Free · Mathematical relations and geometry

Dry-Matter Conservation Through Water Loss

Calculate total mass after water content changes while conserving the dry matter in a mass-balance puzzle.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

A mass of 100 containing 99% water has dry mass 1. At 98% water, the same dry mass makes the new total mass 50.

dry=M₁(1−w₁); M₂=dry/(1−w₂)

Worked example

Enter these known values and leave the other values blank.

Make a guess...
50 kg
Total mass
100 kg
Water percentage
99 %
Water percentage
98 %
Dry potato mass
1 kg
Water mass
99 kg
Water mass
49 kg
Dry potato mass
1 kg
Total mass
50 kg

Assumptions and limitations

  • Only water is lost or added; the dry matter stays constant. This is a mathematical mass-balance puzzle.
  • Water inputs are percentages between zero and 100, excluding endpoints in the retained model.
  • Masses are positive and all masses use the same chosen unit; no mass selector is provided.
  • The guess control compares a positive estimate to the model without changing mass balance.

Common questions

How can I solve for a missing quantity?

Leave the unknown control empty and enter the quantities needed by the selected relation. Read the assumptions for any branch or domain restrictions.

How should I interpret the worked example?

It is an exact mathematical model with independently checked numbers. Display rounding does not change the values used for subsequent calculations.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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