Detention pond sizing calculator

How pond routing works: the storage indication method

A detention pond reduces a flood peak by holding water while the inflow exceeds what the outlet can release, then letting it go over a longer period. The routing rests on one equation, conservation of volume:

Written over a time step $\Delta t$, with inflow and outflow averaged across the step and the unknowns gathered on the left, it becomes the storage indication form used by the Modified Puls method:

Everything on the right is known at the start of each step. Storage and outflow both depend only on the water level, so $2S/\Delta t + O$ can be tabulated once against elevation. Each step then reads the new water level off that table and interpolates $S_2$ and $O_2$ from it, with no iteration. This assumes a horizontal water surface across the pond (level-pool routing), which holds for detention ponds and compact reservoirs.

The method needs three inputs: the stage-storage curve, the stage-discharge curve of the outlets, and the inflow hydrograph.

Stage-storage-discharge inputs

Storage

The calculator builds the stage-storage curve in one of three ways:

For a trapezoidal pond with floor $L \times W$ and side slope $z$, the volume to depth $h$ is $V = LWh + (L+W)zh^2 + \tfrac{4}{3}z^2h^3$.

Outlets

Total outflow at any level is the sum of every outlet that is active at that level. Seven outlet types can be combined in any number:

$Q$ is outflow (m³/s), $A$ the orifice area (m²), $L$ the weir crest length (m), $H$ the head over the crest (m), $w$ and $a$ the gate width and opening (m) and $g$ = 9.81 m/s². While the water is below the crown of an orifice, the opening runs part-full and is rated as a weir, $Q = Q_{crown}(y/D)^{1.5}$, so the rating has no step at the crown.

Where the inputs come from

• Inflow hydrograph. The post-development design hydrograph for the site, as a time-discharge table. Generate it with the unit hydrograph generator, driven by a storm from the design storm generator. A constant inflow (a rectangular pulse) is also accepted for a first, conservative estimate.
• Release target. Usually the pre-development peak for the same return period, for example from the rational method calculator, or the capacity of the receiving pipe or channel. Many South African municipalities set it instead as a release rate in litres per second per hectare.
• Pond shape. From the site layout, a contour plan or a survey. Side slopes of 3H:1V or flatter suit mowable earth banks; many South African municipalities require 4H:1V where the public has access.
• Outlet levels. Crest and invert elevations on the same datum as the pond floor. A datum mismatch produces plausible numbers that mean nothing.

Worked example

A developed site produces a triangular 1:50-year inflow hydrograph: 0 m³/s at 0 min, a peak of 3.0 m³/s at 20 min, and back to zero at 60 min, a volume of 5 400 m³. The release target is the pre-development peak of 1.0 m³/s.

The outlet is a standpipe: a 450 mm base orifice with its invert on the pond floor (100.00 m, $C_d$ = 0.61) and a 900 mm riser with its crest at 101.40 m, giving a crest perimeter of 2.83 m. The pond is trapezoidal, 2.0 m deep, with 3H:1V side slopes. Time step: 1 minute.

Trial 1: 40 m × 20 m floor (2 416 m³ to the top of the bank). Peak outflow is 1.85 m³/s, a 38.3% reduction. The water rises to 101.96 m, 40 mm below the bank. The pond fails the target and very nearly overtops.

Auto-size does the search for you. From this trial, with a 1.0 m³/s target, it returns a 62.11 m × 31.06 m floor (2.41 times the floor area, same depth and side slopes) that peaks at 1.00 m³/s with the water at 101.61 m. Trial 2 rounds that up to whole metres.

Trial 2: 64 m × 32 m floor (5 344 m³ to the top of the bank). The stage-storage-discharge table, with the storage indication value at $\Delta t$ = 60 s:

Above about 101.74 m the riser crest stops behaving as a weir: the 900 mm barrel runs full and its own orifice capacity limits the flow, which is why the crest column grows more slowly at the top. The design level of this example stays below that.

Routing gives:

The 64 m × 32 m pond meets the 1.0 m³/s target. The next steps are to route the smaller return periods against their own pre-development peaks, and to set an emergency spillway crest between the 1:50-year level of 101.58 m and the bank.

Orifice discharge coefficients

A standpipe’s base orifice is pre-filled with $C_d$ = 0.6. Change it when the outlet geometry calls for it:

A trash screen over an orifice reduces its effective area. Lowering $C_d$ by 10–20%, or entering a measured rating, accounts for it. For weir coefficients by weir type, see the weir flow calculator.

Channel routing: Muskingum and Muskingum-Cunge

The same tool routes a hydrograph along a channel reach instead of through a pond. Muskingum takes a storage constant $K$ and weighting factor $X$ (0 to 0.5) and computes the outflow from

with $C_0 = (\Delta t - 2KX)/D$, $C_1 = (\Delta t + 2KX)/D$, $C_2 = (2K(1-X) - \Delta t)/D$ and $D = 2K(1-X) + \Delta t$. The calculator checks the stability window $2KX \le \Delta t \le 2K(1-X)$ and can split the reach into sub-reaches. Muskingum-Cunge derives $K$ and $X$ from reach length, slope, Manning’s $n$ and a trapezoidal, rectangular or circular cross-section, so it needs no calibration data.

Limitations

• Level-pool routing assumes a flat water surface. Long, narrow reservoirs where the surface slopes during a flood need dynamic routing.
• One storage element per run. Ponds in series are routed one after the other, using each outflow as the next inflow.
• Simple weir outlets assume free discharge. If tailwater can drown the crest, define the weir as submerged (the Villemonte correction) through the weir calculator, or enter a rating table.
• The run extends to 1.5 times the last time in the inflow table. To see the pond drain fully, add zero-flow rows to the end of the inflow table; until it drains, outflow volume will be less than inflow volume.
• If the water level exceeds the top of the stage-storage curve, the result is flagged as over capacity. Treat it as a failed design, not as attenuation.
• Evaporation, seepage and baseflow are ignored. Add any significant baseflow to the inflow table.
• Embankment breach is not modelled. For spillway adequacy and dam classification, use dam safety evaluation.
• The Modified Att-Kin channel method is not yet available; use Muskingum-Cunge instead.

What the full Studio tool adds

The Studio tool, named Flood Routing, runs both reservoir and channel routing in one workspace. It draws the inflow and outflow hydrographs and the storage curve, tabulates the stage-discharge rating and the flow through each outlet at every time step, and for known-geometry ponds draws a cross-section and plan view. Weirs import from a saved weir analysis and culverts from a saved culvert calculator design, so the outlet hydraulics in the pond match the structure you sized elsewhere. Auto-size finds the smallest pond that holds the flood and meets a target peak outflow, scaling a known-geometry pond’s floor length and width (or every row of an elevation-area or elevation-volume table) and leaving the depth and outlets as entered. Designs save to a project, export the routing time series, storage curve and summary to CSV, and produce a Word, Excel or PDF report.