Reynolds Number Formula

Reynolds Number Formula

Air and liquids are fluids because they move, and that motion is a flow. Additionally, this topic examines the property of fluid flow known as the Reynolds number and then examines the Reynolds Number Formula. Furthermore, its value determines whether the fluid is turbulent or laminar. Students can refer to the Extramarks website for more information on Reynolds Number Formula.

Reynolds Numbers

The Reynolds Number Formula represents the ratio of the inertial force of the liquid to the viscous force. Inertial force is also the momentum force of the mass of the flowing fluid. Simply put, it is a measure of how difficult it is to change the velocity of a flowing liquid.

Viscous forces, on the other hand, are forces that deal with friction in flowing liquids. For example, pouring tea and pouring cooking oil. In addition, edible oils are difficult to flow, resulting in high viscosity. Inertial and viscous forces are very similar. Also, they have the same units. In other words, the Reynolds Number Formula has no units. Additionally, based on the Reynolds number, students can infer whether the flowing fluid is turbulent or laminar.

Most notably, laminar flow occurs at Reynolds numbers below 2,300. On the other hand, values ​​above 4,000 indicate turbulence and values ​​between 2,300 and 4,000 indicate unsteady flow. This means that fluid flow transitions between laminar and turbulent.

In addition, it occurs briefly at the beginning or end of liquid flow.

Reynolds Number Formula

The Reynolds Number Formula is a very important quantity for studying fluid flow patterns. It is a dimensionless parameter and is widely used in fluid dynamics. The Reynolds Number Formula of a flowing fluid is defined as the ratio of the fluid’s inertial and viscous forces and quantifies the relative importance of these two types of forces for a given flow condition. The concept of the Reynolds Number Formula was introduced by George Stokes in 1851. However, the name “Reynolds number” was given by the British physicist Osborne, who popularized its use in 1883, after his Reynolds name. The Reynolds Number Formula depends on the relative internal motion due to different fluid velocities. The Reynolds Number Formula is considered a prerequisite for flow analysis. 

  • Importance of Reynolds number:

Reynolds number (Re) is a useful parameter that helps predict whether fluid flow is laminar or turbulent. Students must know that Reynolds Number Formula (Re) = inertial force/viscous force.

When viscous forces dominate inertial forces, the flow is smooth and slow. The value of the Reynolds Number Formula is relatively low, and the flow is called laminar. On the other hand, when inertial forces dominate, the value of the Reynolds number is relatively high and the fluid flows faster at higher velocities, and the flow is called turbulent. At low Reynolds number values ​​(Re < 2100), the viscous forces are sufficient to keep the liquid particles aligned, and the flow becomes laminar and is characterized by smooth and constant fluid motion. For large values ​​of Reynolds number (Re > 4000), the flow tends to generate chaotic eddies, vortices, and other flow instabilities that disturb the flow. As the Reynolds number increases, the tendency of the flow to become turbulent increases.

Solved Examples On Reynolds Number Formula

  1. Let’s say you’re doing a research project about water flowing through pipes. Also, let’s compare the diameters of two pipes that show laminar flow, where water flows smoothly in the traditional way.

Furthermore, where water flows chaotically, turbulent pipes make its flow difficult to predict. Additionally, vibrations can occur, which can lead to premature wear and tear of the flow system and its failure. Our research project requires a Reynolds number of 2200 for water flowing through two separate pipes. The diameter of the first tube is 2.75 cm (0.0275 m) and the density of water is 1,000 kg/m3. First, the viscosity of water is 0.0013 kg/(m s). Calculate the velocity of the water that must flow through the pipe to match these parameters. 


2000 = 1000(kgm3)ν(0.0275 m)0.00133Pa・s

ν≈0.01 ms

Now students have to use different pipes of the same construction with different diameters and also calculate the speed of water flowing through them. Also, add the dye to the running water flowing through the pipe at the calculated velocity.

It just shows how dynamic similarity works, even if the dye water comes out in a laminar flow. Now let’s do the final calculations to determine the velocity of water flowing through a small pipe.

2000 = 1000(kgm3)ν(0.005 m)0.00133Pa・s


After calculation, it follows that water in small pipes will flow faster than water in large pipes. Even after faster water flow in the small pipe, it still exhibits a laminar flow mode because the Reynolds Number Formula is the same as in the previous scenario.

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