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Wastewater Mass Balances and Retention Ratios

Calculate rectangular wetted volume, demand loading, solids inventory, retention time and normalized sludge-volume index.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

A 10 m by 5 m tank with 2 m wetted depth contains 100 m³; a 25 m³/h flow gives four hours hydraulic retention.

V=L×W×(wall depth−freeboard); loading=flow×concentration; HRT=V/Q; MCRT=total solids inventory/daily solids loss; sludge age=aeration solids/daily influent solids; SVI=30-minute settled mL in 1 L/MLSS g/L.

Worked example

Enter these known values and leave the other values blank.

I'd like to find...
HRT (hydraulic retention time)
Is the volume known?
No
Length
10 m
Width
5 m
Side wall depth
3 m
Free-board
1 m
Flow rate through tank
25 m³/hr
Volume
100 m³
HRT
4:0 hrs / min

Assumptions and limitations

  • Use measured, representative flows and concentrations for the same operating interval. Demand removed in primary treatment is subtracted from untreated demand; it is not the remaining effluent concentration. These balances do not predict treatment efficiency.
  • Tank geometry assumes a rectangular basin with horizontal water surface. Freeboard must be nonnegative and smaller than side-wall depth. Choose known volume when actual usable geometry differs.
  • Daily solids loads are displayed with the retained mass selector and refer to mass per day. F/M ratios are daily BOD or COD mass loading divided by the supplied volatile-solids inventory; keep BOD and COD conventions distinct.
  • Hydraulic retention is volume divided by hourly flow. Mean cell residence time divides aeration-plus-clarifier solids inventory by daily wasted-plus-effluent solids loss. The separately captured sludge-age convention divides aeration inventory by incoming suspended-solids load. These quantities are distinct.
  • For SVI, enter the volume settled after 30 minutes from a one-liter mixed-liquor sample and the measured MLSS in g/L. Normalize another sample size to one liter before entry. The ratio is mL/g; it is not a universal process-quality threshold.
  • All selectors, units and supported inverses are retained. The Everything view follows captured visibility and does not show the HRT flow input. Use the dedicated HRT mode for hydraulic retention.

Common questions

Can these calculations set a plant operating target?

They report supplied operating measurements and defined ratios. Design limits, sampling procedures and treatment targets require the applicable plant protocol.

References

Enforce positive wetted rectangular geometry, nonnegative demand and flow balances, removal bounded by influent demand, and the one-liter settled-volume domain; use exact US-gallon conversions.

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