# Mass flow rate explained (kg/s)

What is mass flow rate and how to calculate mass flow rate

3 You will often see flow rates listed on engineering designs and specifications, these are usually measured in either

• Velocity flow rates ( usually m/s)
• Volume flow rates (usually L/s or m3/s or m3/h)
• Mass flow rate (usually kg/s)

## What is a mass flow rate?

Mass flow rate is simply a measurement of the amount of mass (weight) passing by a single point over a length of time. (Click here to see the difference between weight and mass). We (pretty much the entire world) measure mass flow rate in the SI units of kilograms per second (kg/s) except in America where they still use British Imperial units of pounds mass per second (Ibm/s).

The symbol for mass flow rate is an m with a dot above e.g.

## Why is mass flow rate important?

Mass is always conserved, it is not created or destroyed. Therefore, if water enters a pipe at 1 kg/s it must leave the pipe at 1 kg/s also, as long as there are no leaks! However, the volume flow rate can change and will do so if the density changes either through a change in pressure or temperature.

## Example

Water enters a pipe at 50°c at 1kg/s, it is heated and exits at 80°c at 1kg/s, assuming no change in pressure, what will the volumetric flow rate be. Density of water at 50°c (323K) at atmospheric pressure = 988.05kg/m3Density of water at 80°c (323K) at atmospheric pressure = 971.80kg/m3Inlet Volume flow rate = 0.001012m3/s Mass flow rate at inlet = 988.05kg/m3 x 0.001012m3/s = 1kg/sMass flow rate at inlet = 1kg/s ÷ 971.80kg/m= .00103m3/sAnswer: 00103m3/s

## How do we measure mass flow rate?

There are two common methods to measure a mass flow rate

• Let the liquid flow into a weigh tank and measure the time taken.
• Calculate it using velocity or volume flow rate multiplied by the fluids density.

The second method is most common and practical.

The first method is usually impractical for many applications. But in the rare case that this is practical, the measurement can be achieved by either

• Placing an empty tank and a specified mass (e.g 10 kg) on either side of a counter balance weigh scale. The person taking measurements then uses a stopwatch to time how long (in seconds) it takes to flip the scales from the side with the 10 kg mass to the tank side (which will now be 10 kg) and divides the mass (weight) by the amount of seconds it took, thus giving you mass per time (kg/s). As you can probably tell, this is a fairly inaccurate method but it will give you a rough idea of the mass flow rate.
• The other method is to let the liquid flow into an empty tank for a specified amount of time, then stop the flow and weigh it’s mass..

Don’t forget to zero the scales for the mass of the empty tank.

• The final and most practical method is to measure, or calculate, the volumetric flow rate and multiply this figure by the density of that fluid.

Density is measured in kilograms per meter cubed (kg/m3). Multiplying volumetric flow rate in the units of meters cubed per second (m3/s) by kilograms per meters cubed (kg/m3) = kilograms per second (kg/s).

Remember though that the density and volume of a fluid will change with pressure and temperature so you will need to lookup the values first, to make life simple, we have conveniently tabulated the density, as well as other properties, of some common fluids at different temperatures, follow the links. Carbon Dioxide (CO2), Air (O2), Water (H2O).

## Example

Density of water at 50°c (323K) at atmospheric pressure = 988.05kg/m3Volume flow rate = 0.001012m3/s Mass flow rate = 988.05kg/m3 x 0.001012m3/sAnswer: 1 kg/s

Often a device will be used to compute the mass flow rate by measuring the volume flow rate (from the pressuere difference ΔP ) and then multiplying this by the density of the fluid at the measured temperature (T) and pressure (P).

## Summary

• Mass flow rate is conserved
• Volume flow rate changes
• Mass flow is measured in SI units of kg/s
• Mass flow can either be measured of calculated
• Mass flow rate is calculated from the volume flow rate x the fluid density

1. samuel f garcia