## How to Calculate and Solve for Newton’s Laws of Viscosity of Gases | Transport Phenomena

The image above represents newton’s laws of viscosity of gases.

To compute for newton’s laws of viscosity of gases, four essential parameters are needed and these parameters are Number of Molecules (m), Boltzmann’s Constant (KB), Temperature (T) and Pipe Diameter (d).

The formula for calculating newton’s laws of viscosity of gases:

η = 2(mKBT)0.5 / 1.5.d²

Where:

η = Newton’s Law of Viscosity of Gases
m = Number of Molecules
KB = Boltzmann’s Constant
T = Temperature
d = Pipe Diameter

Let’s solve an example;
Find the newton’s law of viscosity of gases when the number of molecules is 14, the boltzmann’s constant is 1.380E-23, the temperature is 10 and the pipe diameter is 21.

This implies that;

m = Number of Molecules = 14
KB = Boltzmann’s Constant = 1.380E-23
T = Temperature = 10
d = Pipe Diameter = 21

η = 2(mKBT)0.5 / 1.5.d²
η = 2((14)(1.380e-23)(10))0.5 / 1.5.(21)²
η = 2(1.93e-21)0.5 / (16.70).(441)
η = 2(4.396e-11) / 7366.89
η = 8.79e-11 / 7366.89
η = 1.19e-14

Therefore, the newton’s law of viscosity of gases is 1.19e-14 m²/s.

## How to Calculate and Solve for Mean Free Path | Transport Phenomena

The image above represents mean free path.

To compute for mean free path, two essential parameters are needed and these parameters are Pipe Diameter (D) and Number of Molecules (m).

The formula for calculating mean free path:

λ = 1 / √(2)π.D²m

Where:

λ = Mean Free Path
D = Pipe Diameter
m = Number of Molecules

Let’s solve an example;
Find the mean free path when the pipe diameter is 35 and the number of molecules is 7.

This implies that;

D = Pipe Diameter = 35
m = Number of Molecules = 7

λ = 1 / √(2)π.D²m
λ = 1 / √(2)π..(35)²(7)
λ = 1 / (4.442).(1225)(7)
λ = 1 / (4.442).(8575)
λ = 1 / 38097.721
λ = 0.0000262

Therefore, the mean free path is 0.0000262.

## How to Calculate and Solve for Average Speed of Gases | Transport Phenomena

The image above represents average speed of gases.

To compute for average speed of gases, three essential parameters are needed and these parameters are Boltzmann’s Constant (KB), Absolute Temperature (T) and Number of Molecules (m).

The formula for calculating average speed of gases:

v’ = (8KBT / πm)0.5

Where:

v’ = Average Speed of Gases
KB = Boltzmann’s Constant
T = Absolute Temperature
m = Number of Molecules

Let’s solve an example;
Find the average speed of gases when the boltzmann’s constant is 1.380E-23, the absolute temperature is 12 and the number of molecules is 2.

This implies that;

KB = Boltzmann’s Constant = 1.380E-23
T = Absolute Temperature = 12
m = Number of Molecules = 2

v’ = (8KBT / πm)0.5
v’ = (8(1.3806e-23)(12) / 3.142(2))0.5
v’ = (1.325e-21 / 6.2831)0.5
v’ = (2.109e-22)0.5
v’ = 1.45e-11

Therefore, the average speed of gases is 1.45e-11 m/s.