# Kinematic Viscosity Formula

Kinematic viscosity is the measure of the inherent resistance of a fluid to flow when no external force is exerted, except gravity. It is the ratio of the dynamic viscosity to its density, a force independent quantity. Kinematic viscosity can be obtained by dividing the absolute viscosity of a fluid with the fluid mass density.

Kinematic viscosity = Dynamic viscosity / Fluid mass density

The equation is written

ν = η / ρ

We have:

ν: Kinematic viscosity

ρ: fluid density

η: Dynamic viscosity

Kinematic Viscosity Formula Questions:

1) In a liter of mercury that weights 2 Kg, what is its kinematic viscosity?

Answer: The dynamic viscosity of mercury is η= 1.526 Pa*s. First calculate the density mass of mercury using the formula ρ = mass/volume.

ρ = 2 Kg/ 1 L = 2 Kg/ 0.001 m^{3} = 2000 Kg/m^{3}

Then calculate the kinematic viscosity using its formula,

ν = η / ρ

ν = 1.526 Pa*s / 2000 Kg/m^{3} = (1.526 N*s/m^{2}) / (2000 Kg/m^{3})

ν = 0.000763 m^{2}/s

2) what is the density of a fluid that has a kinematic viscosity of 1 m^{2}/s and a dynamic viscosity of 0.018 Pa*s?

Answer: From the formula of kinematic viscosity we can find the density,

ρ = η / ν and then substituting the values,

ρ = (0.018 N*s/m^{2}) / (1 m^{2}/s) = 0.018 Kg / m^{3}

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