Free Online Dimensionless Numbers Calculator

Welcome to the CFDLAND free online calculator for essential non-dimensional numbers. This powerful tool allows you to instantly calculate key values used in fluid mechanics, heat transfer, and transport phenomena. Simply choose the number you need, enter your parameters, and get your result.

For a complete guide on what these numbers mean, their importance, and how they are derived, please read our detailed blog post: What is a Dimensionless Number? A Complete Guide.

Reynolds Number (Re) Calculator

The Reynolds number is a critical value in fluid dynamics. It helps engineers predict if a fluid flow pattern will be smooth and steady (laminar flow) or chaotic and irregular (turbulent flow).

[latex] \text{Re} = \frac{\rho V L}{\mu} [/latex]

Parameters Explained:

• Flow Type: Choose if the fluid is flowing inside a confined space (internal flow, like a pipe) or over a surface (external flow, like wind over a wing).
• Characteristic Length (L) / Hydraulic Diameter (Dₕ): This is the main dimension of your geometry. For external flow, it’s a simple length (like the length of a plate). For internal flow in non-circular ducts, you use the Hydraulic Diameter.
• Density (ρ): The mass of the fluid per unit of volume (e.g., kg/m³).
• Free-stream Velocity (U): The speed of the fluid (e.g., m/s).
• Dynamic Viscosity (μ): A measure of the fluid’s internal resistance to flow, or its “thickness” (e.g., Pa.s).

Mach Number (Ma) Calculator

The Mach number is used in aerodynamics and high-speed flows. It compares the speed of an object (or a fluid) to the speed of sound in the surrounding medium. It tells us if the flow is subsonic (Ma < 1), supersonic (Ma > 1), or transonic (Ma ≈ 1).

Ma=V/c

Parameters Explained:

• Speed of object (U): The velocity of your object or fluid flow (e.g., m/s).
• Adiabatic Index (γ): Also known as the heat capacity ratio. It is a dimensionless value, typically around 1.4 for air.
• Molar gas constant: A universal physical constant. Its value is approximately 8.314 J·mol⁻¹·K⁻¹.
• Absolute temperature (T): The temperature of the gas in Kelvin (K).
• Molar mass (M): The mass of the gas per mole (e.g., kg/mol). For air, this is approximately 0.029 kg/mol.

Prandtl Number (Pr) Calculator

The Prandtl number is very important in heat transfer problems. It compares how quickly momentum spreads through a fluid (related to viscosity) to how quickly heat spreads through it (related to thermal conductivity).

[latex] \text{Pr} = \frac{\mu c_p}{k} [/latex]

Parameters Explained:

• Dynamic Viscosity (μ): A measure of the fluid’s internal resistance to flow (e.g., Pa.s).
• Specific heat at constant pressure (Cp): The amount of heat required to raise the temperature of a unit mass of the fluid by one degree (e.g., J·kg⁻¹·K⁻¹).
• Thermal conductivity (k): A measure of the fluid’s ability to conduct heat (e.g., W·m⁻¹·K⁻¹).

Schmidt Number (Sc) Calculator

The Schmidt number is used in fluid flows where there is both momentum transfer and mass transfer happening at the same time. It compares the rate of momentum diffusion (viscosity) to the rate of mass diffusion. It is the mass transfer equivalent of the Prandtl number.

[latex] \text{Sc} = \frac{\nu}{D} [/latex]

Parameters Explained:

• Density (ρ): The mass of the main fluid per unit of volume (e.g., in kg/m³).
• Dynamic Viscosity (μ): The fluid’s resistance to flow, or its “thickness” (e.g., in Pa.s).
• Mass Diffusivity (D): A measure of how quickly one substance diffuses through another (e.g., in m²/s).

Peclet Number (Pe) Calculator

The Peclet number decides whether a transport process is dominated by convection (the bulk motion of the fluid) or by diffusion (the random motion of particles). It is used for both heat and mass transfer.

Governing Formula: The Peclet number has two forms depending on the process:

• For Heat Transfer: Pe = (Reynolds Number) × (Prandtl Number)

[latex] \text{Pe}_{\text{heat}} = \frac{UL}{\alpha} = \frac{\rho UL c_p}{k} [/latex]

• For Mass Transfer: Pe = (Reynolds Number) × (Schmidt Number)

[latex] \text{Pe}_{\text{m}} = \frac{L V}{D} [/latex]

[latex] \text{Pe}_{\text{m}} = \text{Re} \cdot \text{Sc} [/latex]

Parameters Explained:

• Select a choice: Choose whether you are analyzing heat transfer or mass transfer. The required inputs will change based on your selection.* Characteristic Length (L): The main dimension of your geometry or flow path (e.g., in m).* Free-stream Velocity (U): The speed of the fluid (e.g., in m/s).
• Mass Diffusivity (D): (For mass transfer) How quickly a substance diffuses through another (e.g., in m²/s).
• Density (ρ): (For heat transfer) The mass of the fluid per unit volume (e.g., in kg/m³).
• Specific heat at constant pressure (Cp): (For heat transfer) The amount of heat needed to raise the temperature of the fluid (e.g., in J·kg⁻¹·K⁻¹).
• Thermal conductivity (k): (For heat transfer) The ability of the fluid to conduct heat (e.g., in W·m⁻¹·K⁻¹).

Strouhal Number (St) Calculator

The Strouhal number is important for describing oscillating or unsteady flows. It relates the frequency of the oscillation to the mean flow velocity and a characteristic length. It is commonly used to analyze the vortex shedding that occurs when a fluid flows past a blunt object, like a cylinder.

St=f/LU

Parameters Explained:

• Characteristic Length (L): Typically the diameter or width of the object causing the oscillation (e.g., in m).
• Free-stream Velocity (U): The speed of the fluid flowing past the object (e.g., in m/s).
• Frequency of vortex shedding (f): The rate at which vortices are shed from the object, measured in Hertz (Hz), or cycles per second.

Froude Number (Fr) Calculator

The Froude number is used for flows where gravity is a significant force. It is common in naval architecture (designing ships), river engineering, and any situation with open-channel flow. It compares the flow’s inertia to the force of gravity.

[latex] \text{Fr} = \frac{V}{\sqrt{gL}} [/latex]

Parameters:

• Characteristic Length (L): A dimension that represents the size of the flow, such as the depth of a river or the length of a ship at the waterline (e.g., in m).
• Free-stream velocity (U): The speed of the fluid flow (e.g., in m/s).
• Acceleration due to gravity (g): The standard acceleration of gravity, which is approximately 9.81 m/s² on Earth.

Weber Number (We) Calculator

The Weber number is important in flows where two different fluids meet, or where a liquid interacts with a gas. It helps determine if the inertia of the fluid is more powerful than its surface tension. It’s used to analyze droplets, bubbles, and thin films.

[latex] \text{We} = \frac{\rho V^2 L}{\sigma} [/latex]

Parameters:

• Characteristic Length (L): A representative dimension, such as the diameter of a droplet or bubble (e.g., in m).
• Density (ρ): The mass of the fluid per unit of volume (e.g., in kg/m³).
• Surface tension (σ): The force that holds the surface of a liquid together (e.g., in N/m).
• Free-stream velocity (U): The speed of the fluid or droplet (e.g., in m/s).

Knudsen Number (Kn) Calculator

The Knudsen number is used for very low-density gas flows, often found in vacuum technology or high-altitude aerodynamics. It compares the molecular mean free path (the average distance a particle travels before hitting another particle) to a physical length scale. It tells you if the gas can be treated as a continuous fluid or as a collection of individual particles.

[latex] \text{Kn} = \frac{\lambda}{L} [/latex]

Parameters:

• Characteristic Length (L): The typical size of the object or the space the gas is flowing through (e.g., in m).* Temperature of the gas (T): The absolute temperature of the gas, measured in Kelvin (K).
• Particle hard-shell diameter (m): The effective diameter of the gas molecules (e.g., in m).
• Static pressure of the gas (Pa): The pressure of the gas when it is not in motion (e.g., in Pascals).