Reservoir Routing Calculator
Modified Puls (Storage-Indication) level-pool routing of a triangular inflow hydrograph through a reservoir with a broad-crested or ogee weir spillway. Returns peak outflow, peak headwater, attenuation, and time-lag — the four numbers a spillway capacity check needs.
Triangular hydrograph: rises linearly to Qp at Tp, recedes linearly to zero at Tb. Reservoir surface area is linear in head: A(h) = A₀ + (dA/dh)·h. Solver: 200 timesteps with Newton-Raphson on the spillway rating at each step.
How to use this calculator
Enter the reservoir surface area at spillway crest and how that area grows with depth above crest (you can read both off a stage-area curve). Enter spillway crest length and pick a coefficient — broad-crested for an earth or grass-lined emergency spillway, ogee for a designed concrete service spillway. Enter the design inflow hydrograph as peak flow, time to peak, and total base time (a triangular SCS-style hydrograph is a good first-pass approximation for the inflow design flood).
The calculator integrates the level-pool continuity equation for 200 timesteps using the Storage-Indication form, with Newton-Raphson at each step to solve the implicit equation O(H) = Cd·L·H^(3/2) for the new pool elevation. Output is the peak outflow, peak head over crest (which sets your required spillway capacity and freeboard), the attenuation percentage, and the outflow peak time.
When level-pool routing applies
Level-pool routing assumes a horizontal water surface — the entire reservoir is at one elevation at every instant. This holds when the reservoir's flow-through time is small relative to the inflow hydrograph rise time. For most flood-control basins, detention ponds, water-supply reservoirs < 5 miles long, and small impoundments, level-pool routing is the appropriate method.
For long, narrow reservoirs where significant wedge storage develops during a flood event, use a hydraulic routing method instead — Muskingum-Cunge for moderately steep reaches, or full unsteady-flow modeling (HEC-RAS, MIKE-11) for backwater-dominated systems.
Spillway coefficient reference
| Crest type | Cd (US) | Cd (SI) | Source |
|---|---|---|---|
| Broad-crested weir, square corners | 3.09 | 1.70 | Brater & King, Henderson |
| Broad-crested weir, rounded U/S corner | 3.30 | 1.82 | USBR DSD |
| Sharp-crested weir, fully aerated | 3.33 | 1.84 | Francis 1855 |
| Ogee crest, vertical U/S face, P/Hd ≥ 1.33, He = Hd | 3.95 | 2.18 | USACE EM 1110-2-1603 |
| Ogee crest, He = 1.33·Hd (5% over design) | 4.05 | 2.23 | USACE EM 1110-2-1603 |
| Ogee crest, He = 0.5·Hd | 3.55 | 1.96 | USACE EM 1110-2-1603 |
Source: USACE EM 1110-2-1603 (1992) Hydraulic Design of Spillways, Plate 3-1; USBR Design of Small Dams (1987) Chapter 9.
Worked example — small detention basin
Example — 25-yr storm through a 2-ac detention basin
Why outflow always lags inflow
When inflow exceeds outflow, the pool rises and storage builds. When inflow drops below the (now higher) outflow, the pool starts to fall. The outflow peaks at the instant inflow equals outflow on the falling limb — which by definition is after the inflow peak. The lag time depends on the storage-to-inflow-volume ratio: large storage relative to inflow gives long lag and high attenuation.
References: Chow, V.T., Maidment, D.R. & Mays, L.W. (1988). Applied Hydrology, Chapter 8. USACE EM 1110-2-1417 (1994), Flood-Runoff Analysis. USDA NRCS NEH-630, Chapter 17 (Flood Routing).
Related tools
- Ogee spillway discharge — pick a Cd at off-design heads
- Broad-crested weir — for emergency / auxiliary spillways
- Time of concentration — get Tp for the inflow hydrograph
- NRCS curve-number runoff — get the inflow volume
- Inflow design flood (IDF) — pick the design storm by hazard class