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I am building a water cooling system for my pc whereby the water can be individually redirected to each of the three individual graphics cards depending on temperature. Can the relationship between flow rate and angular velocity be expressed thusly so that I can then to proceed to solve for K or is the relationship more complicated? Thanks. :

$$ \frac {dV}{dt} = kA $$ (where A is the angular velocity of the impeller and k is a constant)

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It depends on the type of pump.

For a positive displacement pump (pistons, for example) a fixed volume is pumped per rotation. Pump speed and flow rate are directly proportional over a wide range. Eventually suction tries to cause negative pressure and you don't have a all-liquid system anymore.

Things get a bit more complicated for a impeller type pump. Pump speed and flow rate will be mostly linearly proportional of some region of operation, but there are other effects. Things start getting non-linear fast when cavitation happens, for example.

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