1. Moore, A., and Derry, L., 1995, Understanding Natural Systems through Simple Dynamical Systems Modeling, JGE, v. 43, p. 152-157. Introduce systems thinking with a simple physical model Inflow = outflow, so steady state but dynamic, not static How might we model this in STELLA? 8 Liters 0.011 Liters/sec The Moore and Derry (1995) Coleman Cooler Example 0.011 Liters/sec

2. STELLA representation dV/dt = inflow – outflow At steady state, dV/dt = 0, so inflow = outflow Residence time = V/inflow or V/outflow

3. ½ dt rule To ensure simulation is running properly, always check the time step. First, run model with chosen time step. Next, cut time step in half. If results are identical, proceed with larger time step. If results are different, continue halving time step until results are the same.

4. What will happen if we double the inflow? Students typically predict overflow.

5. Bob Mackay (Clark University) videos: http://www.youtube.com/watch?v=CoTQ7LCpwgAhttp://www.youtube.com/watch?v=CoTQ7LCpwgA - filling bucket http://www.youtube.com/watch?v=dVUh1JraiLkhttp://www.youtube.com/watch?v=dVUh1JraiLk - draining bucket http://www.youtube.com/watch?v=CcHohK458XMhttp://www.youtube.com/watch?v=CcHohK458XM - filling and draining http://www.youtube.com/watch?v=iYtDxf4V1lAhttp://www.youtube.com/watch?v=iYtDxf4V1lA - bucket too full to begin with In reality, outflow depends on the volume of water in the cooler. Opportunity to explain “Garbage In Garbage Out.”

6. Pink connector arrows show dependency of drain flow on cooler volume and rate constant drain = cooler * k but

7. The analytical solution: at t = 0, V(t) = V 0 so C = V 0 – i/k at t = 0, V(t) = V 0 as t  infinity, V(t)  i/k

8. 32 Liters 0.011 Liters/sec 0.022 Liters/sec Let starting volume = 8 Liters and initial inflow and outflow = 0.011 Liters/sec At time = 600 seconds, double inflow to 0.022 Liters/sec Note difference between true volume and STELLA model volume – indicates not all of the physics of the system are included in our simple model!

9. Bernoulli’s equation for gravitationally fed pipe flow gives a better solution: