Introduction:
Tiliapiine
Cichlids are kept in a tank filled with oxygen saturated water. Fresh oxygen
saturated water flows into the tank at a determined flow rate, and an equivalent
amount flows out. The cichlids in the tank use the oxygen from the water to
sustain growth and life. This model simulates the amount of oxygen in the tank overtime.
Oxygen
concentration:
The oxygen concentration
in the water, and thereby the concentration in the inflow water and the initial
concentration in the tank, is determined by temperature. The temperature is
said to be a boundary condition.
Respiration:
The methabolic respiration (MR) is described by
michalis menten kinetics:
MR=T.resp * (conc.out/(conc.out+ Km))The temperature dependent respiration is the maximum
possible respiration of that temperature. This is calculated from experimental
data (Fry and Hart, 1948). The concentration of oxygen in the water which flows
out of the tank is calculated from the oxygen concentration in the tank. Km
is the concentration where half the maximum respiration is reached. With a low Km the fish’s oxygen affinity is high,
and with a higher Km value the
affinity is lower. With the lower Km the fish needs less oxygen to sustain life.
The Km value is fitted to data obtained
by Fry and Hart (1948). The initial conditions used when fitting Km in the model is 15˚C and tank volume of
1000L.
Fig 1: the figure illustrates the concept of Km.
Results:
The oxygen level
in the tank decreases linear until (XY) where the line flattens. The starting
point at 15˚C is 318 μM at 0 hours and decreases linear until about 53 μM at 2000
hours. Very little oxygen is left at 3000 hours. From this model it is evident
that the fish is able to live and grow in a tank with no aeration except from
inflow of new water for around 125 days. A system that would increase the
aeration of the tank could improve the condition for the fish.
ref: Fry and Hart, The relation of Temperature to oxygen consumption in the gold fish, 1948.