Wetlaid Headbox Flow, Jet-to-Wire Ratio & Crowding Number

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 9 inputs are read from the form on every keystroke: Basis Weight, Wire Width, Wire Speed, Slice Opening, Headbox Consistency, Fibre Length, Fibre Diameter, Fibre Density and Target Crowding Number.
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 Crowding Number together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Fibre Throughput, Stock Flow to Headbox, Water in that Flow, Jet Velocity, Jet-to-Wire Ratio, Drag (negative) or Rush (positive), Volumetric Concentration, Fibre Aspect Ratio, Consistency for Target Crowding and Web Produced — 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 Crowding Number 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 — Sheet & Wire and Stock & Fibre. 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 Crowding Number in the dark results panel — that is the headline figure, expressed in N.
4. Check the supporting rows underneath (Fibre Throughput, Stock Flow to Headbox, Water in that Flow, Jet Velocity, Jet-to-Wire Ratio, Drag (negative) or Rush (positive), Volumetric Concentration, Fibre Aspect Ratio, Consistency for Target Crowding and Web Produced) 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 Crowding Number before a trial is booked, so machine time and material in Nonwovens, Filtration, Hygiene & Technical Webs are committed against a calculated figure rather than an estimate.
• Costing and quotation — Crowding Number 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 Basis Weight) shows how much of the gap in Crowding Number each variable explains.
• Teaching and study — the accepted ranges bracket normal Nonwovens, Filtration, Hygiene & Technical Webs practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• The crowding number is a suspension property and says nothing about what the wire, the dewatering profile or the shear in the slice then do with it - two machines at the same crowding number can form very differently, and a well-designed hydraulic headbox will beat a poor one at identical stock. Read it as the constraint the machine has to work against rather than as a prediction of formation. Note that the tool will often report a crowding number far above the target at the consistency the flow actually requires, and that is not an error in the arithmetic: it is the central tension of wetlaid, where the consistency needed to lay a given basis weight through a given slice at a given speed is frequently well above the consistency the fibre length can tolerate. The resolutions are all structural - a wider slice, a slower wire, shorter fibre, or dilution with a correspondingly larger white-water system - and the tool exists to make the size of the gap explicit before a machine is bought. Jet-to-wire ratio here is a geometric result of flow and slice opening rather than a setting; on a real machine it is trimmed by slice adjustment and by headbox pressure, and a ratio far from unity in either direction orients fibre in the machine direction and costs cross-direction strength. Fibre length is taken as a single value, while a real furnish has a distribution, and the longest tail of that distribution drives flocculation more than the mean does.
• Every input is bounded to the range normal practice occupies (Basis Weight 5 to 400 g/m2, Wire Width 0.3 to 10 m and Wire Speed 5 to 1500 m/min, 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