Ratio of the molecular free path to characteristic length scale of flow is:

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AAI JE (Technical) Official Paper 2020

Option 1 : Knudsen number

ST 2: Strength of materials

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__Explanation:__

Knudsen number:

The **Knudsen number** is defined as the ratio of the molecular mean free path length to physical(characteristic) length scale. It is a dimensionless number It is denoted as 'Kn'

\(Kn= {molecular free path \over Characterstic length scale }\)\(= { \lambda \over L}\)

Mean free path (\(\lambda\)): It is the average distance travelled by the moving particle between successive impacts (collisions),which modifies direction or properties

Characteristic Length(L): It is the ratio of volume of a body to surface area

This length scale : for example, the radius of a body in a fluid.

**Laplace number:**

The Laplace number is also known as the **Suratman number**. It is a dimensionless ratio of the surface energy to **the momentum or dissipation** in a fluid, such as is encountered in liquid-phase sintering or liquid atomization. The Suratman number Su is given as follows:

\(Su = \frac{γ_{LV} {ρ}{ R}}{η}\)

Where ρ is the liquid density in kg/m^{3} (Convenient units: g/cm^{3}), R is the characteristic length scale in m and for most cases is taken as the particle size, γ_{LV} is the liquid-vapor surface energy in J/m^{2}, and η is the fluid viscosity in pa.s

**Galilei number:**

Galilei number (Ga) is also referred as Galileo number it is a dimensionless number, it is proportional to the gravity forces divided by the viscous forces. It is used in viscous flow and thermal expansion calculations.

\(Ga = \frac{gL^3}{ν^2}\)

Where g = gravitational acceleration (m/s^{2}), L = characteristic length (m), ν = characteristic kinematic viscosity (m^{2}/s).

**Marangoni number:**

It is a dimensionless number, equal to the ratio of surface tension gradient to the product of viscous drag and the rate of heat diffusion.