# Prandtl Number Calculator

This Prandtl number calculator helps you determine this **dimensionless number** for different fluids. The **Prandtl number** is a **function of the fluids' viscosity and thermal diffusivity**. This dimensionless entity relates the **momentum transport to heat transport**.

The value of the Prandtl number tells us **by what means the heat would diffuse faster**, i.e., whether heat conduction is more dominant than convection for a fluid. Prandtl number plays a vital role in heat transfer via fluids — a phenomenon extensively used in boundary layer flows. Read on to understand what the Prandtl number is and how to calculate the Prandtl number of air?

## What is Prandtl number?

Consider a fluid, say water flowing over a hot flat plate. If you want to find out the **rate of energy or heat transferred via conduction or convection** phenomenon, a dimensionless number known as the **Prandtl number** is used. In other words, the Prandtl number is the **ratio of momentum diffusivity to thermal diffusivity.**

* Momentum transport (or diffusivity):* In simple terms, it is the

**diffusion of momentum between particles in a fluid**. The momentum diffusivity is also known as

**kinematic viscosity**. We know that

**dynamic viscosity**$\mu$ refers to the internal resistance of fluid layers against each other. The

**kinematic viscosity**$\nu$ is the

**ratio of dynamic viscosity and the density of fluid**, $\rho$. Mathematically, this is:

The momentum diffusivity (or kinematic viscosity) have dimensions as area per time, i.e., $\text{m}^2/\text{s}$ or $\text{ft}^2/\text{s}$.

* Thermal (or heat) transport (or diffusivity):* It is the

**rate of heat transfer**from one point to another. In other words,

**how fast can the heat travel from one location to another**. The thermal diffusivity is measured in the units of area per time, i.e., $\text{m}^2/\text{s}$ or $\text{ft}^2/\text{s}$, and is a

**function of thermal conductivity specific heat capacity, and density of fluid**. For a fluid having thermal conductivity, we can write $k$ and specific heat at constant pressure $C_p$, the thermal diffusivity, $\alpha$ as:

An alternative Prandtl number formula can be written **in terms of dynamic viscosity**, $\mu$:

There are several variations of defining Prandtl number i.e., it is the ratio of:

- Kinematic viscosity to thermal diffusivity; or
- Momentum boundary layer to the thermal boundary layer.

Mathematically, we can write:

where:

- $\delta_t$ – Thermal boundary layer thickness; and
- $\delta$ – Momentum boundary layer thickness.

## How to calculate Prandtl number?

To calculate Prandtl number:

- Enter the
**dynamic viscosity**, $\mu$ of the fluid. - Insert the
**specific heat capacity**, $C_p$ of the fluid. - Fill in the
**thermal conductivity**, $k$ for the fluid. - The calculator will return the
**Prandtl number**, $\text{Pr}$.

Alternatively, you can utilize the `preloaded data of common fluids`

from the list to directly obtain the Prandtl number of the said fluid.

💡 You can also use the `advanced mode`

of the calculator in case you want to enter other parameters like **kinematic viscosity, thermal diffusivity, and density** of the fluid. You can find more in diffusivity on thermal diffusivity calculator.

## Example: Using the Prandtl number calculator

Use the calculator to find the Prandtl number of water, given the following data:

**Density**, $\rho = 997 \text{ kg/m}^3$,

**Dynamic viscosity**, $\mu = 1.002 \text{ mPa⋅s}$,

**Specific heat**, $C_p = 4184 \text{ J/kg⋅K}$, and

**Thermal conductivity**, $k = 0.607 \text{ W/m⋅K}$.

To calculate Prandtl number of water:

- Enter the
**dynamic viscosity**, $\mu = 1.002 \text{ mPa⋅s}$. - Insert the
**specific heat capacity**, $C_p = 4184 \text{ J/kg⋅K}$. - Fill in the
**thermal conductivity**, $k = 0.607 \text{ W/m⋅K}$. - Using the Prandtl number formula:

🔎 Use the `advanced mode`

and enter the value of **density** to receive the values of **momentum and thermal diffusivity.**

## Prandtl number of different fluids

The following table has the Prandtl number for some common fluids:

Fluid | Prandtl number |
---|---|

Air | 0.7-0.73 |

Water | 0.69 |

Seawater | 7.2-13.4 |

Oxygen | 0.63 |

Argon | 22.7 |

## Physical significance of Prandtl number

The physical significance of the Prandtl number is that when the number is **less than 1**, the **conductive heat transfer is a more dominant** phenomenon, i.e., the significant component of heat is transferred via conduction compared to convection. Similarly, when the Prandtl number is **greater than 1**, the **convective heat transfer is more significant** than conduction. For the fluids having a Prandtl number **near 1**, the heat transfer rate is more or less **similar for both conduction and convection**.

## FAQ

### What do you mean by Prandtl number?

Prandtl number is the ratio of **momentum diffusivity to thermal diffusivity**. In other words, it is the ratio of **heat transfer rate via convection and conduction**. For the boundary layer phenomenon, it is known as the ratio of thicknesses of **momentum and thermal boundary layers.**

### What are the factors that affect Prandtl number of a fluid?

The factors affecting Prandtl number are:

- Dynamic viscosity (μ);
- Density (see density calculator);
- Thermal conductivity (k); and
- Specific heat capacity (Cp) of the fluid (cf. specific heat calculator).

Mathematically, `Pr = μ × Cp / k`

. The Prandtl number also varies with temperature.

### How do I calculate the Prandtl number?

To calculate the Prandtl number:

**Multiply****dynamic viscosity**with the**specific heat**of the fluid.**Divide**the product by the thermal**conductivity**of the fluid.

### What is the Prandtl number of water?

The Prandtl number of water is **6.9**. For a dynamic viscosity of `1.002 mPa⋅s`

, thermal conductivity of `0.607 W/m⋅K`

and specific heat of `4184 J/kg⋅K`

, the Prandtl number is calculated as `Pr = 0.001002 × 4184 / 0.607 = 6.9`

.

### What is the Prandtl number of air?

The Prandtl number of water is **0.715**. For a dynamic viscosity of `0.0182 mPa⋅s`

, thermal conductivity of `0.025596 W/m⋅K`

and specific heat of `1006 J/kg⋅K`

, the Prandtl number is calculated as `Pr = 0.0000182 × 1006 / 0.025596 = 0.715`

.

**Prandtl number.**