# Reynolds Number and Turbulence: Why Does Increasing Density Affect Flow?

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• chir89
In summary, the Reynolds number is a ratio between the inertial forces and the viscous forces and higher density means higher inertial forces. This causes higher velocity gradients in the flow, which causes flow instabilities, causing turbulence.
chir89
hi. I have a question regarding rheology. the Reynolds number increases when density of a fluid increases. so the flow becomes more turbulent. but I wonder why it is that the flow becomes more turbulent when density increases. why is that?

You should see the Reynolds number as a ratio between the inertial forces and the viscous forces. Higher density of course means higher inertial forces.

So think of a flat plate along which a boundary layer develops (laminar, for now). The outer flow has a certain velocity and the velocity at the wall is zero by definition (the well known no-slip condition, as observed through many experiments). It is the viscosity that inhibits the flow from attaining the free-stream velocity instantly (even with the no-slip condition I mean, this would then cause an infinite gradient, which is of course not physical), so the higher the viscosity the lower the gradient in the flow (and thus the thicker the boundary layer, but I want to keep it to local gradients in the flow).

But, you can flip the argumentation. For equal viscosity, the more momentum is behind the flow, the less viscosity is able to slow down the flow towards the wall, in other words, the higher the momentum, the higher the gradients in the flow.

So, both lower viscosity and higher momentum (either through more fluid, L, higher velocity, V, or higher density, ##\rho##) cause higher gradients in the flow. Turbulence starts when gradients in the flow become too high and thus instabilities arise. This means that small perturbations in the flow do not damp out and grow towards full fledged chaotic flow (eddies and all that).

So, the short answer: higher density causes higher velocity gradients in the flow, causing flow instabilities, causing turbulence.

Lnewqban and pinball1970
Thanks so much! Got it :)

Arjan82 and Lnewqban

## 1. What is Reynolds Number and how is it calculated?

Reynolds Number is a dimensionless quantity used to predict the type of flow (laminar or turbulent) in a fluid. It is calculated by multiplying the fluid velocity, characteristic length scale, and fluid density, and dividing by the fluid viscosity.

## 2. How does increasing density affect flow?

Increasing density has a direct effect on Reynolds Number, which in turn affects the type of flow. As density increases, the Reynolds Number also increases, resulting in a transition from laminar to turbulent flow. This is because higher density fluids have a higher resistance to flow, which leads to more chaotic and turbulent motion.

## 3. Why is turbulence undesirable in certain applications?

Turbulence can cause increased drag, energy losses, and uneven distribution of forces in a fluid. This can be undesirable in applications such as aircraft design, where efficiency and stability are crucial. Turbulence can also cause wear and tear on equipment and structures, leading to maintenance and safety concerns.

## 4. How does Reynolds Number affect the onset of turbulence?

Reynolds Number plays a critical role in determining the onset of turbulence. At low Reynolds Numbers, the flow is typically laminar, meaning the fluid moves in smooth, parallel layers. As the Reynolds Number increases, the flow becomes unstable and transitions to turbulent, characterized by chaotic and irregular motion.

## 5. Can turbulence be controlled or reduced?

Yes, turbulence can be controlled or reduced through various methods, such as using flow control devices, altering the shape of objects in the flow, or changing the properties of the fluid. However, completely eliminating turbulence is not always possible, and it is important to consider the trade-offs and limitations of each method in different applications.

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