Material Balances

Material balances are typically mass balances, based on the Law of Conservation of Mass. This can be explained with this statement:
"total mass input" = "total mass output".
The general balance equation, a form of the previous statement, is:

Input is the mass that enters through the system boundaries.
Generation is the mass that is produced within the system.
Output is the mass the exits the system boundaries.
Consumption is that consumed within the system.
Accumulation is the buildup within the system.
Here is a basic schematic of a system:

```                  _____________
|           |
----------------->|  Process  |----------------->
flow rate in    |   Unit    |   flow rate out
q(in), mass/time  |___________| q(out), mass/time

```
Material balances are heavily used in Chemical Engineering and Biomedical Engineering to determine flow rates and ideality of a system, and can also be applied to other fields as in population models.

Here is a simple example population problem solved with a material balance:

Every year 30,000 people move into East Newark, 70,000 people move out, 20,000 are born, and 17,000 die. Using a material balance, determine how much the City's population changes each year (accumulation).

Solution:
Let P stand for people.
Using the equation above,

```                  ______________
|             |
----------------->|    East     |----------------->
30,000 P/yr    |   Newark:   |   70,000 P/yr
|+20,000 P/yr |
|-17,000 P/yr |
|_____________|

Input       + Generation -  Output -      Consumption = Accumulation
30,000 P/yr + 20,000 P/yr - 70,000 P/yr - 17,000 P/yr = Accumulation
Accumulation = -37,000 P/yr
```
This means that 37,000 people leave East Newark each year.