Introduction

Measuring the rate at which water flows from one container to another container is not only an useful activity in environmental science just on its own, but it is a metaphor for many other mass-balance approaches. We would need to know the flow rate of water and the parameters that control that in the following situations:

• stream flow out of a pond or lake
• river flow over a dam
• height of water behind an impoundment (such as a solid bridge) in a stream
• flow of water through a culvert

The flow of a mass of water is also a metaphor for the flow of carbon, nitrogen or phosphorus between reservoirs in biogeochemical cycles. We even use hydrology terms (reservoirs, valves, etc) in describing these processes and STELLA uses a graphical interface that looks like tanks, pipes and valves. This is a powerful metaphor because it establishes right at the beginning that there is a limited amount of stuff (like water) and that it is going to flow from one location to another. If you apply this to carbon pathways in the envirornment, it helps you think about carbon as going from one form to another distinct form (CO2 in the atmosphere to dissolved CO2 in the ocean for example) and that you can track the flow along this pathway. This metaphor may fail to describe more subtle aspects, but highlights one of the key elements of systems modelling which is that you need to follow some energy or material and know where it goes within your system. The metaphor also suggests that you can't just mix units. Just as if you are following water, it doesn't turn into something else, when you follow carbon you can track that carbon in CO2, organic material, fossil fuels but you are not following carbon as it turns into fish or algae. You are following the carbon in it different forms.

The rate of flow of a material from one reservoir to another is very interesting. Just focusing on water, the rate of flow of water from one container to another can be controlled in many ways. It can be pumped, it can drip, it can flow through a hole or over a wier, or it can be poured. Each of these has different flow characteristics. We are going to focus on how fast water is driven by water pressure to flow over a wier or through a set size hole. The water pressure is a direct function of the depth of the water and as the water level drops the flow rate will drop. This is what you will be measuring inititally. Later you will measure the rate at which water flows out of one container, into a second and finally into a third. This is a very dynamic process with the flow rate and water levels constantly changing in the first two containers. You will collect enough information to create a STELLA model of this process.

Description of Exercise

This exercise has four parts:

part 1: first week in lab - measure the flow rate of water out of a hole in a container

part 2: second week in lab - measure the heights and flow rates in a multiple cup system

part 3: third week on computers - create a STELLA model for the 3 cup system

part 4: written assignment - compare measured to modeled

 

Part 1: first week in lab - measure the flow rate of water out of a hole in a container

You will need:

• plastic cup with a hole in the side near the bottom
• graduated cylinder
• stop watch or other timer
• ruler

Measure the rate of flow out of the cup into the graduated cylinder.

• fill the cup with water and put your finger over the hole
• release your finger and let the water flow out into the graduated cylinder while you record time and volume
• simultaneously record the height in the cup
• do this several times to both improve your technique and get reproducible results

Plot the flow rate (in mL per second) vs. the height of water in the cup (in cm)

• create an Excel table
• calculate the rate of water that flowed during a time interval (such as 20 seconds, but that depends on the size of the hole)
• calculate the average height of water during that interval
• put your results into Excel and generate individual or average plots

Determine the relationship between the volume and the height of water in the cup. Since your cup is not a cylinder (but more like a conical frustrum), higher in the cup holds more volume. Here's a simple way to do that:

• pour 50 mL of water at a time into your cup (with the hole plugged) and measure the depth
• make a plot of the total volume vs. depth

If you have this data and there is relatively good comparison between several runs, then you are done. Please record all the data and each of you in the group should have a copy.

Consider how you would describe (and then model) the height of water in the cup with time as water flows out.

Part 2: second week in lab - measure the heights and flow rates in a multiple cup system

You will need:

• same materials as for part 1
• another 2 cups, one with a hole in it and one final cup
• some stands for propping the cups such that "cup one" flows into "cup two" flows into "cup three"

Calibrate the flow vs. height relationship for each cup. You can't assume that the holes are the same.

Put the three cups in order and measure the height of the water in the three cups with time. Run this several times, record and compare the data so that you know you have good data to work with.

Part 3: third week on computers - create a STELLA model for the 3 cup system

Create a STELLA model for the 3-cup system.

The diagram should look like your physical system.

The equations you will need to supply convert the volume of the each cup into a height and use that to determine flow. It might look like this, or you might have another way to do it.

flow_1_to_2 = cup_1 * (height/volume relationship) * flow_rate_constant_1

Checking the units of this equations ---

volume/time = volume * height/volume * volume/(time * height)

 

Part 4: written assignment - compare measured to modeled

Each student in a group that has worked together will submit a separate report. The report will contain four parts:

1. a description of the overall assignment
2. the data and graphs (in a neat and presentable manner) from the measurement of the 3-cup system
3. a description of the STELLA model and example output
4. A comparison and evaluation of how closely the model described your direct observations and reasons why they might be different. Suggestions how what might have lead to errors and what you might do differently if you were to do this again.

The total report should only be about four pages.