Dye Bath Dosing Pump Profile & Addition Schedule

The formula

This is the expression the tool evaluates. Every term is named underneath, with the unit it must be supplied in.

How the result is derived

Step by step, from the values you type to the figure on screen.

1. The 7 inputs are read from the form on every keystroke: Dye to Dose, Stock Concentration, Bath Volume, Dosing Time, Profile Exponent, Addition Steps and Pump Maximum Rate.
2. Each value is checked against the accepted range in the input table below. A value outside its range stops the calculation rather than producing a misleading figure — the results blank out and a message appears.
3. The validated values are substituted into the expression above, which resolves Peak Dosing Rate together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Stock Solution to Dose, Average Rate, Pump Utilisation at Peak, Shortest Dosing Time this Pump Holds, First Step, Last Step, Last Step / First Step, Delivered at Half Time and Bath Concentration at End — come from the same pass, so they always describe the same case as the headline figure.
5. Results are rounded for display only. The full-precision value is used throughout the chain, so reading a rounded intermediate figure back into the tool by hand can shift the last digit.

What each input means

Where to read each value on the floor, the unit it must be in, and the range the tool accepts.

What the tool returns

The headline figure and every supporting value it is built from.

Worked example

The tool loads with this case already solved — the Peak Dosing Rate shown above is its answer. Change one value and the difference from this baseline is the sensitivity of the result to that variable.

How to use it

1. Work through the input groups in order — Dye & Stock Solution and Profile. The defaults are a realistic case, so you can change one value at a time and watch what moves.
2. There is no calculate button. Every figure recalculates as you type or drag, which is what makes this usable for a what-if sweep rather than a single answer.
3. Read Peak Dosing Rate in the dark results panel — that is the headline figure, expressed in L/min.
4. Check the supporting rows underneath (Stock Solution to Dose, Average Rate, Pump Utilisation at Peak, Shortest Dosing Time this Pump Holds, First Step, Last Step, Last Step / First Step, Delivered at Half Time and Bath Concentration at End) before acting on the headline — they are where an implausible input usually shows itself first.
5. Reset to defaults returns every field to the reference case, which is the quickest way to check whether a surprising result came from the tool or from an input you had changed earlier.

Where this is used

• Process planning — establishing Peak Dosing Rate before a trial is booked, so machine time and material in Dyeing, Printing, Color Management & Chemical Control are committed against a calculated figure rather than an estimate.
• Costing and quotation — Peak Dosing Rate is an input to the cost sheet, and quoting from a worked number rather than a remembered one is what keeps a margin intact.
• Troubleshooting — when the floor result drifts from plan, entering the measured values (starting with Dye to Dose) shows how much of the gap in Peak Dosing Rate each variable explains.
• Teaching and study — the accepted ranges bracket normal Dyeing, Printing, Color Management & Chemical Control practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• The profile is a power law, which is the shape almost every dosing controller implements even when its screen calls it "progressive" or numbers it one to five; if the machine uses a true logarithmic or a tabulated custom curve the peak rate will differ and only the average rate and the stock volume carry across unchanged. Peak rate is quoted at the end of the profile because that is where a power law with an exponent above one is steepest, and it is the figure that decides whether the pump can hold the curve — a pump at more than about 80 percent utilisation has nothing left for the viscosity of a cold stock solution on a winter morning. Step volumes assume the controller divides the profile into equal time slices and doses the difference in cumulative volume each slice, which is the usual implementation; a controller that instead divides into equal volume steps and varies the interval produces the same schedule read the other way round. Nothing here models levelness itself: the profile is a means of keeping strike below migration, and whether it succeeds depends on the dye, the fibre, the temperature ramp and the electrolyte, none of which appear in this calculation.
• Every input is bounded to the range normal practice occupies (Dye to Dose 0.01 to 500 kg, Stock Concentration 1 to 600 g/L and Bath Volume 10 to 100000 L, and so on for the rest). Those bounds are guard rails against typing errors, not a claim that the formula fails one unit outside them.
• The calculation is deterministic: the same inputs always give the same result. It carries no allowance for machine condition, operator skill, ambient conditions or lot-to-lot material variation unless an input above explicitly represents one.
• Nothing is sent anywhere. The maths runs in your browser, so the numbers you type never leave the page.

Questions people ask