Engineering calculators · Wastewater

Clarifier and settling tank sizing calculator

Size a primary settling tank or a final (secondary) clarifier from average and peak flow. The calculator finds the area needed at the design overflow rates, rounds it to a practical diameter or length and width, and reports the actual overflow rate, retention time, weir loading and, for final tanks, the solids loading, a solids flux check using the state point method, and the ATV-DVWK-A 131 sludge volume loading and depth zones. Every result is checked against the ranges in WEF MOP 8 and Metcalf & Eddy.

Inputs

Typical design overflow rates: primary 30 to 50 m/d average and 80 to 120 m/d peak; final 16 to 28 m/d average and 30 to 40 m/d peak (WEF MOP 8, Metcalf & Eddy). Diameters are rounded up to 0.5 m; rectangular widths and lengths to 0.5 m. The RAS ratio is applied to both average and peak flow for the solids loading.

Results

Required area500 m²total, governed by peak flow; 250 m² per tank

2 × tank size18.0 m dia.254 m² each, 2,036 m³ total at 4 m deep

Actual SOR9.82 / 29.5 m/daverage / peak

Retention time9.77 h3.26 h at peak

Weir loading44.2 m³/m/d133 at peak, 56.5 m weir per tank

Solids loading2.51 kg/m²/h7.52 at peak; limiting flux 5.87 kg/m²/h

Average SOR of 9.82 m/d is within (or below) the 16 to 28 m/d range for final clarifiers.
Peak SOR of 29.5 m/d is at or below 40 m/d.
Average solids loading of 2.51 kg/m²/h is at or below 6 kg/m²/h.
Flux check: applied flux 2.51 kg/m²/h is below the limiting flux of 5.87 kg/m²/h (Daigger settling parameters for SVI 100).
Clarification check: mixed liquor settles at 2.76 m/h, above the peak overflow velocity of 1.23 m/h.
ATV-A 131 sludge volume loading of 430 L/m²/h at peak flow is within the 500 L/m²/h limit.
Sludge blanket check: ATV-A 131 depth zones total 3.80 m, within the 4 m side water depth.
Weir loading of 44.2 m³/m/d at average flow (133 at peak) is at or below 150 m³/m/d.

State point summary

State point at average flow: overflow velocity 0.409 m/h, underflow velocity 0.307 m/h, MLSS 3.50 g/L. Applied flux 2.51 kg/m²/h against a limiting flux of 5.87 kg/m²/h (42.7% loaded). The underflow concentration by mass balance is 8.17 g/L. Settling velocity of the mixed liquor 2.76 m/h against a peak overflow velocity of 1.23 m/h. ATV depth zones at peak: clear water 0.5 m, separation 1.65 m, thickening 0.451 m, storage 1.19 m, total 3.80 m.

Nearby tank sizes

The same flows in 2 tanks of a slightly different size, to see what a standard mechanism diameter or an existing tank would give.

Tank	Area each, m²	SOR avg, m/d	SOR peak, m/d	HRT avg, h	Weir, m³/m/d	SLR avg, kg/m²/h	ATV q_SV, L/m²/h
16.0 m dia.	201	12.4	37.3	7.72	49.7	3.17	544
17.0 m dia.	227	11.0	33.0	8.72	46.8	2.81	482
18.0 m dia.	254	9.82	29.5	9.77	44.2	2.51	430
19.0 m dia.	284	8.82	26.5	10.9	41.9	2.25	386
20.0 m dia.	314	7.96	23.9	12.1	39.8	2.03	348

How the calculation works

Hydraulic area. A = max(Q_avg/SOR_avg, Q_peak/SOR_peak). The surface overflow rate is the upflow velocity a particle must beat to settle, so the area rather than the depth sets removal [M&E] [MOP 8].
Solids flux (final tanks). Settling velocity follows Vesilind, v_s = v₀ e^−kX, with v₀ = 7.97 m/h and k = 0.168 + 0.00135 × SVI from Daigger's correlation [Daigger 1995]. The limiting flux is the minimum over X_i ≥ X of X_i(v_s(X_i) + u_r), where u_r = Q_r/A is the underflow velocity. The applied flux is (1 + R) Q X / A. The area is increased until applied ≤ limiting, which is the state point lying under the settling flux curve [Ekama et al.].
Tank size. Area per tank = required ÷ number of tanks. Circular: D = √(4A/π), rounded up to 0.5 m. Rectangular: W = √(A ÷ L:W), L = W × L:W, both rounded up to 0.5 m. All loadings are then recalculated on the rounded size.
Loadings. SOR = Q/A; solids loading = (1 + R) Q X / A; weir loading = Q ÷ total weir length (π D for a single perimeter weir, 2 π D for a double-sided inboard launder); HRT = A × depth ÷ Q.
ATV-DVWK-A 131 check. Sludge volume loading q_SV = q_A × X × SVI at peak flow, limited to 500 L/m²/h. Depth zones: clear water h₁ = 0.5 m; separation h₂ = 0.5 q_A(1 + R)/(1 − DSV/1000); thickening h₃ = 0.3 q_SV(1 + R)/500; storage h₄ = X q_A(1 + R) t_Th/X_BS with a thickening time of 2 h and bottom sludge X_BS = (1000/SVI) × t_Th^1/3 [ATV-A 131].

Worked example with the default inputs

Final clarifier, 5,000 m³/d average and 15,000 m³/d peak, two tanks, SOR 20 and 30 m/d, MLSS 3,500 mg/L, RAS 0.75, SVI 100. Area at average = 5,000/20 = 250 m²; at peak = 15,000/30 = 500 m², so peak governs and each tank needs 250 m²: D = √(4 × 250/π) = 17.8 m, rounded to 18.0 m (254 m² each). Actual SOR = 5,000/509 = 9.82 m/d average and 29.5 m/d peak. Solids loading = 1.75 × 5,000 × 3.5 / 509 / 24 = 2.51 kg/m²/h. Settling velocity at 3.5 g/L: k = 0.168 + 0.135 = 0.303 L/g, v_s = 7.97 e^−1.06 = 2.76 m/h, well above the peak upflow of 1.23 m/h. With u_r = 0.307 m/h the limiting flux is 5.87 kg/m²/h, so the state point is 42.7% loaded. Weir loading on a perimeter weir of π × 18.0 = 56.5 m per tank is 44.2 m³/m/d. ATV: q_SV = 1.23 × 350 = 430 L/m²/h; depth zones total 3.80 m against 4 m side water depth.

What this cannot tell you. It sizes the surface and checks the solids flux and depth, but it does not design the inlet (energy dissipation, flocculation well), the sludge collection mechanism, the hopper or the hydraulic profile. Settling parameters from an SVI correlation have a wide scatter; use measured zone settling velocities or a stirred SVI where the design is critical. Primary tank removal efficiency is not predicted; typical 50 to 65% TSS and 25 to 40% BOD at 30 to 50 m/d. Chemically enhanced primary treatment, lamella plates, and flow splitting between unequal tanks are outside the model.

Sources

Frequently asked questions

Why does peak flow govern the size of my final clarifier?

UK works are designed to pass 3 DWF (or Formula A) to full treatment, so the peak flow is often three times the average. With a peak SOR limit of 30 to 40 m/d, the area at peak exceeds the area at average flow with a 16 to 28 m/d limit. Storm flow also carries the solids flux to its highest value, which is why the solids loading and ATV sludge volume loading are checked at peak.

What is the solids flux check actually testing?

Solids leave a final clarifier only through the underflow (RAS and WAS), at a rate set by gravity settling plus the bulk downward velocity of the underflow. Flux theory finds the concentration at which this combined capacity is smallest, the limiting flux. If the solids applied per square metre exceed it, sludge accumulates and the blanket rises until it spills over the weirs. The settling parameters come from Daigger's SVI correlation; a measured zone settling curve is better when you have one.

How does the ATV-DVWK-A 131 method differ from the WEF and Metcalf and Eddy approach?

ATV sizes the tank on sludge volume loading (overflow rate times MLSS times SVI, limited to 500 L/m²/h for horizontal flow tanks) rather than solids flux, and sets the depth from four zones: clear water, separation, thickening and storage. It tends to give deeper tanks and larger areas when SVI is high. Both methods are shown here so the result can be defended against either design basis.

Can I use this for lamella or inclined plate settlers?

Not directly. Lamella units are rated on the projected plate area, so the effective SOR is 5 to 10 times the plan area value, and the flux and depth checks do not apply. See the lamella clarifier design article for that method.

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