# Exam Problem #24 (The Prandtl Number)

## Question

Concerning the Prandtl Number, which of the following statements is FALSE.

A) There is no increase or decrease with a change in density?

B) The Prandtl Number decreases with an increasing thermal diffusivity.

C) The volume of the fluid can increase or decrease the Prandtl Number

D) When the Prandtl Number is low, heat dissipates quickly compared to the velocity.

## Answer

Today’s PE/EIT problem is about the Prandtl Number and what factors can cause a change.

### Equation

The **Prandtl Number** (*Pr*) is the ratio of kinematic viscosity to thermal diffusivity

### Variables

ρ is Density

*u* is Dynamic Viscosity

*v* is Kinematic Viscosity

*k* is Thermal Conductivity

c_{p} is Specific Heat

α is Thermal Diffusivity

### Solution

Since thermal diffusivity and the kinematic viscosity both use the same density, the Prandtl number will not change. Choice A is true

With the thermal diffusivity in the denominator a larger value will result in a lower Prandlt Number if the kinematic viscosity is held constant. Choice B is true

Since there is no variable that is for volume, Choice C is false.

When the Prandtl Number is small the heat diffuses very quickly compared to the velocity. Choice D is true

Choice C is correct since it is the only false statement.

Click here to view the previous PE/FE engineering sample question