The Reynolds Number calculator computes the Reynolds Number (NRe), a dimensionless property of fluid flow, based on the fluid velocity, tube diameter, density and viscosity.
INSTRUCTIONS: Choose your preferred units and enter the following:
Reynold's Number (NRe): The calculator returns the Reynold's Number (no units).
The formula for the Reynold's Number is:
where:
Reynolds number ( NRe) is a dimensionless property of fluid flow which is characterized by patterns that emerge in various fluid flow situations. Fluid flow conditions may be categorized based on the Reynolds number computed from this equation.
In fluid mechanics, the Reynolds number (Re) is a dimensionless quantity that is used to help predict similar flow patterns in different fluid flow situations. The concept was introduced by George Gabriel Stokes in 1851, but the Reynolds number is named after Osborne Reynolds (1842–1912), who popularized its use in 1883.
The Reynolds number is defined as the ratio of inertial forces to viscous forces and consequently quantifies the relative importance of these two types of forces for given flow conditions. Reynolds numbers frequently arise when performing scaling of fluid dynamics problems, and as such can be used to determine dynamic similitude between two different cases of fluid flow. They are also used to characterize different flow regimes within a similar fluid, such as laminar or turbulent flow:
laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion;
turbulent flow occurs at high Reynolds numbers and is dominated by inertial forces, which tend to produce chaotic eddies, vortices and other flow instabilities.
In practice, matching the Reynolds number is not on its own sufficient to guarantee similitude. Fluid flow is generally chaotic, and very small changes to shape and surface roughness can result in very different flows. Nevertheless, Reynolds numbers are a very important guide and are widely used.
Reynolds number interpretation has been extended into the area of arbitrary complex systems as well: financial flows, nonlinear networks, etc. In the latter case an artificial viscosity is reduced to nonlinear mechanism of energy distribution in complex network media. Reynolds number then represents a basic control parameter which expresses a balance between injected and dissipated energy flows for open boundary system. It has been shown [7] that Reynolds critical regime separates two types of phase space motion: accelerator (attractor) and decelerator. High Reynolds number leads to a chaotic regime transition only in frame of strange attractor model.
For shapes such as squares, rectangular or annular ducts where the height and width are comparable, the characteristical dimension for internal flow situations is taken to be the hydraulic diameter, D_H, defined as:
DH = 4A/P
where
The wetted perimeter for a channel is the total perimeter of all channel walls that are in contact with the flow.[11] This means the length of the channel exposed to air is not included in the wetted perimeter.
For a circular pipe, the hydraulic diameter is exactly equal to the inside pipe diameter, D. That is,
DH = D.
For an annular duct, such as the outer channel in a tube-in-tube heat exchanger, the hydraulic diameter can be shown algebraically to reduce to
DH,annulus = Do - Di
where
For calculations involving flow in non-circular ducts, the hydraulic diameter can be substituted for the diameter of a circular duct, with reasonable accuracy.
The Kind of flow depends on value of Re
If Re < 2000 the flow is Laminar
If Re > 4000 the flow is turbulent
If 2000 < Re < 4000 it is called transition flow.
Question 1: Find the reynolds number if a fluid of viscosity 0.4 Ns/m2 and relative density of 900 Kg/m3 through a 20 mm pipe with a Velocity of 2.5 m/s?
Solution:
Viscosity of fluid μ = 0.4 Ns/m2
Density of fluid ρ = 900 Kg/m3,
Diameter of the fluid L = 20 × 10-3 m
The Reynold formula is given by Re = ρVD/μ
= 900×2.5×20×10−3/0.4
= 112.5
Here we observe that the value of Reynolds number is less than 2000, so the flow of liquid is laminar.
Question 2: Calculate the reynolds number if a fluid flows through a diameter of 80 mm with velocity 5 m/s having density of 1400 Kg/m3 and having viscosity of 0.9 Kg/ms.
Solution:
Given: Diameter of pipe L = 80 mm,
Velocity of the fluid v = 5 m/s,
Density of fluid ρ = 1400 Kg/m3,
Viscosity of fluid μ = 0.9 Kg/ms
The Reynolds number is given by Re = ρVD/μ
= 1400×5×0.08/0.9
= 560/0.9
= 622.22.
The flow is laminar.