Nm3 Conversions

One of the frequent conversion problems encountered in our industry is to convert from or to Nm3. We all know that the volume of gases change according to pressure. So, the conventional unit of m3/hr cannot be used to measure volumetric gas flow rates. Nm3 simply provides a standard of gas flow measurement. Nm3 is the equivalent flow at a standard temperature and pressure.
Temperature standard can be either at 0 °C, 15 °C or 25 °C. Pressure standard is mostly taken at 1 atm.
Suppose, to convert 1 Ton of Nitrogen into Nm3, we can safely use the ideal gas law for all practical estimates:

The volume, V is the volume in Nm3 as it is the volume under defined conditions of 1 atm and 0 °C.

Again, to convert 1 litre of Liquid Nitrogen into Nm3, we can use the same method:

Time taken to drain a cylindrical tank

Probelm: Consider a cylindrical tank with a cross-sectional area of ‘A’, liquid filled to a height ‘h’. It has a drain line of cross-sectional are ‘a’. The tank is being drained under gravity, how much time will it take to drain the tank (ignoring effects due to friction and viscosity)?


Solution: The key to solve the problem is to equate the drain flow rate to the level drop in the tank. But the trick is that the drain flow rate depends on the level.
Drain flow rate = cross-sectional area x velocity
=
Velocity is obtained by equating potential energy to kinetic energy as it is freely falling under gravity,

Rate of volume drop in the tank = cross-sectional area x rate of infinitesimal level drop in the tank
=
Equating both, we have

Solving which, we get:

which is the time taken to drain the tank completely.