Mass Flux Calculator

Enter the values you know and leave the unknown blank. Use density and velocity for G = ρ · v, or a mass flow rate with the pipe area for G = &mdot; / A. Fill in both sides and the calculator bridges between them.

Density (rho)

Velocity (v)

Cross-sectional area (A)

Mass flow rate (ṁ)

Mass flux (G)

Show the Reynolds number and flow regime

Add the Reynolds number from the mass flux and pipe size, and label the flow laminar, transitional, or turbulent.

Please input values into the fields

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Show how mass flux grows with velocity

See the straight-line relationship G = rho times v at your fluid's density.

Show mass flux for common fluids

Compare the mass flux of air, water, oil, mercury and more at your velocity.

Mass flux indicates how concentrated a flow is at a particular point within a pipe or channel. While mass flow rate gives the total mass flowing per second, mass flux divides this by the cross-sectional area to eliminate the effect of the dimensions of the pipe and reflect only the strength of the flow at that point. It is therefore used in areas where local intensity is more important than overall quantity, such as selecting boiler tubes, designing nozzles or constructing reactors.

This calculator supports two common methods of determining mass flow rate; one method calculates from the mass flow rate and area, while another determines directly from density and velocity.

What is mass flow?

Mass flux is usually denoted by G or j_m and gives the rate of mass transport per unit area. Assuming two pipes are pumping the same mass of water per second, if one pipe has twice the cross-sectional area, then the same amount of mass flux will be spread out over a larger area, halving the strength of the mass flux.

This is why the mass flow rate is so useful in engineering correlations; since geometric factors are eliminated small laboratory tubes and large industrial pipes can be considered on the same scale.

Two equations for mass flow rate:

If mass flow rate and area are known, then mass flux is calculated by dividing the mass flow rate by the area.

G = \frac{\dot{m}}{A}

If the density and velocity of a liquid are known, then mass flow is calculated as the product of these two values.

G = \rho \, v

Both methods give the same result as mass flow rate is itself the product of density, velocity and area. By substitution, the area cancels out.

\dot{m} = \rho \, v \, A \;\Rightarrow\; G = \frac{\dot{m}}{A} = \rho \, v

The SI unit is the kilogram per square metre-second, written as kg/(m²·s), which represents the mass in kilograms passing through a square meter area per second.

Instructions for using this calculator:

Enter the known values and leave the unknown fields blank. Simply enter density and velocity to get mass flow instantly. If you also enter cross-sectional area, the calculator will show total mass flow rate and volumetric flow rate as well. If you already know the volume flow rate and pipe area, just enter those values directly. If you enter density, the tool calculates mass flow and velocity.

Each field has a corresponding unit. Density can be entered in either kg/m3 or lb/ft3, velocity in either m/s or ft/s and area in either cm2 or in2. The results will automatically convert.

Example calculation:

Let's take water as an example. The density is 998 kg/m^3 and if the water flows through a pipe at a velocity of 2 m/s, then the mass flow rate would be:

G = 998 \times 2 = 1996 \ \text{kg/(m}^2\text{s)}

If now the same water is passed through a nozzle and its speed is increased to 10 m/s, then the mass flow changes.

G = 998 \times 10 = 9980 \ \text{kg/(m}^2\text{s)}

Although the fluid remains the same and only the opening becomes smaller, the flow increases fivefold. In nozzles or boiler tubes this can mean that there are reserves in normal operation but also that the equipment is about to fail.

Symbol	Meaning	Example
G	Mass flux	1996 kg/(m^2 s)
m_dot	Mass flow rate	5 kg/s
A	Cross-sectional area	0.0025 m^2
rho	Density	998 kg/m^3
v	Velocity	2 m/s

Mass flow applications:

In heat exchangers and boilers engineers monitor the mass flux to prevent a failure mode called "drying out". This is when the liquid film covering the tube wall evaporates, leading to overheating of the metal. Boiler codes specify safe ranges for mass flux for each tube shape and thermal load, and many operating problems are due to operation outside these limits.

They also play an important role in fixed bed reactors. The rate of reaction and pressure drop is not determined by the total volumetric flow but rather by the mass flow through the catalyst bed. If you double the diameter of a reactor without changing the volumetric flow, then the process will change even if feed does not change.

Nozzles see the same numbers but for different reasons. The quality of atomization depends on the local mass flow rate at the nozzle exit. In HVAC systems both the mass flow rate through filters, coils and ducts as well as pressure drop and heat transfer efficiency are determined. So even pipes of the same size have different performance when one transports warm air and another dense cold air.

Mass flow rate and Reynold's number

Mass flow rate is a natural input to the Reynold's number. The Reynold's number is used to determine whether a flow is laminar or turbulent. Expressed in terms of mass flow rate G and pipe diameter D, the Reynold's number is given by the product of G and D divided by viscosity.

Re = \frac{G \, D}{\mu} = \frac{\rho \, v \, D}{\mu}

Values below about 2300 are laminar, values above about 4000 are turbulent and in between is a transition region. This should be avoided if possible. By activating the Reynolds option this value and flow state can be determined from the mass flow rate and dimensions of the pipe.

Typical values for mass flow rate

The following sections are intended to give an idea of the values that can be achieved with commonly used instruments.

Setting	Typical mass flux
Water in industrial piping	500 to 3000 kg/(m^2 s)
Steam in boiler tubes	200 to 2000 kg/(m^2 s)
Air in HVAC ducts	1 to 5 kg/(m^2 s)

Frequently asked questions

What is the difference between mass flow rate and mass flux?

The mass flow rate (m_dot, units kg/s) is the total mass passing a given point per second and depends on the dimensions of the pipe. The mass flux (G, units kg/(m^2 s)) is calculated by dividing this by the area which gives a flux-like quantity that is independent of the shape of the pipe. Even if two pipes with different diameters carry the same mass flow rate, the mass flux can be very different.

How to calculate mass flow?

There are two equivalent methods. You can multiply the density of the fluid by its velocity to get G = rho*v. Alternatively you can divide the mass flow rate by the cross-sectional area to get G = m_dot/A. Since the mass flow rate is the product of density, velocity and area both methods will give the same result in kg/(m^2 s).

Can mass flow rate be negative?

Conventionally a minus sign only indicates that the flow direction is opposite to the surface defined as positive. As this tool outputs a magnitude value please input positive values.

What is the relationship between mass flow rate and Reynold's number?

The Reynolds number can be written as follows: Re = (G*D)/mu where G is the mass flow rate, D is the pipe diameter and mu is the viscosity. Values below about 2300 indicate laminar flow while values above about 4000 indicate turbulent flow. The mass flow rate is a convenient input because it already combines density and velocity.

What are typical values of mass flow rate?

In industrial pipes water usually flows with a mass flux of 500 to 3000 kg/(m2s). Steam in boiler tubes is about 200 to 2000 kg/(m2s). Air in HVAC systems is much lower, about 1 to 5 kg/(m2s).

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

Engineering ToolBox: Mass Flow and Mass Flux
Reference for mass flow rate, flux, and fluid density data.
NIST Chemistry WebBook: Fluid Properties
Authoritative density and viscosity data for common fluids.