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%