Storm tanks are the front line of the UK’s spill reduction obligations, and a badly designed one fails in three ways at once: it silts up, it smells, and it lets the dirtiest part of the storm straight past. All three trace back to hydraulics.
Weir hydraulics
Discharge over a sharp-crested rectangular weir follows the standard relation:
Q = Cd · (2/3) · √(2g) · L · H3/2Cd ≈ 0.62 for a sharp crest; L = weir length (m); H = head above crest (m)
The three-halves power is what makes weir design unforgiving: doubling the discharge needs only a 59 per cent increase in head, so a modest rise in level passes a great deal more flow than intuition suggests — and a weir that drowns loses that relationship entirely.
| Weir type | Cd | Behaviour | Use |
|---|---|---|---|
| Sharp-crested rectangular | ≈0.62 | Efficient, predictable; vulnerable to debris and to drowning | Small tanks, clean flows |
| Vortex | ≈0.45 | Lower coefficient, but self-cleaning and tolerates high head without drowning; the central air core prevents negative pressure and cavitation | Large CSOs with debris |
Sediment: self-cleansing or not
Whether a tank silts depends on the balance between the bed shear stress the flow generates and the critical shear stress needed to move cohesive sewer sediment, typically 0.5–2.0 N/m².
τb = ρgRSfR = hydraulic radius (m); Sf = friction slope
- Hydraulic radius: R = (10 × 3) / (10 + 2×3) = 30/16 = 1.875 m.
- Bed shear stress: τb = 1000 × 9.81 × 1.875 × 0.001 ≈ 18.4 N/m².
- Against a critical shear of 0.5–2.0 N/m², this comfortably scours — while flowing.
The qualifier matters more than the number. That shear exists during filling and emptying, when the tank is conveying. Between storms the tank is a still pond and everything in suspension settles. Self-cleansing geometry reduces the deposition rate; it does not eliminate the need to manage sediment.
Deposition accumulates across storms in proportion to the solids that were not carried out:
hdep = n · (1 − ηsettling) · Css · Vstorm / Atankn = number of storms; Css = suspended solids in storm flow
Practical rules: hold a longitudinal slope above about 0.0005, and design flushing or jetting into any tank with long quiescent periods. Grit behaviour is covered in grit removal systems, odour consequences in hydrogen sulphide control.
First flush — and what the number actually means
The first flush is the disproportionate pollutant load carried in the opening part of a storm. Cumulative mass is simply the integral of concentration against flow:
M(t) = ∫0t C(t) · Q(t) dt
- Mass fraction — the share of total pollutant mass in the first 30 per cent of volume. This is a fraction, so it cannot exceed 1. UK combined sewers typically fall in the range 0.45–0.90.
- Enrichment ratio — that mass fraction divided by the volume fraction (0.30). Typically 1.5–3.0.
They describe the same behaviour: 30 per cent of the volume carrying 45–90 per cent of the mass is an enrichment of 1.5 to 3. A ratio quoted as though it were a fraction, or vice versa, will size a tank wrongly by a factor of three — so state which one you mean.
Capture volume
Sizing follows from the flow you intend to intercept and how long the enriched portion lasts:
- Intercepted flow: 6 × 0.5 = 3 DWF.
- Volume: 3 DWF × 0.5 h = 1.5 DWF-hours.
Typical UK combined sewer practice lands at 1–2 DWF-hours. Note that the enrichment figure informs whether first-flush capture is worth designing for — a weakly enriched catchment gains little — but it does not multiply the volume; the volume follows from flow and duration.
Real-time control
A passive tank fills when the level rises and spills when it is full. That wastes capacity, because it cannot distinguish the beginning of a storm from the end.
- Level-triggered overflow — hold the spill until the tank reaches around 80 per cent, so the enriched early flow is retained rather than displaced.
- Weather radar — two to four hours of rainfall forecast allows a tank to be emptied to the works ahead of the event, presenting an empty tank to the first flush instead of a half-full one.
- Predictive control — estimating first-flush volume from antecedent dry weather period and forecast intensity, so the split between treat and store is set before the storm rather than during it.
Reported gains are of the order of 20–30 per cent additional capture over passive operation, for control investment rather than concrete — which is why it usually appears first in any options appraisal. The catchment-scale picture is in storm overflow spill reduction and sewer network hydraulic modelling; the surface-water side in SuDS and discharge consents.
Design rules
- Vortex weirs on anything carrying debris. The lower discharge coefficient buys self-cleaning and drowning tolerance.
- Longitudinal slope above 0.0005 for self-cleansing during filling and emptying — and design flushing anyway.
- 1–2 DWF-hours of capture volume for a typical UK combined sewer.
- State whether your first-flush figure is a fraction or a ratio. Confusing the two mis-sizes the tank threefold.
- Cost real-time control before more concrete. A 20–30 per cent capture gain from instrumentation is almost always cheaper than the equivalent volume.
Frequently asked questions
What is the difference between FF50 as a fraction and as a ratio?
The mass fraction is the share of pollutant mass in the first 30 per cent of storm volume — typically 0.45 to 0.90, and by definition never above 1. The enrichment ratio divides that by the volume fraction, giving 1.5 to 3.0. Both describe the same behaviour, but quoting one as though it were the other will mis-size a tank by roughly a factor of three.
If the shear stress calculation shows self-cleansing, why do tanks still silt?
Because that shear only exists while the tank is conveying flow. Between storms it is a still pond, and anything in suspension settles. Self-cleansing geometry slows accumulation; it does not remove the need for jetting or flushing, particularly on tanks with long dry periods.
Why accept a lower discharge coefficient with a vortex weir?
Because a sharp-crested weir fails badly when it blocks — it surcharges upstream and spills somewhere unplanned. A vortex weir self-cleans, tolerates high head without drowning, and its central air core prevents the negative pressures that cause cavitation. On a CSO carrying rag and gross solids that reliability outweighs the efficiency.
How much capture volume does a UK storm tank need?
Typically 1 to 2 DWF-hours for a combined sewer. The figure follows from the flow you intend to intercept and how long the enriched portion of the storm lasts — not from the first-flush enrichment itself, which tells you whether the exercise is worthwhile rather than how big the tank should be.