Introduction to mass, energy and momentum balances

Mass, energy and momentum balances

Have you ever learned about the concept of setting up balances? Setting up balances is on of the most important weapons of the Chemical Engineer. It can be used to study and solve problems related to mass, energy and momentum problems. This post will give an introduction to the concept of setting up balances on control volumes.

General balances

The general form of a balance is made up out of accumulation, inflow, outflow, production and consumption. A balance is always made on a control volume. This control volume specifies the borders of the balance. The in- and outflowing terms pass this border and production/accumulation terms take place inside these bordes.

These terms can be combines into the following equation:

Accumulation = in – out + production – consumption

The consumption term is sometimes treated as a negative production term. The equation therefore simplifies into:

Accumulation = in – out + production

Population growth

An example is the best way to illustrate the concept of balances. The Netherlands, for example, had a population of 16 900 726 people in 2016 (source: cbs). If we want to determine the population growth of the Netherlands with the help of balances, then we have to choose the entire country as our control volume.

The immigration has been a loaded subject in recent years. Today, in our balance, it will serve as the inflowing term. A total of 230 739 people (legally) entered the Netherlands in the year 2016. The inflowing term therefore amounts 230 739 people/year. A total of 151 545 people left the country in 2016 by emigration. This number represents the outflowing term. A total of 172 520 babies were born in 2016. This represents the production term.The production was counteracted by a death rate of 148 977 people. We can treat this term as consumption. There are of course other minor influences as people illegally entering the country or people moving on holiday. However, effective engineers make assumptions to make problems more manageable. We therefore neglect these terms.

Population growth Netherlands with balances

Now we can setup our balance to determine population growth:

Accumulation = in – out + production – consumption

Population growth = immigration – emigration + birthrate – death rate

Population growth = 230730 – 151545 + 172520 – 148 997 = 102 717 people/year

This means that the population of people grew with 102 717 people in the year 2016. This represents a growth rate of 102 717/16 900 726 = 0.6%.

Balances can also be used for solving mass, energy and momentum problems. This, however, will be covered in future posts.

@ Transport phenomena

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