The rain begins to fall and is collected as [Inflow] into a [Rain Barrel]. Our experience tells us there is a volume of water measured in gallons (liters), and the flow is in cu. cm./hr (cu. in./hr). However for this model, all the measurements are in centimeters of water (rainfall) because the height of the water in the barrel is what we want to know.
The calculations and initial graph show the height of the water in the [Rain Barrel] changing over time when the drain valve is closed and the outflow is zero.
Measuring rainfall in centimeters per hour, the [Inflow] causes the height of water in centimeters in the [Rain Barrel] to increase (or not, if the rain stops). Assume the barrel is at atmospheric pressure and there is no evaporation.
The [Drain] has a valve to control the flow. [Rate] contains a value that represents the position of the valve relative to the open position. .1 is 10% of full open and .5 is 50% of full open. The [Drain] calculation includes the [Rate] in order to get a per hour value using a decimal fraction, so that opening the drain valve to 10% initial value becomes 0.1 as the value for [Rate] in the calculation.
[Rate] represents the size of the hole the water flows through. According to the Bernoulli equation (see reference at end of story), the size of the hole is proportional to the rate of flow.
What happens when water flows out of the [Rain Barrel]? You might assume a linear or straight line graph of the water level similar to when the [Drain] valve was fully closed.
Actually the water outflow depends on the level of water in the [Rain Barrel]. Each time period, a fraction (percentage) of the water flows out of the barrel.
The height of the rain in the [Rain Barrel] is proportional to the flow from the [Drain]. The equation for [Drain] becomes [Rain Barrel] times [Rate]. Where [Rate] is proportional to the radius of the valve opening compared to full open.
A goal seeking model follows a parabolic shape based on a difference calculation. This model follows an exponential shape based on a decimal fraction calculation. Very difficult to tell the difference unless you study the equations and understand the mathematics (see reference at end of story).
Using initial values or your own, click on [Run Simulation]. The question is always: Why does the system behave the way it does? Write or dialogue with someone about why this system shows this behavior over time on the graph.
Click on "Step Forward" one more time.
Make a table of input values (assumptions) for each stock and flow. Each row in your table represents a [Run Simulation]. Leave room to draw a small graph or describe the behavior over time of the level in the [Rain Barrel] for each [Run Simulation]. You can Experiment using a STEP function for [Inflow] : 10 + Step(10, 10) Why? or for the [Rate]: 0.1 - STEP(10,0.8) Why?
Reference: Bernoulli's Equation on Wikipedia.