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Engineers use the Reynolds number to determine whether a fluid flow is laminar or turbulent. This is significant because turbulent flow causes more mixing and shearing. This causes increased viscous losses, which reduces hydraulic machine efficiency.

**Example: –** The rising smoke from a cigarette is a nice example of laminar and turbulent flow. The smoke moves in smooth, straight lines at first (laminar flow), then “waves” back and forth (transition flow), and finally appears to mix randomly (turbulent flow). These ranges will be covered further down.

The dimensionless Reynold number plays a major role in predicting patterns in the behavior of a fluid. The Reynold number, called Re, is used to determine whether a fluid flow is laminar or turbulent. It is one of the main controlling parameters in all viscous flows where a numerical model is selected according to the pre-calculated Reynolds number.

Although the Reynold number includes both the static and kinetic properties of a fluid, it is specified as a flow property because the dynamical conditions are examined. Technically speaking, the Reynolds number is the ratio of inertial forces to viscous forces. This ratio helps classify laminar flows from turbulent ones.

## Reynolds number definition

Inertial forces oppose the change in velocity of an object and are the cause of fluid motion. These forces are stronger in turbulent flows. Otherwise, if viscous forces, defined as the resistance to flow, are dominant – the flow is laminar. Reynold number can be specified as below:

## Reynolds number formula | reynolds number equation

The ratio of inertial forces to viscous forces is known as the Reynold number. The Reynold number is a dimensionless number that is used to classify fluid systems in which the impact of viscosity is crucial in determining fluid velocities or flow patterns. the Reynold number was first described by Reynolds in 1883.The Reynold number, N_{Re}, is defined mathematically as

When determining whether a fluid is in laminar or turbulent flow, the Reynold number is utilised. A Reynold number less than or equal to 2300 indicates laminar flow, whereas a Reynold number more than 2100 indicates turbulent flow, according to API 13D standards. so **reynolds number for laminar flow is 2300** and **Reynolds number for turbulent flow** is above 4000. The equation for computing the **Reynolds number unit** in field is

**Laminar to Turbulent Transition**

Fluid flow can be specified under two different regimes: laminar and turbulent. The transition between systems is an important issue driven by both fluid and flow properties. As mentioned earlier, the critical Reynold number can be classified as intrinsic and extrinsic. Yet while the Reynold number with respect to the laminar–turbulent transition can be reasonably defined for internal flow, the definition of external flow is difficult to specify.

Flow Type |
Reynold Number |

Laminar | Up to 2300 |

Transition | 2300 to 4000 |

Turbulent | Above 4000 |

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