Residence Time: Application to Small Boat Basins

Definitions are presented for transit time, age, flushing time and residence time. Using a continuous exchange model, analytical expressions for the transit time distribution function and the age distribution function are derived for a basin having a constant volume. The residence time for instantaneous as well as continuous dye injections equals the volume of the basin divided by the rate at which new water is added to the basin. Using the tidal prism model it is shown that the normalized residence time for an instantaneous dye injection is a function of three dimensionless parameters. These parameters are: (1) The average basin volume divided by the volume of new water returning on the flood; (2) the fraction of the flood volume $(=\mathrm{tidal}\mathrm{prism})$ that is new water; and (3) the phase of the tide at which the dye is injected. For a continuous dye injection, the normalized residence time is a function of the first two parameters only. Numerical computations show that, to a first approximation, the residence times equal the average basin volume divided by the volume of new water entering during flood with secondary effects introduced by the other parameters.