Question

The Knudsen number plays an important role in low-density flow problems, defined as K_n = \lambda / LK n ​ =λ/L, where \lambdaλ is the mean free path and LL a characteristic length. Flow for which K_n \geq 1K n ​ ≥1 is called free molecular flow because very few collisions take place over the distance LL. Consider a 30-cm sphere traveling through the atmosphere and take the diameter as the characteristic length. Find the altitude (in km) above which free molecular flow prevails. Assume a collision diameter of 3.7 Angstroms and a temperature of 280 K. Use the following relation to relate atmospheric number density to altitude. n​/n(H=0) = exp(-0.00010603 H)

Answer 1

Knudsen Number is the ratio of the molecules' mean free path to the system's longitude scale.  

Explanation:

Knudsen Number is the ratio of the molecules' mean free path to the system's longitude scale.  

• When a gas is stored in a cubic container then the length of the box can be chosen as the characteristic length and mean free path as the average distance traveled by a molecule prior to collision. The mean free path depends on molecular diameter and number of molecules present in the system. Larger diameter and greater number of molecules would the the molecules' mean free path.
• Knudsen Number is important because we want to know whether or not the structure that we are dealing with can be called a continuum. To hold that true, typically the Knudsen Number should be below 0.1. Conversely, if the Knudsen number is high then the mean free path between individual molecules is greater than the length scale of the system. For gases, it implies that there is plenty of free space in the system which means low molecular density or less molecules per unit volume, particularly in the case of rarefied gasses or vacuum like conditions.