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How to Compute Flow Rate from Half Life

NASA Earth Observatory image modified by SkyTruth

SkyTruth Oil Spill Reports

Oil Spill Reporting Resources: How to Computer 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%