# How to compute the residence time for given flow rate in standard cubic meters?

I'm given a flow rate of a gas mixture of $3\ \mathrm{Nm^3/h}$ in standard cubic meters through a cylinder of length $50\ \mathrm{cm}$ and cross section $70\ \mathrm{cm^2}$, can I compute how long a particle will stay inside of the cylinder (which would equal the time the particle can react inside the cylinder)?

And what if the temperature changes during the reaction?

If the flow rate would be given in volume per time, I had an idea to compute this, but the use of standard cubic meters is baffling to me.

• $Nm^3/h$ is volume per time, you just need to transform it the the units you need. the correction for temperature can be done with the ideal gas law (Or Redlich-Kwong, if you want to be really exact). Also note that you will get a mean retention time, not all particles will spend the same time in the reactor. – mart Aug 14 '12 at 15:14
• Isn't the the unit with the N in from something else than just a length? – Nikolaj-K Aug 14 '12 at 17:29
• @chm: The English Wiki has only standard cubic feet... – cbeleites unhappy with SX Aug 16 '12 at 13:45

The N stands for "norm" and should be avoided (in fact, the German Wiki page lists the Nm³ as wrong abbreviation) as it can create confusion.(qed)

So your flow should be written as "3 m³/h under standard condtions". If you can guess German, have a look at the German Wiki page. It is much better than the English one.

Standard conditions vary a bit between different norms

T = 0 °C or 15 °C or 20 °C p = 1.01325 bar (sometimes 1 bar)

The gas is supposed to be dry.

• k, I'm still not sure how this solves the problem. Like does this mean that for other T and p values, the flow rate is different? Does this deviation depend on the specific gas? I'm really interested in the residence time, the unit thing is just keeping me from it. – Nikolaj-K Aug 15 '12 at 16:25
• cbeleites understood your question better than me. Think of the amount (in moles or kg) of gas you have in a m³ under standard conditions, and adjust for the p and T you actually have. In most cases, you can wotk with the ideal gas law and then it's not specific to a certain gas. – mart Aug 16 '12 at 6:51