Finishing Trough Changeover: Purge Volume & Time

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: Trough Volume, Drain Efficiency, Previous Recipe Concentration, Acceptable Carryover, Fill or Purge Flow Rate, Drain and Refill Handling Time and Water and Effluent Cost.
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 Drain-and-Refill Cycles Needed together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Heel Fraction, Heel Left by a Drain, Concentration After One Rinse, Concentration After the Cycles, Water Used, Rinsing, Time, Rinsing, Water Used, Flow-Through Purge, Time, Flow-Through Purge, Water Saved by Rinsing and Cost Saved per Changeover — 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 Drain-and-Refill Cycles Needed 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 — Trough and Operation. 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 Drain-and-Refill Cycles Needed in the dark results panel — that is the headline figure, expressed in nos.
4. Check the supporting rows underneath (Heel Fraction, Heel Left by a Drain, Concentration After One Rinse, Concentration After the Cycles, Water Used, Rinsing, Time, Rinsing, Water Used, Flow-Through Purge, Time, Flow-Through Purge, Water Saved by Rinsing and Cost Saved per Changeover) 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 Drain-and-Refill Cycles Needed before a trial is booked, so machine time and material in Finishing, Coating, Lamination & Functional Performance are committed against a calculated figure rather than an estimate.
• Costing and quotation — Drain-and-Refill Cycles Needed 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 Trough Volume) shows how much of the gap in Drain-and-Refill Cycles Needed each variable explains.
• Teaching and study — the accepted ranges bracket normal Finishing, Coating, Lamination & Functional Performance practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• The flow-through comparison assumes the trough is perfectly mixed, which is the pessimistic idealisation: a real trough has short-circuiting and dead corners, so some liquor leaves faster than the model says and some stubbornly does not, and the tail of a continuous purge is worse than exponential rather than better. That makes the case for draining stronger, not weaker. Drain efficiency is the input that decides everything and it is a machine property worth measuring once - fill with a traceable salt, drain, refill with clean water and titrate, and the heel fraction falls straight out. It is usually worse than the operator believes, because the heel hides in pipework, pumps and the doctor blade recess rather than in the visible trough. The concentration model tracks a soluble carried species and says nothing about a deposit: a pigment, a silicone or a crosslinked resin film on the trough wall does not dilute at all, and a changeover between chemistries that leave films needs mechanical cleaning that this arithmetic cannot substitute for. Where the next recipe is sensitive to a trace rather than a percentage - a white after a dark, or a hydrophilic finish after a fluorocarbon - set the carryover limit accordingly and expect the cycle count to rise steeply, since it grows with the logarithm of the ratio.
• Every input is bounded to the range normal practice occupies (Trough Volume 5 to 5000 L, Drain Efficiency 40 to 99.9 % and Previous Recipe Concentration 0.5 to 500 g/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