Dynamic Viscosity Ratio of Air and Water: Exploring Fluid Dynamics at Standard Conditions

What is the ratio of the dynamic viscosity of air to that of water at standard pressure and a temperature of 20 degrees Celsius?

a) 1,81 x 10^-5

b) 1.81 x 10^-3

c) 1.81 x 10^-2

d) 55.249 x 10^-5

e) 55.249 x 10^-2

Final Answer:

The ratio of the dynamic viscosity of air to that of water at standard pressure and a temperature of 20 degrees Celsius is option (d) 55.249 x 10^-5.

Dynamic viscosity is a measure of a fluid's resistance to flow. It is given by the formula:

μ = ρ * ν,

where μ is the dynamic viscosity, ρ is the density of the fluid, and ν is the kinematic viscosity (ratio of dynamic viscosity to density).

At standard pressure and a temperature of 20 degrees Celsius (293.15 K), the density of air (ρ_air) is approximately 1.204 kg/m³ and the kinematic viscosity of air (ν_air) is approximately 1.48 x 10^-5 m²/s.

For water at the same conditions, the density of water (ρ_water) is approximately 998 kg/m³ and the kinematic viscosity of water (ν_water) is approximately 1.004 x 10^-6 m²/s.

Now, let's calculate the ratio of dynamic viscosity:

Ratio = (μ_air / μ_water) = (ρ_air * ν_air) / (ρ_water * ν_water).

Substituting the values, we get:

Ratio = (1.204 kg/m³ * 1.48 x 10^-5 m²/s) / (998 kg/m³ * 1.004 x 10^-6 m²/s) ≈ 55.249 x 10^-5.

Therefore, the correct answer is option (d) 55.249 x 10^-5, which represents the ratio of the dynamic viscosity of air to that of water at standard pressure and 20 degrees Celsius.