Free Reynolds Number Calculator – Internal & External Flow
This is our online Reynolds Number Calculator. This tool helps you calculate the Reynolds number (Re). The Reynolds number is a very important value when you study how fluids move.
Our calculator is easy to use and has two main functions.
First, you can find the Re for both internal flow and external flow.
- Internal flow is when a fluid moves inside an object, like water in a pipe.
- External flow is when a fluid moves around an object, like air flowing over a wing.
Figure 1: Schematic of velocity profile on internal & external flow
Second, the calculator can also work in reverse. If you already have a Reynolds number, this tool can calculate the fluid velocity (speed) that you need. This is very helpful for engineering and design tasks.
How to Use the Reynolds Number Calculator
Using this calculator is very simple. Follow these steps to get your result.
- Choose Your Calculation: First, select what you want to find. You can choose to calculate Reynolds number or to calculate velocity from a known Reynolds number.
- Select Your Flow Type: Next, tell the calculator if you have an internal flow or an external flow. This choice is important because it changes the next steps.
- Enter Your Numbers: Fill in the boxes with your information. You will need to enter values like fluid density, velocity, and characteristic length. It is very important to use the correct units for each value.
- Get Your Answer: Click the “Calculate” button. The calculator will show you the result right away.
The Reynolds Number Formula
Our calculator uses a famous equation in fluid mechanics. This is the Reynolds number formula. The main formula looks like this:
Re = (ρ × V × L) / μ
This Reynolds number equation helps us understand the fluid’s behavior. Here is what each symbol in the formula means:
- Re is the Reynolds Number. It has no units.
- ρ (rho) is the Fluid Density. This tells you how heavy the fluid is for its size.
- V is the Fluid Velocity. This is simply how fast the fluid is moving.
- L is the Characteristic Length. This is the main size of the pipe or the object in the flow.
- μ (mu) is the Dynamic Viscosity. This tells you how “thick” a fluid is. For example, honey has a high viscosity, and water has a low viscosity.
Sometimes, you will see the formula written like this:
Re = (V × L) / ν
Here, ν (nu) is the Kinematic Viscosity. It is just the dynamic viscosity divided by the density(ν = μ / ρ)
This formula is very powerful. To learn more about what the final number means and see more examples, please read our detailed article.
-> Read our Comprehensive Guide: What is Reynolds Number?
Characteristic Length (L): What to Use for Internal vs. External Flow
The Characteristic Length (L) is a very important part of the Reynolds number formula. The correct value to use for L depends on your flow type. Our calculator asks you to choose between internal flow and external flow for this reason.
- For Internal Flow:
Internal flow happens when a fluid moves inside a boundary, like water flowing through a pipe or air in a duct.
- Circular Pipes: If your fluid is in a simple round pipe, the characteristic length is just the inner diameter of that pipe.
- Non-Circular Ducts: If you have a square, rectangular, or other non-circular duct, you must use the Hydraulic Diameter (Dh) as the characteristic length. The hydraulic diameter is a special value that lets you use the same Reynolds number formula for any duct shape.
Need help finding the hydraulic diameter? We have another tool for that. Use our free Hydraulic Diameter Calculator.
- For External Flow:
External flow happens when a fluid moves around the outside of an object, like wind blowing over a building or a car.
For external flow, the characteristic length is the dimension of the object along the direction of the flow. Here are some common examples:
- Flow over a Sphere or Cylinder: The characteristic length is the diameter of the sphere or cylinder.
- Flow over a Flat Plate: The characteristic length is the length of the plate from the front edge to the back edge.
- Flow over an Airfoil: The characteristic length is the chord length of the airfoil.
Figure 2: Characteristic length for external flows: over a) an airfoil b) plate c) cylinder/sphere
Frequently Asked Questions
- What does my calculated Reynolds number mean? Is the flow laminar or turbulent? The Reynolds number (Re) tells you if the fluid flow is smooth or chaotic. For flow inside a pipe, if Re is less than 2300, the flow is laminar (smooth and orderly). If Re is greater than 4000, the flow is turbulent (messy and chaotic). The range in between is called transitional. These values can change for other shapes, like flow over a flat plate. To learn more about these flow types, please read our detailed article. -> The Differences Between Laminar and Turbulent Flow
- What units should I use in this calculator? For the best results, you should use standard SI units. This means: Density (ρ) in kg/m³, Velocity (V) in m/s, Characteristic Length (L) in m, Dynamic Viscosity (μ) in Pa·s
- How do I find the Reynolds number for a square or rectangular duct? For any duct that is not a circle, you must use the Hydraulic Diameter (Dh) as your Characteristic Length (L). We have a separate tool to help you find this value easily.
- Why is the Reynolds number called “dimensionless”? It is called dimensionless because it does not have any units like meters (m) or seconds (s). During the calculation, all the units cancel each other out. This makes the Reynolds number a pure number that can be used to compare different types of fluid flow anywhere in the world.
Reynolds Number Calculator
Free Reynolds Number Calculator – Internal & External Flow
This is our online Reynolds Number Calculator. This tool helps you calculate the Reynolds number (Re). The Reynolds number is a very important value when you study how fluids move.
Our calculator is easy to use and has two main functions.
First, you can find the Re for both internal flow and external flow.
- Internal flow is when a fluid moves inside an object, like water in a pipe.
- External flow is when a fluid moves around an object, like air flowing over a wing.
Figure 1: Schematic of velocity profile on internal & external flow
Second, the calculator can also work in reverse. If you already have a Reynolds number, this tool can calculate the fluid velocity (speed) that you need. This is very helpful for engineering and design tasks.
How to Use the Reynolds Number Calculator
Using this calculator is very simple. Follow these steps to get your result.
- Choose Your Calculation: First, select what you want to find. You can choose to calculate Reynolds number or to calculate velocity from a known Reynolds number.
- Select Your Flow Type: Next, tell the calculator if you have an internal flow or an external flow. This choice is important because it changes the next steps.
- Enter Your Numbers: Fill in the boxes with your information. You will need to enter values like fluid density, velocity, and characteristic length. It is very important to use the correct units for each value.
- Get Your Answer: Click the “Calculate” button. The calculator will show you the result right away.
The Reynolds Number Formula
Our calculator uses a famous equation in fluid mechanics. This is the Reynolds number formula. The main formula looks like this:
Re = (ρ × V × L) / μ
This Reynolds number equation helps us understand the fluid’s behavior. Here is what each symbol in the formula means:
- Re is the Reynolds Number. It has no units.
- ρ (rho) is the Fluid Density. This tells you how heavy the fluid is for its size.
- V is the Fluid Velocity. This is simply how fast the fluid is moving.
- L is the Characteristic Length. This is the main size of the pipe or the object in the flow.
- μ (mu) is the Dynamic Viscosity. This tells you how “thick” a fluid is. For example, honey has a high viscosity, and water has a low viscosity.
Sometimes, you will see the formula written like this:
Re = (V × L) / ν
Here, ν (nu) is the Kinematic Viscosity. It is just the dynamic viscosity divided by the density(ν = μ / ρ)
This formula is very powerful. To learn more about what the final number means and see more examples, please read our detailed article.
-> Read our Comprehensive Guide: What is Reynolds Number?
Characteristic Length (L): What to Use for Internal vs. External Flow
The Characteristic Length (L) is a very important part of the Reynolds number formula. The correct value to use for L depends on your flow type. Our calculator asks you to choose between internal flow and external flow for this reason.
- For Internal Flow:
Internal flow happens when a fluid moves inside a boundary, like water flowing through a pipe or air in a duct.
- Circular Pipes: If your fluid is in a simple round pipe, the characteristic length is just the inner diameter of that pipe.
- Non-Circular Ducts: If you have a square, rectangular, or other non-circular duct, you must use the Hydraulic Diameter (Dh) as the characteristic length. The hydraulic diameter is a special value that lets you use the same Reynolds number formula for any duct shape.
Need help finding the hydraulic diameter? We have another tool for that. Use our free Hydraulic Diameter Calculator.
- For External Flow:
External flow happens when a fluid moves around the outside of an object, like wind blowing over a building or a car.
For external flow, the characteristic length is the dimension of the object along the direction of the flow. Here are some common examples:
- Flow over a Sphere or Cylinder: The characteristic length is the diameter of the sphere or cylinder.
- Flow over a Flat Plate: The characteristic length is the length of the plate from the front edge to the back edge.
- Flow over an Airfoil: The characteristic length is the chord length of the airfoil.
Figure 2: Characteristic length for external flows: over a) an airfoil b) plate c) cylinder/sphere
Frequently Asked Questions
- What does my calculated Reynolds number mean? Is the flow laminar or turbulent? The Reynolds number (Re) tells you if the fluid flow is smooth or chaotic. For flow inside a pipe, if Re is less than 2300, the flow is laminar (smooth and orderly). If Re is greater than 4000, the flow is turbulent (messy and chaotic). The range in between is called transitional. These values can change for other shapes, like flow over a flat plate. To learn more about these flow types, please read our detailed article. -> The Differences Between Laminar and Turbulent Flow
- What units should I use in this calculator? For the best results, you should use standard SI units. This means: Density (ρ) in kg/m³, Velocity (V) in m/s, Characteristic Length (L) in m, Dynamic Viscosity (μ) in Pa·s
- How do I find the Reynolds number for a square or rectangular duct? For any duct that is not a circle, you must use the Hydraulic Diameter (Dh) as your Characteristic Length (L). We have a separate tool to help you find this value easily.
- Why is the Reynolds number called “dimensionless”? It is called dimensionless because it does not have any units like meters (m) or seconds (s). During the calculation, all the units cancel each other out. This makes the Reynolds number a pure number that can be used to compare different types of fluid flow anywhere in the world.
