Recipe targets
- Batch size to make
- Active strength of concentrate (w/w)
- Target strength of batch (w/w)
- Concentrate density (example)
- Water density
Process · worked example · 3 pages
Batch mixing and dilution
Diluting a concentrate to a working-strength batch: how much concentrate and water make the target mass, checked by a mass balance on the active ingredient. Every concentration here is BY MASS (w/w) — mixing that up with by-volume (v/v) figures is the classic dilution error, and the density rows show why the two differ.
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What this calculation covers
Masses to weigh out
The active ingredient all comes from the concentrate, so the batch's active mass fixes the concentrate mass directly.
- Concentrate to weigh in
- Dilution water to add
- Active ingredient in the batch
Mass-balance checks
- Total mass closes
- Active mass hits the target strength
Volumes for the measuring jugs
Note the mismatch: 12.5% of the batch's mass is concentrate by weight of jug — but only 11.5% of its volume, because the concentrate is denser than water. A v/v recipe is a different recipe.
- Concentrate by volume
- Water by volume
Scaling the recipe
- Concentrate for a batch of mass m
- Water for a batch of mass m
- Concentrate for a 400 kg batch
- Water for a 400 kg batch
Results summary
- A 250 kg batch at 5% w/w takes 31.25 kg of the 40% concentrate (28.4 L) and 218.75 kg of water (219.2 L); both balances close exactly. The functions scale any batch size in one line — 400 kg needs 50 kg and 350 kg respectively.
Try changing…
- Use a 32% concentrate — the concentrate mass rises a quarter and the water shrinks to match.
- Ask for 8% strength — concentrate scales up in direct proportion (50 kg for this batch).
- Set C_t above C_c — the water mass goes negative: dilution cannot concentrate.