This model describes the oxygen level in a tank of water in which a fish respires. The respiration rate depends on the temperature, the weight of the fish, the kinetics of the respiration (reflected by the half-saturation constant, Km) and the oxygen level in the tank. The variables are presented below
Weight-specific oxygen consumption rate: an equation that describes the weight-specific oxygen consumption as a function of the temperature. The equation is based on empirical data by Fry and Hart, 1948.
Vmax: The maximum respiration rate determined as mass of fish times the weight‐specific oxygen consumption rate
Oxygen consumption rate: The oxygen consumption rate (= the respiration rate) is determined by the Michaelis Menten equation:
where [S] represents the oxygen concentration in the tank.
Km: The half-saturation constant of the respiration proces.
Temperature, weight of fish and oxygen in tank are self-explanatory variables. The outflow of oxygen due to respiration equals the oxygen consumption rate.
The model as well as data generated by Fry and Hart, 1948 was used to determine the Km-value. In the experiment performed, 0,8 kg fish were allowed to deplete the oxygen in a tank (7,13 cc/L) containing 1 L of water with no inflow of oxygen at 15 degrees Celcius. These boundary conditions were applied in the model, and the simulation was compared to the empirical data. The Km-value was adjusted until the simulation of the oxygen level in the tank fitted the empirical data satisfactory.