Equilibrium. Stable equilibrium (negative feedback)
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Transcript of Equilibrium. Stable equilibrium (negative feedback)
Equilibrium
Equilibrium
Stable equilibrium (negative feedback)
Unstable equilibrium (positive feedback)
• ,
At Equilibrium:Inflows=Outflows
At Equilibrium:Inflows=Outflows
80 gal/min120 gal ???
Assume Equilibrium:Inflows=Outflows
80 gal/min120 gal 80 gal/min
At Equilibrium:Inflows=Outflows
80 gal/min120 gal 20 gal/min
Is water levela) rising b) Fallingc) Staying the same
At Equilibrium:Inflows=Outflows
80 gal/min120 gal 20 gal/min
Is water levela) rising b) Fallingc) Staying the same
At Equilibrium:Inflows=Outflows
80 gal/min120 gal 80 gal/min
Is water levela) rising b) Fallingc) Staying the same
At Equilibrium:Inflows=Outflows
80 gal/min120 gal 80 gal/min
Is water levela) rising b) Fallingc) Staying the same
At Equilibrium:Inflows=Outflows
80 gal/min120 gal 140 gal/min
Is water levela) rising b) Fallingc) Staying the same
At Equilibrium:Inflows=Outflows
80 gal/min120 gal 140 gal/min
Is water levela) rising b) Fallingc) Staying the same
At Equilibrium:Inflows=Outflows
Is water levela) rising b) Fallingc) Staying the same
=2 min
8 gal/min 20 gal??=_________
At Equilibrium:Inflows=Outflows
Is water levela) rising b) Fallingc) Staying the same
=2 min
8 gal/min 20 gal??=_10 gal/min________
At Equilibrium:Inflows=Outflows
Is water levela) rising b) Fallingc) Staying the same
=2 min
8 gal/min 16 gal??=_________
At Equilibrium:Inflows=Outflows
Is water levela) rising b) Fallingc) Staying the same
=2 min
8 gal/min 16 gal??=__8 gal/min_______
At Equilibrium:Inflows=Outflows
Is water levela) rising b) Fallingc) Staying the same
=2 min
8 gal/min 12 gal??=_________
At Equilibrium:Inflows=Outflows
Is water levela) rising b) Fallingc) Staying the same
=2 min
8 gal/min 12 gal??=___6 gal/min_____
At Equilibrium:Inflows=Outflows
Is pollutant levela) rising b) Fallingc) Staying the same
8 ppm/yr12 ppm
=.2 (1/yr)
??=_________
At Equilibrium:Inflows=Outflows
Is pollutant levela) rising b) Fallingc) Staying the same
8 ppm/yr12 ppm
=.2 (1/yr)
??=__2.4 ppm/yr____
At Equilibrium:Inflows=Outflows
Is pollutant levela) rising b) Fallingc) Staying the same
8 ppm/yr??
=.2 (1/yr)
8 ppm/yr
What is the lifetime?
At Equilibrium:Inflows=Outflows
Is pollutant levela) rising b) Fallingc) Staying the same
8 ppm/yr??= 40 ppm
=.2 (1/yr)
8 ppm/yr
What is the lifetime?Lifetime=1/(DecayConstant)=5 yr
Whenever the
net flow = -k*stock you get exponential decay to zero**
Summary (exponential decay/Goal seeking)
kteXX 0
Sometimes we like to use the concept of lifetime (decay time constant) instead of decay rate constant.
Here k is the decay rate constant.
k
1
kXdt
dXas wrtten be wouldmath thisin **
Whenever the
net flow = inflow-k*stock you get exponential decay to a Goal, Xeq
Summary (exponential decay/Goal seeking)
eqkt
eq XeXXX 0
The Goal is the value of X (the stock) that makes the net flow zero
Inflow=outflow
Inflow=k*stock at equilibrium
Here X is any stock.
*inf
*inf
lowX
or
XXklow
eq
eqeq
Ceq=Inflow*lifetime
Ceq=Inflow/(DecayRateConstant)
Outflow=Content/(lifetime)
Outflow=DecayRateConstant*Content
Summary (exponential decay/Goal seeking)