Converting Air Flow Rate Between Kg/s And M^3/s

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Learn more about Teams Converting air flow rate between kg/s and m^3/s Ask Question Asked 9 years, 7 months ago Modified 5 years, 4 months ago Viewed 170k times 2 $\begingroup$

Is 1 kg/s of air flow rate equivalent to 1 m3/s?

I am calculating supply air flow rate into a zone for an air conditioning system. The simulation software gives the result in m3/s but the mathematical formula that I used takes in kg/s.

Do I need to convert the flow rate, and if so, how do I convert between kg/s and m3/s?

• mechanical-engineering
• hvac
• airflow

Share Improve this question Follow edited Apr 21, 2015 at 14:58 Air 3,21144 gold badges2525 silver badges4646 bronze badges asked Apr 21, 2015 at 4:19 twfxtwfx 16111 gold badge11 silver badge44 bronze badges $\endgroup$ 1

• $\begingroup$ 1 kg/s of air flow rate is about equivalent to 1 m^3/s at around 1km altitude... $\endgroup$ – SF. Commented Jul 3, 2019 at 10:41

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4 Answers 4

Sorted by: Reset to default Highest score (default) Date modified (newest first) Date created (oldest first) 8 $\begingroup$

You need to consider the density of the air, which varies with temperature and air pressure. At 15 degrees Celsius, at sea level, the density of air is 1.225 ${kg}/{m^3}$. The table here gives air densities at 5 degree intervals.

Now density is mass divided by volume,

${\rho} = m/v$

Hence, to get the volume flow rate (in ${m}^3/s$), for a know mass flow rate, divide the mass flow rate (in $kg/s$) by the density (in $kg/{m}^3$).

Thus, a flow rate of $1 kg/s$ is,

$1 / 1.225 = 0.8163 {m}^3/s$

To get the mass flow rate for a know volume flow rate multiple the volume flow rate by the air density.

Share Improve this answer Follow edited Apr 21, 2015 at 13:48 Trevor Archibald 2,82922 gold badges1414 silver badges2424 bronze badges answered Apr 21, 2015 at 4:59 FredFred 9,7521313 gold badges3333 silver badges4646 bronze badges $\endgroup$ 2

• $\begingroup$ Are four significant digits warranted? $\endgroup$ – Peter Mortensen Commented Apr 21, 2015 at 10:29
• 3 $\begingroup$ @PeterMortensen Take a look at the density values in the table Fred linked. A 5 °C change in temperature corresponds to roughly a 0.02 $kg/m^3$ change in density. Since the values given go to 4 sig figs, I'd say staying at that level of accuracy is appropriate. $\endgroup$ – Trevor Archibald Commented Apr 21, 2015 at 13:56

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HVAC-Systems usually give a Volume-Flow-Rate, hence $m^3/s$. If you need Mass-Flow-Rate ($kg/s$) you simply need to multiply with the density ($\rho$) of the fluid. The density can be calculated using the ideal gas law (see 1):

$$ \rho_s = \frac{p_s}{R T_s}$$

Please observe that you need static values for the pressure ($p_s$, see 2) and temperature ($T_s$, see 3). The specific gas constant ($R$, see 4) for air is depending on the humidity of the air but $287.058 J/kg/K$ is a good starting point. For low velocities static and absolute values are so close to each other that you should be able to use the absolute/ambient pressure and Temperature. However, the density is changing with pressure and temperature, neglecting either will decrease the accuracy of the measurement.

From my experience the HVAC system has a measurement-error ($5\%$) which is larger than the error which is made by assuming static=total.

All values in SI units!

Share Improve this answer Follow edited Apr 21, 2015 at 5:30 answered Apr 21, 2015 at 5:09 rul30rul30 1,2021010 silver badges2424 bronze badges $\endgroup$ Add a comment | 1 $\begingroup$

Constant Mass Flow:

$$ \dot{m} = \rho A V $$

(Hence mass flow is equal to density times area times velocity.

So assuming you have an area of $1$ m^2 with a velocity of $1$ m/s, air with a density of $1.225$ kg/m^3 will equate to a mass flow of $1.225$ kg/s. For incompressible flows, the mass flow rate is constant.

Share Improve this answer Follow answered Apr 21, 2015 at 16:42 BeyondLegoBeyondLego 95066 silver badges1111 bronze badges $\endgroup$ 1

• 1 $\begingroup$ Caution! Incompressibility (Velocity<<Ma=0.3) only shows constant density as far as the flow field is concerned. When pressure, temperature or humidity change due to weather or other process influences (flight altitude etc.) density changes as well. $\endgroup$ – rul30 Commented Apr 21, 2015 at 22:16

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You need to understand that whilst the flow rates may remain static, the mass will not be so because warmer air is lighter and less dense whilst chilled aircon air is substantially heavier. The difference between them determines the power required to transfer the air by the machine to the zone your looking into.

The difference in calculations is to answer two different questions: power consumption or airflow {m^3 \cdot s}

Share Improve this answer Follow answered Jul 11, 2018 at 2:09 RhodieRhodie 98244 silver badges1616 bronze badges $\endgroup$ Add a comment |

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