The bathtub example will form the basis for a first look at the Vensim software.

After completing this worksheet, you should know how to use Vensim for

• drawing models,
• assigning equations and units to model variables,
• setting up the simulation time properties,
• running simulations and getting simulation results as tables or graphs.

Software you need for this modelling prompt:

• Vensim

Please use Vensim to compute the status of the systems explained below for each minute of their lifetime (i.e. 10 minutes or until equilibrium is reached). Use the Vensim functionality to visualize the dynamics as xy plot. You are already familiar with the systems from the Bathtub Quiz.

Setup 01: Constant inflow
Consider a simple system from daily life: a bathtub and a faucet.
The facts are these:

• At time 0, there is no water in the bathtub and the faucet is closed.
• The faucet is opened for 10 minutes (and shut afterwards). It has a constant flux of 10 l/min.
• The water from the faucet is running into the bathtub.
• The bathtub has no leak.

Setup 02: Constant inflow and constant outflow
We stay with the bathtub and the faucet but now the bathtub has a leak.
The facts are these:

• At time 0, there is no water in the bathtub and the faucet is closed.
• The faucet is opened for 10 minutes (and shut afterwards). It has a constant flux of 10 l/min.
• The water from the faucet is running into the bathtub.
• The bathtub has a leak with a constant flux of 5 l/min.

Setup 03: Variable inflow and constant outflow
We stay with the bathtub, the faucet and the leak but now we vary the inflow.
The facts are these:

• At time 0, there is no water in the bathtub and the faucet is closed.
• The water flux from its faucet can be regulated between 0 and 10 l/min.
• The bathtub has a leak with a constant flux of 5 l/min.
• The faucet (its water is running in the bathtub) is fully opened until the water level in the tub reaches 100 l. Afterwards, the inflow is adjusted to level the outflow.

Setup 04: Constant inflow and volume dependent outflow
We stay with the bathtub, the faucet and the leak but now the leak shows a variable flux.
The facts are these:

• At time 0, there is no water in the bathtub and the faucet is closed.
• The faucet is opened. It has a constant flux of 10 l/min.
• The water from the faucet is running into the bathtub.
• The bathtub has a leak with a water level depending flux of 0.5 times the water volume in the bathtub per min.