# What should be the density of a compressed gas while measuring the flow rate using Rotameter?

Say we have a required mass flow rate, in order to have equivalent volume flow rate, we need to consider density of the operating fluid (compressible fluid).

To measure the volume flow rate in LPM, I'm using a rotameter. I'm controlling the flow using a needle valve upstream of the rotameter. The regulated pressure upstream of the needle valve is 20 bar and the pressure downstream the rotameter is ambient (1 atm).

Should I consider the density of the operating fluid (say oxygen) relating to the upstream pressure (20 bar) or the downstream (1 bar ambient)

In, compressible flow, the mass flow rate remains constant throughout the flow. But volume flow rate is changed according to the local velocity and area of cross-section. So one can calculate the volume flow rate locally by diving the mass flow rate by local density.

Let say, If you need volume flow rate at the exit,

At the exit, the pressure is 1 bar and the ambient temperature is 27$^\circ$C which gives ~ 1.88 kg/m$^3$. (refer equation given by solar mike).

So your volume flow rate at the exit is $\dot V = \dot m$/1.88 m$^3$/s.

Note: It looks like your flow is a choked flow since the pressure comes down from 20 bar to 1 bar. So keep this in mind while calculating and interpreting the values.

Gas density can be calculated from:

$$\rho = \dfrac{P}{RT}$$

where $\rho$ is the density, $P$, the pressure, $R$, the gas constant, and $T$, the temperature.

You should evaluate the change in density between the two pressures and decide what to do - this will be based on the fluid you are using...

• @SamFarjamirad typo - put the brackets for the division.... edited now BTW a way we remembered it was rho=prat ... – Solar Mike Aug 24 '18 at 14:06
• For ideal gases, molar density (mol/m$^3$) is $p / RT$ and (mass) density (kg/m$^3$) is $M p / R T$ where $M$ is molar mass of the gas. – Jeffrey J Weimer Aug 24 '18 at 14:16