This model simulates the experiment conducted by Hart and Fry (1948).
The respiration rate of the goldfish is dependent on the weight of goldfish, the temperature and a Michaelis Menten relation to oxygen. A respiration rate was calculated by Hart and Fry data: (0.1929*[Temperature DegC]*[Temperature DegC] + 0.6029*[Temperature DegC] - 0.9571)*(1/0.02241). Where numbers are experimentally calculated and the last factor is a conversion factor to umol from cc/L.
Oxygen dependence is calculated using a MM relation given by: ([Weightspecific respiration rate - umol/kg/hour]*1)*([Concentration - umol/L]/([Concentration - umol/L]+[Km oxygen umol]))
It is assumed that for each mole of oxygen respired, one mole of carbon is assimilated. For each mole of carbon assimilated the goldfish gains 26.4 grams in weight - thus affecting the respiration rate.
Parameters made variable in this simulation is the volume of the aquarium, the flow through the aquarium, the temperature and the weight of the fish.
Km
The Km constant for the oxygen uptake of the goldfish was evaulated based on data made from Fry and Hart.
In this experiment the system temperature is 15 degrees celcius, the initial fish weight is 0.08kg (approximatley 20 goldfish), and there is no flow in the 1L aquarium.
When evaluating the Km the waightgain of the fish is neclected.
The appoximate value of Km was determined to be around 35umol. Using the trial and error method to get the best fit to the Fry and Hart data.
Growth-model
Changing the aquarium to and aquaculture tank of 1000L and turning on weight gain for the goldfish can be done using sliders.
Parameters adjustable by silders are the temperature, the fish mass, tank volume and the flow rate (see below).