# Reynolds Number Calculator and Formula (Equation)

Below is  a handy Reynolds Number Calculator. The Reynolds number (Re) is a dimensionless quantity that is used to determine what type of fluid flow to expect in a given situation. It is an important tool for engineers who are engaged in fluid mechanics, as it can predict the flow patterns to be expected and help in the modification or optimization of the subsequent designs so as to improve the flow.

It can be applied in any kind of flow, from pipes and tubes to completely open channels as the main elements that determine the Reynolds number value are the inertial and the viscous forces of the flowing fluid. That said, and in order to be able to determine the Reynolds number value, we first need to determine the fluid velocity, density, viscosity, and the pipe or channel diameter.

## Reynolds Number Calculator

Free-stream fluid velocity, V:
Characteristic distance (or pipe diameter), D:
Fluid density, ρ:
Fluid viscosity (dynamic), μ:
Calculate
Reynolds number (Re) =

## Reynolds number formula (equation)

The Reynolds Number formula is: “Re = VDρ/μ” or “Re = VD/v” where “V” is the fluid velocity, “D” is the characteristic distance, “ρ” is the fluid density, “ν” is the kinematic viscosity, and “μ” is the dynamic viscosity both of which can be acquired from data tables. This former of these formula’s drives the above Reynolds Number Calculator.

### Reynolds Number Formula for Pipe Flow

When we are investigating the type of flow in a pipe, we use the formula: “Re = QDH/νΑ” where “Q” is the fluid flow rate, “DH” is the hydraulic diameter, “ν” is the kinematic viscosity, and “A” is the pipe cross-sectional area. The hydraulic diameter is determined with: “DH = 4A/P” where “P” is the “wetted perimeter”, or the area that contacts the fluid flow.

### Reynolds Number for ducts or open channels

When the Reynolds number must be determined for wide ducts or open channels like rivers, we may consider the cross-sectional area (A) as the semicircle that is formed between the river banks and the river bed. The corresponding consideration must be made for the hydraulic diameter as well, since the wetted perimeter is determined by the river depth and distance between the two banks.

## Types of flows

There are two types of flows, namely the laminar and the turbulent, while there also is an identifiable transition phase between these two that holds its own significance for practical reasons.

The laminar flow is a fluid flow that occurs in laminas or layers that slip smoothly upon the adjacent laminas and layers, exchanging kinetic momentum on the molecular level. In the case of the laminar flow, the viscous forces of the fluid help to keep the instability and tendency for turbulence under control.

The turbulent flow occurs when the inertial forces overwhelm the viscous forces, so the fluid flow becomes “messy” with characteristics of vertical momentum switching.

## The Reynolds number in practice

The reasons why we care about whether a fluid flow is turbulent or laminar and why we take action to accommodate the latter are the following:

• Laminar flow causes less wear and attrition to the pipes or open channel walls.
• Laminar flow helps improve the performance of pumps and make it more predictable.
• Laminar flow helps retain the fluid’s kinetic energy as well as heat since the outermost layers act as insulating elements to up to a point.

In practice, the Reynolds number is a simple indication of what to expect, but it should never be taken as a fact since the inner surface of pipes, etc., almost always have imperfections that cause turbulence. Even the slightest and smallest serration in a pipe or wall will cause significant changes in the flow of the fluid, so the Reynolds number should only be taken into account with the inclusion of a large safety factor.

Experiments have shown that in general, Reynolds number values between 2000 and 4000 is the range of transition from laminar to turbulent flow. However, it is important to note that the value of the number where the flow type transition occurs depends on the hydraulic system, fluid type, and flow conditions, as researchers have achieved values as high as 40000.

Nonetheless, calculating the Reynolds number is a solid first step to figure out the approximate results to expect in reality for a given flow situation, and that is why engineers have been following that practice for more than a century now.