The Prandtl number is defined as the ratio of thermal diffusivity to momentum diffusivity.

The Prandtl number is defined as the ratio of thermal diffusivity to momentum diffusivity.

• A. The ratio of dynamic viscosity to thermal diffusivity
• B. The ratio of density to viscosity
• C. The ratio of thermal diffusivity to momentum diffusivity
• D. The ratio of kinematic viscosity to the thermal diffusivity

Answer: (D)

The essential idea is that the Prandtl number compares how quickly momentum diffuses through a fluid to how quickly heat diffuses. It is the ratio of momentum diffusivity to thermal diffusivity, written as ν/α. Here, momentum diffusivity is the kinematic viscosity ν (μ/ρ) and heat diffusivity is the thermal diffusivity α (k/(ρ Cp)). Putting these together shows Pr = ν/α = (μ/ρ) / (k/(ρ Cp)) = μ Cp / k. This makes Pr a dimensionless quantity that depends on fluid properties and temperature. Therefore the correct interpretation is the ratio of kinematic viscosity to thermal diffusivity. The other forms either use the wrong diffusivity or involve quantities that do not yield a dimensionless Pr in general (for example, using dynamic viscosity instead of ν, or using α in the numerator).

The essential idea is that the Prandtl number compares how quickly momentum diffuses through a fluid to how quickly heat diffuses. It is the ratio of momentum diffusivity to thermal diffusivity, written as ν/α. Here, momentum diffusivity is the kinematic viscosity ν (μ/ρ) and heat diffusivity is the thermal diffusivity α (k/(ρ Cp)). Putting these together shows Pr = ν/α = (μ/ρ) / (k/(ρ Cp)) = μ Cp / k. This makes Pr a dimensionless quantity that depends on fluid properties and temperature.

Therefore the correct interpretation is the ratio of kinematic viscosity to thermal diffusivity. The other forms either use the wrong diffusivity or involve quantities that do not yield a dimensionless Pr in general (for example, using dynamic viscosity instead of ν, or using α in the numerator).