Clarifier Surface Solids Loading Calculator

Calculator overview

Inputs and outputs

This summary comes from the calculator's published input and output contract.

Inputs

CLR Return Activated Sludge Flow Conditional: About this input

Return activated-sludge flow included only in secondary activated-sludge solids loading; hidden and inert in single-stream mode.

Unit MGD Default 3.8 Range At least 0
CLR Length Conditional: About this input

Nonnegative inside plan length of one rectangular clarifier; hidden and inert in other geometry modes. Zero returns NOT VALID when active.

Unit ft Default 100 Range At least 0
CLR Geometry Mode: About this input

Enter surface area directly or calculate identical per-unit area from circular or rectangular dimensions.

Default Circular clarifiers Allowed Area per clarifier, Circular clarifiers, Rectangular clarifiers
Mixed liquor suspended solids (MLSS): About this input

Suspended-solids concentration applied to the active solids-bearing flow.

Unit mg/L Default 2500 Range At least 0
CLR Width Conditional: About this input

Nonnegative inside plan width of one rectangular clarifier; hidden and inert in other geometry modes. Zero returns NOT VALID when active.

Unit ft Default 50 Range At least 0
CLR Unit System: About this input

Select one internally consistent set of displayed flow, length, area, mass, and loading units.

Default US customary Allowed US customary, Metric
CLR Solids Loading Basis: About this input

Secondary mode uses forward plus return activated-sludge flow; single-stream mode uses forward flow only.

Default Secondary activated sludge Allowed Secondary activated sludge, Single solids-bearing stream
CLR Comparison Mode: About this input

Calculate only, or compare both loading results with user-entered criteria.

Default Calculate only Allowed Calculate only, Compare with entered reference
CLR Clarifiers In Service: About this input

Positive whole number of identical units sharing the entered flow.

Unit clarifiers Default 2 Range At least 1
CLR Area Per Clarifier Conditional: About this input

Nonnegative plan surface area for one clarifier; hidden and inert in both dimension modes. Zero returns NOT VALID when this mode is active.

Unit ft^2 Default 7850 Range At least 0
CLR Diameter Conditional: About this input

Nonnegative inside plan diameter of one circular clarifier; hidden and inert in other geometry modes. Zero returns NOT VALID when active.

Unit ft Default 100 Range At least 0
CLR Forward Flow: About this input

Forward clarifier flow used for surface overflow and as one component of secondary-mode solids loading.

Unit MGD Default 7.5 Range At least 0
CLR Entered SOR Limit Conditional: About this input

Nonnegative user-entered comparison criterion. The shipped hidden value is synthetic and must be replaced for site use. Zero returns NOT VALID when comparison is active; no regulatory or design limit is implied.

Unit gpd/ft^2 Default 1234.567 Range At least 0
CLR Entered SLR Limit Conditional: About this input

Nonnegative user-entered comparison criterion. The shipped hidden value is synthetic and must be replaced for site use. Zero returns NOT VALID when comparison is active; no regulatory or design limit is implied.

Unit lb/day/ft^2 Default 12.345 Range At least 0

Outputs

CLR SOR Utilization Conditional: About this output

Surface overflow rate divided by the user-entered criterion.

Unit fraction
CLR Solids Loading Rate Conditional: About this output

Applied solids mass divided by total in-service plan surface area.

Unit lb/day/ft^2
CLR Surface Overflow Rate Conditional: About this output

Forward flow divided by total in-service plan surface area.

Unit gpd/ft^2
Model Status: About this output

NOT VALID identifies unusable active inputs; CHECK identifies an exceeded user-entered criterion; OK means calculation completed with no configured criterion exceeded.

No unit declared
CLR Total Surface Area Conditional: About this output

Area per clarifier multiplied by identical units in service.

Unit ft^2
Forward plus return activated-sludge flow Conditional: About this output

Active flow basis used for the solids mass calculation.

Unit MGD
CLR Area Per Clarifier Result Conditional: About this output

Active direct or geometry-derived plan surface area for one clarifier.

Unit ft^2
Applied mixed-liquor solids mass Conditional: About this output

Active solids-bearing flow multiplied by entered suspended-solids concentration and the unit-system mass factor.

Unit lb/day
CLR Comparison Result Conditional: About this output

States whether both results are at or below the entered criteria; this is not a regulatory determination.

No unit declared
CLR SLR Utilization Conditional: About this output

Solids loading rate divided by the user-entered criterion.

Unit fraction
CLR Limiting Basis Conditional: About this output

Identifies which entered comparison is closer to or farther beyond its own criterion.

No unit declared

What it is

The Clarifier Surface and Solids Loading Calculator reports the two loading rates that describe how hard a clarifier is being worked: the surface overflow rate, which is flow per unit of plan area, and the solids loading rate, which is the mass of suspended solids arriving per day per unit of that same area.

You give it the flow, the suspended-solids concentration and the geometry. Plan area can be entered directly per clarifier, or calculated from a circular diameter or a rectangular length and width, and it is then multiplied by the number of identical units in service. It reports the area per clarifier, the total in-service area, the solids-bearing flow it used, the applied solids mass per day, and both loading rates, optionally against criteria you enter.

It works in US customary units - MGD, feet, square feet, gpd/ft2 and lb/day/ft2 - or in metric. Use it for operational loading checks and for seeing what taking a clarifier out of service will do.

Methodology

Purpose and model boundary

This calculator evaluates clarifier surface overflow rate (SOR) and solids loading rate (SLR) for identical clarifiers sharing an entered flow. Surface area can be entered directly or calculated from circular or rectangular geometry. The model can optionally compare both rates with user-entered criteria.

The calculation supports hydraulic and solids-loading review. It does not select a clarifier, prescribe a design criterion, or predict effluent quality or settling performance.

Inputs and units

Unit system selects US customary or metric labels; entries must be internally consistent.
Geometry mode uses direct area, circular diameter, or rectangular length and width for one clarifier.
Clarifiers in service, N, is a positive whole-number count of identical units sharing the entered flow.
Forward flow, Q_f, and optional return activated-sludge flow, Q_r, are in MGD or m3/day.
Solids-loading basis uses Q_f + Q_r for secondary activated sludge or only Q_f for the single-stream basis.
Solids concentration, X, is in mg/L and must match the selected stream/basis.
Optional SOR and SLR criteria are user-entered in gpd/ft2 and lb/day/ft2, or m3/m2/day and kg/day/m2.

The exact US mass factor is 8.34540445201933 lb / (MG x mg/L); the metric factor is 0.001 kg / (m3 x mg/L).

Governing relationships

Area for one clarifier is

direct mode: A_1 = entered area;
circular: A_1 = pi x D^2 / 4;
rectangular: A_1 = L x W.

Total area is A = N x A_1. Solids-bearing flow is

secondary activated sludge: Q_s = Q_f + Q_r;
single stream: Q_s = Q_f.

Applied solids mass is

M_s = Q_s x X x k.

The two loading rates are

US SOR: SOR = Q_f x 1,000,000 / A;
metric SOR: SOR = Q_f / A;
SLR = M_s / A.

When criteria are active, SOR utilization = SOR / SOR_limit and SLR utilization = SLR / SLR_limit.

Calculation sequence

Validate the unit, geometry, solids-loading, and comparison choices plus the active numeric fields.
Calculate one-unit surface area from the active geometry and multiply by the in-service count.
Select forward-only or forward-plus-return flow for solids mass; SOR always uses forward flow.
Convert the active flow/concentration product to mass per day and divide the hydraulic and solids quantities by total area.
If requested, calculate utilization against both positive user-entered criteria and identify the limiting basis.
Build the published SOR series for hypothetical in-service counts 1 through 12 and evaluate status.

Outputs and interpretation

Area per clarifier and total area expose the active geometry. Solids-bearing flow and applied solids mass show the SLR basis. SOR and SLR are the two primary rates. Optional utilization values greater than 100% mean the corresponding user-entered criterion is exceeded; comparison result and limiting basis summarize that arithmetic.

An OK status means no configured criterion is exceeded and the active inputs are usable. It does not imply regulatory, permit, or design compliance.

Validation and status logic

The workbook evaluates status in this order:

Condition	Returned status
A listed choice is invalid; in-service count is not a positive whole number; active area/dimensions are not positive; flow or concentration is negative; or active comparison criteria are not positive	`NOT VALID: correct active geometry, flow, solids, and criteria inputs`
Criteria comparison is active and SOR utilization is greater than 1	`CHECK: entered surface overflow criterion exceeded`
Criteria comparison is active and SLR utilization is greater than 1	`CHECK: entered solids loading criterion exceeded`
None of the preceding conditions applies	`OK`

SOR is checked before SLR, so the SOR warning takes precedence if both criteria are exceeded.

Assumptions and limitations

Identical clarifiers are assumed to share flow evenly. Dimensions describe inside plan surface area. Forward and return flows must use the same daily basis, and the entered concentration is applied to the active solids-bearing flow. Secondary mode intentionally applies the entered MLSS to both forward and return activated-sludge flows.

The equations do not model settleability, flocculation, density currents, inlet/outlet hydraulics, short-circuiting, weir loading, sludge-blanket depth, temperature, wind, sidewater depth, sludge withdrawal, or unequal flow splitting. The chart is mathematical sensitivity to the unit count, not a capacity recommendation.

Restrictions and non-computing states

The in-service count is an integer of at least one. The active geometry must produce positive area. Flow and concentration may be zero, but cannot be negative. Comparison mode requires both entered criteria to be positive; the shipped synthetic hidden values are not design guidance. Hidden geometry, RAS, and criteria fields are ignored when their branches are inactive.

The model does not provide default limits. A zero result can be mathematically valid for zero flow or zero solids concentration and must be interpreted in that entered context.

Errors and warnings

This calculator's input rules may reject an out-of-domain scalar or unknown option before calculation. Workbook NOT VALID means an active geometry/loading state is unusable; workbook CHECK means a valid result exceeds a user-entered criterion. Connection and calculation-service failures are not clarifier loading classifications.

References

The workbook implements the loading-rate definitions and the exact dimensional conversions behind its mass factor. No design criteria table, operating band, equipment catalogue or figure from any publication is reproduced.

U.S. Environmental Protection Agency. Process Control Manual for Aerobic Biological Wastewater Treatment Facilities, which defines surface overflow rate and secondary-clarifier solids loading using forward plus return flow, MLSS and surface area, and supplies the worked examples replayed above. https://nepis.epa.gov/Exe/ZyPURL.cgi?Dockey=9100NX8X.TXT
U.S. Environmental Protection Agency. Operational Control Procedures for the Activated Sludge Process, Part IIIA, for the US and metric final-clarifier surface-overflow relations and worked calculations. https://nepis.epa.gov/Exe/ZyPURL.cgi?Dockey=9100LL8N.TXT
National Institute of Standards and Technology. Handbook 133, Appendix E: General Tables of Units of Measurement, which fixes the US gallon at exactly 3.785411784 litres and the international pound at exactly 0.45359237 kilograms, the two identities behind 8.34540445201933. https://www.nist.gov/document/14-app-e-14-hb133-finalpdf
Wikipedia. Sedimentation (water treatment), for background on clarifier operation. https://en.wikipedia.org/wiki/Sedimentation_(water_treatment)

No loading limit for either rate is shipped with this calculator. The criteria you compare against must come from your design basis, your state standards or your permit.

Frequently asked questions

Should the return activated sludge flow be in the surface overflow rate?

No, and the tool never puts it there. The surface overflow rate describes the upward velocity of water in the tank, so it counts only what leaves over the weir, which is the forward flow. Return activated sludge is drawn from the bottom and sent back to aeration - it never crosses the weir. It does belong in the solids loading rate, because those recycled solids genuinely arrive at the settling surface, and that is what secondary mode adds.

Which solids loading basis should I choose?

Secondary activated sludge for a final clarifier receiving mixed liquor with a return stream, which applies your entered concentration to forward plus return flow. Single solids-bearing stream for a primary clarifier or any unit with no return to count, which uses forward flow alone. The difference is large - in the shipped example the loading rate falls by a third when the return is excluded - so choosing the wrong one is not a rounding matter.

What concentration should I enter in secondary mode?

The concentration of the stream entering the clarifier - the mixed liquor - because that same value is applied to both the forward and the return flow. The RAS concentration is a different and higher number, and entering it here will overstate the applied solids mass substantially. If your forward and return streams genuinely carry different concentrations, this single-concentration model is not describing your plant and the loading rate needs computing by hand.

Why does my solids loading differ slightly from my formula sheet?

Because of the mass factor. Operator sheets and government examples use a rounded 8.34 pounds per million gallons per mg/L; this workbook uses the exact 8.34540445201933 derived from the defined US gallon and international pound. The difference is about 0.065 percent, so a rate near 15 lb/day/ft2 shows about 15.016 here against about 15.01 from a rounded calculation. The surface overflow rate is unaffected, since no mass factor enters it.

What limits should these rates be compared against?

Ones you bring. The calculator ships no design criteria for either rate, for any clarifier type or duty, and the hidden default criteria are synthetic placeholders that must be replaced. Loading limits come from your design basis, your state's standards or your permit, and they differ by clarifier type, by wastewater and by what the clarifier is being asked to do. The utilization outputs and the limiting-basis result are arithmetic screening against your numbers, not a regulatory determination.

Will this tell me whether my clarifier will actually settle the solids?

No. Both outputs are loading rates - they describe what is being applied per unit of area, not what the clarifier does with it. There is no solids flux analysis, no state point, no settling velocity, no sludge blanket and no thickening calculation here. A clarifier can sit well inside both loading criteria and still fail on settleability, which is a question for the settling test and the flux curve rather than for these two ratios.

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