Food-to-Microorganism Ratio

\[\frac{F}{M}=\frac{QS_0}{VX}\]

Variables

FMfood-to-microorganism ratio (mass substrate/mass biomass·time)

Qinfluent flow rate (m³/time)

S0influent substrate concentration (mass/volume)

Vaeration tank volume (m³)

Xmixed liquor suspended solids concentration (mass/volume)

Description

What is this formula?

The Food-to-Microorganism Ratio (F/M) measures the amount of biodegradable substrate entering a biological treatment system relative to the mass of microorganisms available to consume it.

When to use it

Use it when designing or operating activated sludge systems, aeration tanks, biological reactors, and wastewater treatment plants.

Example

Data:

Q = 5000 m³/day

S0 = 250 mg/L

V = 2000 m³

X = 3000 mg/L

Formula:

F/M = (Q × S0)/(V × X)

Substitution:

F/M = (5000 × 250)/(2000 × 3000)

Result:

F/M = 0.208 day⁻¹

Applications

Activated sludge design, biological treatment optimization, process control, wastewater treatment plant operation, and reactor performance evaluation.

Note

F/M is an operational design parameter rather than a fundamental physical law. Recommended values depend on the treatment process, sludge age, treatment objectives, wastewater characteristics, and reactor configuration.