Let's be honest. There's a reason people use computational models to figure out mass flux.
In fact, there's a whole field of study learning how fluid dynamics can be done with computers. It's called computational fluid dynamics (CFD).
But that doesn't mean you can't do it yourself. Let's give it a try here.
Step One: Control Volume
The first thing you have to do to figure out mass flux is define the control volume. Your matter is in a space, called a volume.
Its size is constant and predetermined, which is why it's a control volume. It could be a pipe or any other enclosed thing.
Remember, also, the principle of the conservation of matter. It cannot be destroyed or created.
That means the amount of mass you have in your predetermined volume will remain constant.
Mass flux measures the amount of this matter passing in or out of your control volume in time.
Step Two: Cross Section
Next, you need to know what your matter is passing through. This will be a cross-sectional area of your control volume.
You also need to know the velocity of your matter as it passes through this area.
Your final piece of information is the density of the mass flowing through that cross-sectional area. Sometimes the density isn't immediately available, and you have to measure it. Other times, it's assumed.
Step Three: Solve
The equation for mass flux is as follows:
Mathematically, we can define mass flux as the limit.
The flow of mass is m, and the unit of time is t. A is the area the mass is flowing through.
You can also add in other variables, such as surface integrals or vector areas. The flux equations then grow quickly in complexity!
Sometimes you have to convert your units of measurement before you do your equation.
In the next section, let's see why.