Mass flux is an important concept in the study of fluid dynamics. Engineers, physicists, and mathematicians all use mass flux formulas to help them discover the ways fluids (including gases) behave.

    Yet, the equations to make these predictions and the concepts underlying them can be difficult to grasp. To take the confusion out of conversions, use our handy mass flux calculator.

    Below, you'll find a comprehensive guide to mass flux. By the time you're done reading it, you'll be an expert on everything mass flux, including it's formula and applications.


    What is mass flux?

    Before going over the concept of mass flux, let's focus in on the flux definition.


    Flux is a term seen commonly in physics and mathematics, and in general, it refers to a quantity of something passing through a surface or substance.

    That quantity can be air, water, or any other liquid.

    Note that we're including both air and water here. We commonly think of these things as two separate states of matter: gas and liquid.

    While that's true, scientists consider them both fluids. That's because they can both flow.

    Now, let's go over the concept of flux and see how it relates to transport phenomena.

    What is transport phenomena?

    It sounds more complex than it really is. Transport phenomena observe the exchange of things like:

    • Mass
    • Energy
    • Charge
    • Momentum
    • Angular momentum

    It's basically anything that involves mass transfer, heat transfer, or liquid flow (fluid dynamics).

    Within this framework, flux is a vector quality.

    It describes the magnitude and direction of the flow of any of these substances or properties.

    Mass Flux

    Flux can be thought of as the flow per unit area. It measures the movement of some quantity (like mass, heat, or a liquid) per time.

    Mass flux, then, is the rate of mass flow per unit area.

    If you have the area of your object figured out, you can use equations to figure out how much mass is passing through it and how long it's taking the mass to do so.


    In short, mass flux aims to measure the amount of liquid or gas passing in or out of a control volume, per unit of time.

    Which units measure mass flux?

    Remember that mass flux measures the flow of mass across a unit area.

    The standard measurement is kg/h m2 (kilograms per hour meter squared).

    There are other units that you can use to measure mass flux depending on the size or purpose of the project.

    How do you calculate mass flux?

    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:

    j_{m}=\lim \limits _{{ A\rightarrow 0}}{\frac  {I_{m}}{A}}


    I_{m}=\lim \limits _{{\Delta t\rightarrow 0}}{\frac  {\Delta m}{\Delta t}}={\frac  {dm}{dt}}

    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.

    Why convert mass flux?

    It's necessary to convert mass flux when you want to use a different measurement than the standard of kilograms.

    That's because different fluids may need smaller or larger flux units. Maybe instead of kilograms, you need grams.

    Either way, you're still measuring the mass flux of the fluid.

    While the equations for this are fairly straightforward, it's always a good idea to reference a conversion calculator. Why not try ours today?

    What are the applications of mass flux?

    It's important for scientists to know how fluids behave. And, remember, by fluids, we mean both gases and liquids.


    It seems counterintuitive, then, but understanding fluid dynamics makes flight possible.

    In the simplest terms, it helps us understand how airplanes fly through the air (which, again, is a fluid).


    The study of fluid dynamics also allows us to predict how ships and submarines move through water.

    And, it helps us learn about the flow of ocean currents as well as the Earth's weather.

    That's because not only water but also air and clouds are fluids.

    Molecular Diffusion

    Mass flux, in particular, allows us to understand diffusion processes. Think molecular diffusion or turbulent flows (turbulent diffusion).

    In fact, we have to include mass flux in any computational dynamics model where there is conservation of mass across a control volume.

    Chemistry and Biology

    It's also incredibly useful in chemical engineering. This is especially true when there is a flow through a porous medium (like a filtration system).

    Finally, in biology, mass flux can help describe how mass is transported across a semi-permeable membrane.

    As you can see, then, fluid dynamics in general and mass flux, in particular, are useful in many different fields.

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