**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 + Generation - Output - Consumption = Accumulation

**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.