delta t)
C2 = (2K(1−X) − Delta t) / (2K(1−X) + Delta t)
Use consistent time units for K and Delta t.
Storage indication (Modified Puls)
The continuity equation is solved implicitly using a stage-based curve:
The calculator builds a storage-indication table (2S/Delta t + O) vs stage and interpolates to find S2 and O2.
How to Use This Calculator
- Pick a routing method based on your system: reach (Muskingum) or basin (storage routing).
- Enter a routing interval Delta t and keep your hydrograph steps consistent.
- Paste the inflow hydrograph. Use "time,inflow" or just "inflow".
- For Muskingum, set K and X (and optional O0).
- For storage routing, provide stage-storage and stage-discharge curves plus an initial stage.
- Press Submit to see results, then export CSV/PDF for documentation.
Design applications on construction sites
Flood routing supports sizing of temporary diversions, cofferdams, culverts, and detention basins. Enter a design inflow hydrograph from rainfall-runoff modeling or upstream gauge data. The calculator routes the wave to estimate downstream peak flow, peak attenuation percent, and timing lag. These outputs help set safe freeboard, plan pump capacity, and reduce overtopping risk during critical pours and earthworks.
Input data and interval control
Use a constant routing interval (Delta t) that matches your hydrograph resolution. If your inflow points are hourly, keep Delta t = 1 hour; if you use 15-minute data, keep Delta t = 15 minutes. Shorter intervals improve peak definition but increase steps. Ensure consistent flow units (m3/s, cfs, etc.) across inflow and any rating curves. Verify missing values before routing runs.
Muskingum parameter selection
Muskingum is suited to channel or reach routing where storage depends on inflow and outflow. K represents travel/storage time and should be in the same time unit as Delta t. X typically ranges 0.0 to 0.3 and must not exceed 0.5. The tool computes coefficients C0, C1, C2 and produces outflow and reach storage each step.
Storage routing for basins and structures
For ponds, basins, and control structures, the storage indication method uses stage-storage and stage-discharge curves. Provide at least two rows for each curve, spanning expected stages. The calculator builds a (2S/Delta t + O) table and interpolates to find the next stage, storage, and outflow. This is useful for temporary detention, sediment basins, and outlet checks.
Interpreting results and documenting decisions
Review the summary: peak inflow, peak outflow, time of peaks, lag, and routed volumes (flow·s). A large lag indicates delayed downstream impact; a high attenuation indicates effective storage. Export the results table to CSV for design notes and to PDF for submittals, daily reports, and client approvals, keeping assumptions and input tables attached. Where possible, compare routed peaks to permit limits and update erosion controls accordingly.
FAQs
1) Which routing method should I choose?
Use Muskingum for channel or reach routing where storage is related to inflow and outflow. Use storage routing for basins, ponds, or structures where stage-storage and stage-discharge curves represent behavior.
2) What does K mean in Muskingum routing?
K is a travel/storage time constant for the routed reach. Keep K in the same time unit as the routing interval. If K is too small, the outflow will closely follow inflow with minimal lag.
3) Why is X limited to 0.5?
X is a weighting factor that balances inflow and outflow in the storage approximation. Values above 0.5 can produce unstable coefficients and unrealistic oscillations. Practical projects often use 0.0 to 0.3.
4) Do my inflow times have to match Delta t exactly?
Yes, for best accuracy. If your time steps vary, resample the hydrograph to a constant interval first. The calculator will still run, but it assumes the entered routing interval when computing updates.
5) How should I format stage curves for storage routing?
Provide two-column pairs as “stage, value” on each line. Stage-storage uses stage and storage; stage-discharge uses stage and outflow. Curves should cover the expected stage range to reduce extrapolation.
6) What do the exported “flow·s” volumes represent?
They are the trapezoidal integral of flow over time using seconds internally. If your flow unit is m3/s, the result equals cubic meters. For other units, it represents unit-consistent flow multiplied by seconds.