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The phrase "a function of the total flow" is correct and usable in written English.
It can be used in contexts related to mathematics, science, or engineering, where you are describing how one variable depends on or is determined by the total flow of another variable.
Example: "The pressure in the system is a function of the total flow, which affects the overall efficiency of the process."
Alternatives: "dependent on the total flow" or "determined by the total flow".
Exact(1)
This was introduced in [12] using delivery contracts, in which the utility is a function of the total flow over a given time interval; here, we use instead a very simple first-order linear smoothing.
Similar(59)
The flame-development time for methane air mixtures in the flow tube is found to be a function of the total ignition energy and the pulse repetition frequency.
It's a function of the total pressure.
The total pressure was measured as a function of the oxygen gas flow during reactive magnetron sputtering of two different target materials, namely yttrium and aluminum.
Whereas the former is a function of total organ blood flow, the latter is a function of microcirculatory phenomena and the ability of carbon dioxide to diffuse across tissues – processes that are often disturbed in disease states.
A Y-splitter divided the total flow of 20 l min−1 equally between the two instruments.
Using the aforementioned relations, we can express all gas flow rates as a function of the production rates, total system pressure, and partial gas pressures.
As outlined above, the coherence function allows one to estimate the total flow of information through the neural population.
In these systems, it is not the length, but the total flow of the loaded and empty vehicles that drives the objective function.
Figure 10 Hadean hydrothermal flow as a function of total Earth's heat flow (expressed as multiplicities of present day heat flow – PDHF).
Measuring the total flow of migrants is difficult.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com