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Calculate a two-stream mass-flow ratio and a blend fraction, then see why their different denominators matter.
A stream ratio compares one stream with another. A blend fraction compares a component with the combined total. The numbers differ because their denominators differ. Before interpreting a ratio-control calculation, name the numerator, denominator and flow basis.
The original example below uses two pure component streams measured as mass flow, no reaction or loss, and a simple combined outlet. It is arithmetic for a learning exercise, not a complete blend-control design.
Let primary mass flow A = 20 kg/min and secondary mass flow B = 5 kg/min. The secondary-to-primary ratio is r = B/A = 5/20 = 0.25. Total mass flow is A + B = 25 kg/min, so the secondary mass fraction in the combined blend is w = B/(A + B) = 5/25 = 0.20, or 20%.
| Quantity | Calculation | Result |
|---|---|---|
| Secondary/primary ratio | B/A | 0.25 |
| Secondary fraction of total | B/(A+B) | 0.20 |
| Primary fraction of total | A/(A+B) | 0.80 |
| Combined mass flow | A+B | 25 kg/min |
Calling the 0.25 ratio a 25% fraction of the total would be incorrect in this example. The ratio uses primary flow as its reference; the blend fraction uses total flow.
Under the stated two-stream assumptions, w = r/(1 + r). Solving for ratio gives r = w/(1 − w). For a 20% secondary fraction, r = 0.20/0.80 = 0.25. If A is 20 kg/min, the corresponding secondary-flow request is B = rA = 5 kg/min.
For a different fraction w = 0.25, r = 0.25/0.75 ≈ 0.3333. With the same primary flow, B ≈ 6.6667 kg/min and the total is approximately 26.6667 kg/min. This second calculation exposes why ratio and fraction targets cannot simply be interchanged.
Equal numerical volume-flow ratios do not automatically represent equal mass ratios when stream densities differ. Streams with different component concentrations require a component balance rather than the pure-component shortcut above. Measurement quality, response dynamics, actuator capacity and operating limits also matter.
The equations become unsuitable at invalid denominator values; a real design needs its own documented handling rather than copying the example into control logic.
The advanced-control examples guide places ratio requests alongside cascade, feedforward and constraint handling. Review APC275 implementation training for its published examples and prerequisites. The cascade versus feedforward comparison helps distinguish another set of signal roles before assembling a larger scheme.
Technical definitions are supported by the primary references below. The labelled numerical records, timelines and checklists are original teaching examples for this article. They do not establish site-specific design approval or a new course entitlement.
Browse the process-control learning library for the wider subject guides and course routes.
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