Metering Pump Flow Calculation: Formulas From Dose Rate to Pump Size

A metering pump flow calculation has two halves. The process half tells you how many liters of chemical solution per hour the job needs. The pump half says a reciprocating pump delivers stroke volume × stroke rate × stroke length setting. Match the two, add sensible margin, and you have your pump. This guide is for design engineers and operators who want to check a supplier's sizing themselves, and it applies to solenoid, mechanical diaphragm and plunger metering pumps. Every number below is an assumed example to show the method, not data from a real project.

Step one: the chemical feed rate calculation

When you know the water flow and the target dose, the solution flow is:

q (L/h) = Qw (m³/h) × C (mg/L) ÷ (1000 × w × ρ)

Qw is the treated water flow. C is the dose as active ingredient, normally set by jar testing or the process designer. w is the mass fraction of active ingredient in the solution, so 10% becomes 0.1. ρ is solution density in kg/L.

Why the 1000 in this metering pump flow calculation? Cubic meters per hour times mg/L gives grams of active chemical per hour. Dividing by w gives grams of solution, and dividing by density and 1000 turns that into liters.

Assumed example

Take an assumed 100 m³/h of water, a 20 mg/L dose, a 10% solution and an assumed density of 1.2 kg/L (use your supplier's figure or measure it). Then q = 100 × 20 ÷ (1000 × 0.1 × 1.2) ≈ 16.7 L/h. If you think in US gallons, divide liters by 3.785.

If the design gives you kilograms of pure chemical per day, M, the same metering pump flow calculation becomes q = M ÷ 24 ÷ (w × ρ), again in L/h.

Step two: what the pump actually delivers

Each stroke of a reciprocating metering pump pushes out a fixed volume, the stroke volume, usually in mL. Stroke rate is strokes per minute (spm). Stroke length is the percentage set on the adjustment knob, with 100% as full stroke.

Q (L/h) = V (mL) × n (spm) × S (%) × 60 ÷ 1000

That is the theoretical figure. Real output is lower by a volumetric efficiency that depends on back pressure, viscosity, suction conditions and valve condition, and it falls further as you approach rated pressure. Catalog capacity is normally quoted at rated pressure on water, so never treat the theoretical result of a metering pump flow calculation as guaranteed output.

Solenoid pumps usually vary stroke rate; motor-driven mechanical diaphragm pumps usually run at fixed speed and vary stroke length. The same formula covers both, only the variable changes. For working backwards to a setting, see our guide to calculating stroke rate and stroke length.

Metering pump flow calculation and sizing margin

Do not buy a pump whose rated flow equals q exactly. A good metering pump flow calculation always ends with a margin check. Margin has to cover three things:

1. Peak demand. Water flow and quality swing, so maximum dose is often well above average.
2. Losses at pressure. Output at rated pressure is below the theoretical value.
3. Turndown. Normal duty should sit in the middle of the stroke range, because long running at very short stroke hurts repeatability.

Go back to the assumed 16.7 L/h from the first metering pump flow calculation. A pump rated 50 L/h would run at about 33% stroke, which is low. A pump rated 25 L/h would run near 67%, with room to grow. Both "work," but the smaller pump controls better. Our article on why stroke length should not stay below 30% explains the reasoning.

Mistakes we see in a metering pump flow calculation

Mixed concentration bases

If C is active ingredient, w must be active ingredient too. Product strength on the drum label and active content are not always the same, and mixing them throws the result off badly.

Neat versus diluted solution

This error quietly ruins many a metering pump flow calculation. If you dilute in a day tank before dosing, w is the diluted strength. The weaker the solution, the more volume the pump must move for the same dose.

Split injection points

One pump feeding two basins needs the sum of both flows. One pump per basin means calculating each separately.

Cold weather viscosity

No metering pump flow calculation on paper accounts for temperature. Polymer and other viscous chemicals, or a cold dosing room, raise suction losses. A stroke setting that worked in summer may fall short in winter, so measure and reset.

Verify with a calibration column

Any metering pump flow calculation is a starting point. Once the pump is installed, draw down a calibration column or graduated cylinder at real discharge pressure for a timed period and compare it with your number. A large gap points to back pressure, suction lift or a sticking check valve. The method is in our metering pump calibration guide, and dosing rate calculation from water flow walks through more process cases.

Conclusion

The metering pump flow calculation runs in two steps: q = Qw × C ÷ (1000 × w × ρ) for the process, then Q = V × n × S × 60 ÷ 1000 for the pump. Discount the theoretical figure, size so normal duty lands mid-stroke, and confirm with calibration after start-up. You can compare pump types on our metering pump range and mechanical diaphragm pumps pages. Send us water flow, dose, solution strength and line pressure, and contact our engineers to check the numbers and the model.

FAQ

What are the 60 and 1000 in the pump formula?

60 converts minutes to hours and 1000 converts milliliters to liters. Change the units and those factors change with them.

I do not know the stroke volume. What now?

Estimate it from rated flow divided by rated stroke rate, with unit conversion. A calibration test on the installed pump is still the most reliable figure.

Can I assume a density of 1.0?

For weak solutions the error is small. Concentrated acids, caustic and coagulants are clearly heavier than water, so measure instead of guessing.

What is wrong with oversizing by one model?

The pump runs at short stroke all the time, repeatability drops, and a solenoid pump gives very pulsed dosing. Aim for normal flow mid-range.

My metering pump flow calculation does not match measured output. Where do I look first?

Check whether discharge pressure exceeds the pump rating, then look for air leaks on suction and crystallized check valves, and only then suspect the pump itself.