Question

Using Sutherland’s equation and ideal gas law, develop an expression for the kinematic viscosity ratio n/n₀ in terms of pressures p and p₀ and temperatures T and T₀, where the subscript refers to a reference condition

Answer 1

Kinematic viscosity = dynamic viscosity / density

= /   

Ratio of kinematic viscosity

/₀ = ( ₀  x ) / ( x ₀ ) ......... Eq1

From the ideal gas equation

PV = nRT

PV = (m/M) RT

PM = (m/V) RT

Mass(m) /volume (V) = density

PM = RT

For the same gas

₀ / = TP₀ / T₀P ......... Eq2

From the Sutherland’s equation

The ratio of dynamic viscosity

/ ₀ = (T/T₀)^3/2 [(T₀ + S) / (T + S)] ........ Eq3

S = Sutherland’s constant

Now put the values from Eq2 and eq3 into Eq1, we get

/₀ = (T/T₀)^3/2 [(T₀ + STP₀) / (T + ST₀P)]

/₀ = (P₀/P) (T/T₀)^3/2 [(T₀ + S) / (T + S)]