Help with a Differential Equations project modeling Air, Food, Water consumption, and a Hydroponic system
I am working on a differential equations project, and I need to model the food, oxygen(air), and a hydroponic system for astronauts on Mars. This is what I came up with so far.
Mf- Food, Mo-Oxygen, Mh-hydroponic plants (for food and oxygen)
ΔMf = -k Δt
ΔMh = kMh Δt - a Δt
ΔMh/ Δt = kMh-a
Δt => 0
dMh/dt = kMh -a
ΔMf = -k Δt + a Δt
ΔMf/ Δt= a - k
Δt=> 0
dMf/dt = a - k
ΔMo = -k1 Δt -k2 Mh Δt
ΔMo/ Δt = -k1 - k2 Mh
Those will yield a system of equations...
dMf/dt = a-k
dMh/dt = kMh - a
dMo/dt = -k1 - k2Mh
I think I need to take this system of equations a bit further and I also want to consider water in this somehow.
Water = K(initial value) + F1( water from the fuel cells) - F2 (what the humans consume) + F3 ( the human's waste that can be recycled) - Hy( what the hydroponics consume)
I need to turn that into a differential equation.
Am I on the right track? Any suggestions?