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Dosing Equations & Calculations

Every dosing duty starts as a concentration target in mg/L and has to end as a pump setting in litres per hour or strokes per minute. This page gives the conversions that get you there: dose mass from flow and concentration, solution flow from product strength, dilution, flow-pacing and pump-stroke setting — each with units stated and a worked example.

Dose Mass Rate

From flow and concentration to kilograms of active chemical per day.

The foundation of every dosing calculation. A concentration target (mg/L = g/m³) applied to a flow gives the mass of active chemical you must deliver per unit time.

Dose mass rateṀ (kg/h) = Q (m³/h) × C (mg/L) ÷ 1000

Worked example

Flow Q = 120 m³/h, ferric coagulant target C = 45 mg/L as product.

Ṁ = 120 × 45 ÷ 1000 = 5.4 kg/h of product (≈ 130 kg/day at 24 h).

Solution / Pump Flow Rate

Converting the chemical mass into a volume the pump must deliver.

A dosing pump delivers volume, not mass. Convert the required mass rate into a solution flow using the delivered solution's active-chemical concentration. Neat liquid products are quoted as % w/w plus density; dilute solutions as g/L.

Solution flow from mass rateq (L/h) = Ṁ (g/h) ÷ S (g/L)
Active strength of a neat liquid productS (g/L) = 10 × (% w/w) × ρ (kg/L)

Worked example

Need Ṁ = 5.4 kg/h = 5400 g/h. Product is 40% ferric, density 1.43 kg/L.

S = 10 × 40 × 1.43 = 572 g/L
q = 5400 ÷ 572 = 9.4 L/h of neat product.

Dilution

Making a weaker working solution — and what it does to pump flow.

Diluting a concentrate improves pump turndown and mixing but proportionally increases the volume the pump must move. The mass-conservation rule is unchanged.

Dilution (mass conservation)C₁ × V₁ = C₂ × V₂

Always add acid to water

When preparing dilute acid or caustic solutions, add the concentrate to water, never the reverse — the dilution exotherm can boil and spit concentrated reagent. Confirm material compatibility of the make-up tank.

Worked example

Dilute 572 g/L ferric to a 100 g/L working solution for better turndown.

V₂ = C₁V₁ ÷ C₂ = (572 × 1 L) ÷ 100 = 5.72 L working solution per litre concentrate
Pump flow rises to q = 5400 ÷ 100 = 54 L/h — 5.7× more volume, but far easier to control accurately.

Flow-Paced Dose

Holding concentration constant as plant flow varies.

If the dose target (mg/L) is fixed, pump output must track flow. This is the basis of feed-forward control — see dose-rate & control.

Flow-paced solution flowq (L/h) = Q (m³/h) × C (mg/L) ÷ S (g/L)

Pump Stroke / Speed Setting

Turning a required flow into a control-panel number.

A metering pump's output is its maximum capacity scaled by stroke length × stroke frequency. Set the controllable fraction to the duty.

Output settingSetting (%) = qrequired ÷ qmax × 100

Quick-reference conversions

ConvertFormulaNote
mg/L → kg/hQ(m³/h) × C ÷ 1000active mass
kg/h → L/h solution1000 × kg/h ÷ S(g/L)via solution strength
% w/w → g/L10 × %w/w × ρneeds density
L/h → mL/minL/h × 16.67small-pump scale
ppm= mg/Ldilute aqueous

Related Pages

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