# What is Reynold's number: Definition and 25 Discussions

The Reynolds number (Re) helps predict flow patterns in different fluid flow situations. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers flows tend to be turbulent. The turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow (eddy currents). These eddy currents begin to churn the flow, using up energy in the process, which for liquids increases the chances of cavitation. Reynolds numbers are an important dimensionless quantity in fluid mechanics.
The Reynolds number has wide applications, ranging from liquid flow in a pipe to the passage of air over an aircraft wing. It is used to predict the transition from laminar to turbulent flow, and is used in the scaling of similar but different-sized flow situations, such as between an aircraft model in a wind tunnel and the full size version. The predictions of the onset of turbulence and the ability to calculate scaling effects can be used to help predict fluid behaviour on a larger scale, such as in local or global air or water movement and thereby the associated meteorological and climatological effects.
The concept was introduced by George Stokes in 1851, but the Reynolds number was named by Arnold Sommerfeld in 1908 after Osborne Reynolds (1842–1912), who popularized its use in 1883.

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1. ### I How is the Reynolds number derived (is my derivation wrong)?

I'm a HS student so please dumb it down. I'm looking into the Reynolds number of a sphere sinking in a fluid, and I want to determine whether my results meet creeping flow or not Re<<1, here's what I got. **sorry if I misused the prefix, I'm not sure whether it's highschool or undergraduate**...
2. ### Dynamic Viscosity in Reynolds Number

I am trying to run a calculation to work out the overall heat transfer coefficient of an arbitrary ten plate exchanger where the fluid is not determined using Re=puD/mu where mu is dynamic viscosity. When mu is such a strong function of temperature how should I determine which valye to use, say...
3. ### Aerofoil Reynolds number, meaning of a statement in my homework

Homework Statement hello, i have been given a piece of homework which is determining the characteristics on an aerofoils boundary layer. In the brief the following statement is made with no context “Aerofoil is flying in chord Reynolds number 0.2x10^6” am i correct in saying that is the point...
4. ### Beyond Viscous Drag, Cavitation, Laminar Flow, & Reynolds

When using Computational Fluid Dynamic (CFD) modeling you are able to see incredible complexity in water energy transfer. The Thermodynamic energy transfer occurs at much higher velocity so it does not apply in most of the cases I am looking at. What are the other parasitic energy transfers that...
5. ### At what critical Reynolds number does vortex shedding begin?

In: "Fluid Dynamics", Chapter 3 (Turbulence), Section 26, Landau and Lifchitz analyze the problem of the stability of a steady flow past a body of finite size. The fluid is assumed to be incompressible and they reach the conclusion that perturbations that deviate from steady flows start to...
6. ### Relation Between Ma and Re for Isentropic Expansion

Homework Statement Consider the isentropic expansion of air from a fixed given reservoir (i.e. total pressure and temperature). Investigate the behaviour of the value of the Reynolds number of the flow, as a function of the Mach Number M of the expanded flow. For small values of M, the...
7. ### What does FL represent in the drag coefficient equation?

So I did a project about a year ago and I can't remember one of the things I wrote in this equation. The equation apparently I got it from NASA's website. https://www.grc.nasa.gov/www/k-12/airplane/dragco.html This is my equation CD = FL/ (0.5 * Air viscosity * V^2 * Area) = 0.4These are the...
8. ### Turbulence issues within tubing (Exair Vortex system)

Hello, I used the Darcy Friction Factor from the Moody Diagram along with the Reynolds number to find energy losses inside the cold air tubing of our vortex system. My calculations showed that I should decrease transitions, length, diameter, and velocity. I am mainly concerned with the figuring...
9. ### Fluid Flow/Heat Transfer question struggle

Homework Statement I would really appreciate if someone could help me out with this exercise in fluid flow/heat transfer ,because I really struggling with it.Below I am attaching photo of problem+table with values. Thank you in advance !Homework Equations Question link:[/B]...
10. ### Alternative form of Reynold's number

Homework Statement in the third picture , we know that π2 can be written as function of π1 , where π2 is inverse of reynold number , how if i want to change it to π1 = function of π2 , can i write it as (Reynold number ) = F / ρ (D^2)(v^2) ? p/s : π1 is actually inverse of reynold number...
11. ### Confused about Reynolds Number- Fluid Mechanics

Hi, I am working on the laminar flow and during my calculation at the outlet of my nozzle my Re was even greater than 120,000 however my other calculations seemed legit to me. And someone told me that I am calculating the Reynolds number of an open channel and for that flow can remain in laminar...
12. ### Reynold's Number: Understanding Laminar Flow in Smooth Pipes

Homework Statement I was told that the laminar flow can be maintained at much higher Reynold 's number in very smooth pipes by avoiding flow disturbances and pipe vibrations. the Reynold's number is the ratio of inertia forces to viscous force , in high Reynold's number of inertia force will...
13. ### Is Drag Coefficient Constant for same shape, different size?

I've read that drag coefficient depends on the shape of the object but I am confused as to what shape means. Does it mean geometric shape or is area included in that? Say I have one sphere of radius r and keep fluid velocity, density, and viscosity constant and find its drag coefficient. Would...
14. ### Pressure and Flow Rate in a Tank

Homework Statement A tank of cross-sectional area A is initially filled with fluid of density ρ and viscosity μ to height hi. The pressure above the fluid in the tank is atmospheric, Patm. At the base of the tank there are two pipes, which are both open to teh atmosphere, such that fluid...
15. ### How Does Tube Diameter Affect Reynolds Number in Gravity-Driven Laminar Flow?

< Mentor Note -- please remember to use the Homework Help Template when posting schoolwork questions > Consider the fully developed laminar flow due to gravity of water in a vertical circular tube. Assume atmospheric pressure at inlet and outlet. Show that the relationship between diameter and...
16. ### Help With Reynold's Number and Diameter

Hey guys, I am looking at the concept of Reynold's number applying to anesthesia circuits. I understand that one formulation for Reynold's number as it relates to a fluid flowing through a tube of constant dimensions is: R# = (Velocity x Diameter x Density)/Viscocity I know that a high R#...
17. M

### Calculating Reynold's Number for an Infinite Plate | Understanding the Basics

Hi PF! Can you help me out with determining a Reynold's Number over an infinite plate? I know it to be ##U L / \nu## but ##L## isn't exactly defined. Would it be something more like ##U \delta / \nu## where ##\delta## is a vertical distance, say, the distance of the BL? Thanks!
18. ### Turbulence in pipe flow (Reynold's Number)

I have some confusion about how blockages result in the laminar/turbulent flow of fluids in pipes. From my understanding, there is a certain diameter of a blockage in a pipe that will cause the flow to transition from laminar to turbulent (depending on the velocity of flow, etc.) What is the...
19. ### Calculating Reynold's Number for a Passenger Jet Cruise

A passenger jet cruises at 525 mph and an altitude of 39,000 ft. The wing chord is 3 m. If the local density is 6.14 x 10-4sl/ft3 and the dynamic viscosity is 2.97 x 10-7lbf-s/ft2, what is the cruise Re number based on the chord? Make sure your units are consistent in your calculations...
20. ### Calculate Flow Rate for Reynold's Number Homework

Homework Statement A fluid with relative density σ=0.7 and kinematic viscosity \nu=0.6mm2/s is used as a cooling agent in an electrical equipment cooling system. The fluid circulates in a 2m long copper pipe of 3mm in diameter. A pump is used to create a head difference of 0.5m between entry...
21. ### Reynold's Number related to heat transfer coefficient

Hi, I am in a Heat Transfer class at school and my professor has set an interesting challenge before me. It is not a homework problem or anything, just a side project he challenged us to look into relating to external flow. The question is as follows: In fluid (e.g air, water) flow over a...
22. ### Understanding Reynold's Number & Characteristic Length

Hello... Reynold's Number is given by: where: is the mean fluid velocity (SI units: m/s) L is a length of the object that the flow is going through or around (m) μ is the dynamic viscosity of the fluid (Pa·s or N·s/m² or kg/m/s) ν is the kinematic viscosity (ν = μ / ρ) (m²/s) is the...
23. ### Reynold's Number for a Cantilever Beam

Good Evening! I've been looking at this problem for a bit and I am a little stumped on it. I asked two graduate level Fluids TAs and my other classmates and they are stumped as well. I hope that you can help... I am doing an experiment that involves a cantilever beam and wind flow that is...
24. ### Is Reynold's number really matter?

Can I neglect it when talking about drag force or making a wind tunnel test? Why is it so important? Thank you for replying.
25. ### Aircraft Design - Reynold's Number & Stalling Speed

hello all, i was reading up on aircraft design one fine day when they talked about landing speed; they have to be higher than one critical speed, the stalling speed. if i remember correctly, is there another stalling speed, the upper limit? reynold's number increases at increasing speed of...