Physical Interpretation of Reynolds Number

In summary, the Reynolds Number is a dimensionless number that compares the strength of inertial forces to viscous forces in a fluid. Inertial forces refer to the mass and acceleration of the fluid, while viscous forces refer to the resistance of the fluid to flow. When the Reynolds Number is high, the inertial forces dominate and can lead to turbulent flow. Viscous fluids, on the other hand, are more likely to have laminar flow due to the dissipating effect of viscous forces.
  • #1
swmmr1928
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Wikipedia: "Reynolds Number is a dimensionless number that gives a measure of the ratio of inertial forces to viscous forces."

What is meant by the inertial forces?
I have a much better intuition of viscosity. But it seems to be like the Reynolds Number predicts turbulent flow for a viscous fluid like honey if the inertial forces dominate over the viscous forces. I cannot imagine this scenario.

What is the difference between Reynolds Number, inertial forces and viscous forces?

I looked at expressions for the Reynolds Number, but it didn't help.
 
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  • #2
"Inertia force" means the (mass x acceleration) force needed to change the velocity of the fluid. The inertia force depends on the density of the fluid, and the density is one of the terms in the "formula" for the Reynolds number.
 
  • #3
Let me say first that I've no expertise in this area and what I write below is just my reading of some web pages.

Suppose you sweep your hand through a bowl of water. The large scale movements that result are considered inertial; they're as you'd expect from basic Newtonian mechanics.

Theory says that these flows create eddies which are unstable and break up to form smaller eddies. Still inertial.
As this cascade (turbulence) progresses, the diminishing scale alters the balance between inertial forces and viscous ones. Viscous forces dissipate the energy as heat and bring the medium back to rest. With no viscosity, the molecules would go on swirling around forever on the smallest scales.

Viscous fluids are more likely to produce laminar flows. The energy gets dissipated as heat early on, preventing the eddy cascade from arising.
 

1. What is the physical significance of Reynolds Number?

The Reynolds Number is a dimensionless quantity that represents the ratio of inertial forces to viscous forces in a fluid. It is used to classify the type of flow (laminar or turbulent) and predict the behavior of a fluid flow around an object.

2. How is Reynolds Number calculated?

Reynolds Number is calculated by multiplying the fluid density, the velocity of the fluid, and the characteristic length of the object, and then dividing that product by the fluid's dynamic viscosity. The formula is Re = (ρ * V * L) / μ, where ρ is the density, V is the velocity, L is the characteristic length, and μ is the dynamic viscosity of the fluid.

3. What does a low Reynolds Number indicate?

A low Reynolds Number (less than 2300) indicates that the viscous forces dominate and the flow is characterized as laminar. In this type of flow, the fluid moves in smooth layers, and the particles of the fluid do not mix with each other.

4. What does a high Reynolds Number indicate?

A high Reynolds Number (greater than 4000) indicates that the inertial forces dominate and the flow is characterized as turbulent. In this type of flow, the fluid moves in a chaotic manner, and the particles of the fluid mix with each other.

5. How is Reynolds Number used in engineering and everyday life?

In engineering, Reynolds Number is used to design and analyze fluid flow systems, such as pipes, pumps, and turbines. It is also used to optimize the shape and size of objects that interact with fluids, such as airplane wings and car bodies. In everyday life, Reynolds Number is used to understand and predict the behavior of fluids, such as air and water, in various situations, such as weather patterns and water flow in pipes.

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