How to Compute Flow Rate from Half Life

Half Life:  the period of time it takes for the amount of a substance undergoing decay to decrease by half

The way to compute the replacement rate required to maintain a constant volume with a given half-life is

r = ln(2) / h

where ln is natural log, h is the half life and r is the replacement rate required to maintain a steady state.

So, in order to maintain a given volume of oil with a half life of three days and a continuous rate of replenishment, the effective daily rate must be ln(2) / 3 or 23.1% of the total steady state volume.

Some rates for reference:

Half Life    Replacement Rate
  2                34.7%
  3                23.1%
  4                17.3%
  5                13.9%
  6                11.6%
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