# Mass Balance Model

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This material was originally created for Starting Point:Introductory Geology
and is replicated here as part of the SERC Pedagogic Service.

#### Summary

Students are introduced to the concept of mass balance, flow rates, and equilibrium using a simple water bucket model. In this JAVA based online interactive modeling activity students can vary flow rate into the bucket, initial water level in the bucket, and residence time (lifetime) of water in the bucket. After running the model, the bucket's water level as a function of time is presented graphically and in tabular form.

## Learning Goals

• Learn the basics of mass balance;
• Apply this knowledge to two examples with similar structure:
• Temperature and heat loss;
• Bank Balances.
• Learn that at equilibrium the flow rate equals the outflow rate;
• Learn how to calculate equilibrium levels given inflow rate and residence time;
• Make simple graphs;
• Use a model to help develop basic equations.

## Context for Use

This activity is appropriate for introductory geoscience courses in which a fundamental knowledge of mass balance concepts is important.

## Description and Teaching Materials

The complete activity with assignment in PDF format and online model is available at Model Activity page

Mass Balance Activity (Acrobat (PDF) 289kB Jun7 11) is the activity available for students online at Model Activity page

Mass Balance Activity (Microsoft Word 89kB Jun7 11) is an MS Word document that can be modified by you.

## Teaching Notes and Tips

This activity takes about 2-hours to complete.

This activity works best with a PC, but with proper configuration also works on MAC OS X.

Little mathematical background is required to complete this activity.

Students typically have little trouble answering the first 17 questions in this activity. Students usually have to think more carefully when using the online model for the two structurally similar examples at the end of the activity (home heating and bank loan balance). Encourage them to keep units clear in their mind. For the water bucket, level is expressed in gallons and time in min; for the home heating, level is in degrees Celsius and time in hours; and for the bank loan, level is in US\$ and time is in months.

I often use a 2-liter pop bottle, with flow from a hose into the top and a hole in the bottom, as a physical model during an in class discussion of mass balance and the water bucket model. The lifetime (residence time) for this water bucket model is then related to the hole size in the bottle and viscosity of the water.

## Assessment

Mass Balance Activity Answers (Acrobat (PDF) 292kB Aug18 04) in PDF format for easy grading.

Grading the completed activity sheet provided can be used as an assessment of student understanding. Follow-up discussions in class, essay questions on exams, and the future success of students on other related activities are also useful measures of student understanding.

## References and Resources

The water bucket mass balance model described here is the first of four activities that I use in my courses when discussing Earth's Climate and Stratospheric Ozone.

The next activity in the sequence, Trace Gases , is designed to extend these fundamental ideas and the terminology of mass balance into an atmospheric science context. If you are short on time you can highlight key aspects of this activity in a lecture and then assign one or both of the related activities below.

These last two related activities can be done in any order.

See more Mathematical and Statistical Models Exampels »