Drag & Viscosity: Exploring Effects at High Reynolds Numbers

• GT1
In summary, the drag at high Reynolds numbers is calculated using the formula 0.5*ρ*V²*Cd*A. At the molecular level, the drag is independent of viscosity due to the relationship between density and viscosity. However, at high turbulent zones, the drag is still affected by density, which is indirectly related to viscosity. The Reynolds number, which represents the ratio of inertia forces to viscous forces, determines whether viscosity can be neglected in the drag calculation. At high Reynolds numbers, the viscous forces can be neglected, but in some flow situations, the drag coefficient is a function of Reynolds number. This is because at high Reynolds numbers, the effects of viscosity on the fluid flow can be neglected, but the visc
GT1
Drag at high Reynolds numbers is given by the formula: 0.5*$$\rho$$*V2*Cd*A
Why does at the molecular (or at the micro) level the drag is independent of the viscosity?

The density is related with the viscosity of the fluid:
density=viscosity/kinematic viscosity

uros said:
The density is related with the viscosity of the fluid:
density=viscosity/kinematic viscosity

Kinematic viscosity is Viscosity/Density
Viscosity/Kinematic viscosity = Viscosity/Viscosity/Density = Density.

So still no matter how high is the viscosity (concrete..), as long as we are at the high turbulent zone, the drag is independent of the viscosity. It sounds counterintuitive to me.

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GT1 said:
So still no matter how high is the viscosity (concrete..)...

Drag is a force exerted by the motion through fluids, doesn't make sense to relate it with solids (or very viscous fluids).

GT1 said:
... as long as we are at the high turbulent zone, the drag is independent of the viscosity. It sounds counterintuitive to me.

The density (ρ) is proportional to the viscosity (μ), the kinematic viscosity (η) expresses this ratio, with the kinematic viscosity you can turn viscosity into density and vice versa.
η=μ/ρ
Since the drag depends of the density it also is indirectly related to the viscosity.
If you're more comfortable expressing the drag through the viscosity instead of the density change the density by the ratio of viscosity (μ) and kinematic viscosity (η).
F=0.5*ρ*v²*A*Cd
F=0.5*μ/η*v²*A*Cd

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Reynolds number represents the the ratio of the inertia forces to the viscous forces in the flow.

So for high Reynolds numbers (e.g. Re >= 10^6) the viscous forces can be neglected.
For "creeping" or Stokes flow at very low Reynolds number (Re << 1) the inertia forces can be neglected.

Of course the Reynolds number depends on the viscosity (and other physical parameters), so in that sense the viscosity DOES influence the drag calculation - but only to the extent of deciding whether your $\rho V^2 C_d A / 2$ formula is relevant or not.

For some flow situations (e.g. in the transition between laminar and turbulent flow) $C_d$ is a function of Re, not a constant value.

AlephZero said:
Reynolds number represents the the ratio of the inertia forces to the viscous forces in the flow.

So for high Reynolds numbers (e.g. Re >= 10^6) the viscous forces can be neglected.
For "creeping" or Stokes flow at very low Reynolds number (Re << 1) the inertia forces can be neglected.

Of course the Reynolds number depends on the viscosity (and other physical parameters), so in that sense the viscosity DOES influence the drag calculation - but only to the extent of deciding whether your $\rho V^2 C_d A / 2$ formula is relevant or not.

For some flow situations (e.g. in the transition between laminar and turbulent flow) $C_d$ is a function of Re, not a constant value.

Why at high Reynolds numbers the viscosity can be neglected? Eventually all the energy is dissipated through viscosity, the energy has to pass from high scale turbulence (where viscosity is can be neglected) to small scale turbulence (where viscosity can't be neglected) so at some point the viscosity is important.
Also you can see that at high Reynolds numbers the drag coefficient (Cd) vs. Reynolds number is almost flat line.

GT1 said:
Why at high Reynolds numbers the viscosity can be neglected? Eventually all the energy is dissipated through viscosity, the energy has to pass from high scale turbulence (where viscosity is can be neglected) to small scale turbulence (where viscosity can't be neglected) so at some point the viscosity is important.
"The viscous forces acting on the body can be neglected relative to the inertia forces on the body" is exactly what "high Reynolds number" means.

"The viscous forces on the body can be neglected compared with the inertia forces" does NOT mean the same thing as "the effects of viscosity on the fluid flow can be neglected". For inviscid flow, the lift and drag forces would be indentically zero for any shape of body.

But if you are considering the wing of a large aircraft for example, the aerodynamic forces in the tip vortex a few kilometers behind the plane, where the energy in the vortex is being slowly dissipated by the air viscosity, do not contribute anything to the drag force on the wing.

The calculation of Re uses the velocity, density, and a length parameter which is often related to the cross section area. The velocity, density and area are explicitly included in the drag formula. So in a sense, the "effect of Re on the drag" is mainly represented in the formula by the velocity, density and area, not by Re itself. The second-order effects are represented empirically, for a particular shape of body, by the variation of Cd with Re.

1. What is drag and how does it affect objects moving through a fluid?

Drag is the force that resists the movement of an object through a fluid, such as air or water. It is caused by the friction between the fluid and the surface of the object. The faster an object moves through the fluid, the greater the drag force will be.

2. How is drag related to viscosity?

Viscosity is the measure of a fluid's resistance to flow. The higher the viscosity, the thicker the fluid and the greater the drag force it will exert on an object moving through it. Therefore, drag and viscosity are directly related, with higher viscosity fluids resulting in higher drag forces.

3. What is meant by "high Reynolds numbers" in the context of drag and viscosity?

The Reynolds number is a dimensionless number used to determine the type of flow (laminar or turbulent) in a fluid. High Reynolds numbers indicate turbulent flow, which is characterized by chaotic and unpredictable movement. In the context of drag and viscosity, studying effects at high Reynolds numbers allows us to explore how these forces behave in more complex and dynamic fluid flows.

4. What are some real-life applications of understanding drag and viscosity at high Reynolds numbers?

Understanding the effects of drag and viscosity at high Reynolds numbers is crucial in many industries, such as aerospace, marine engineering, and sports. For example, in the design of airplanes, engineers must consider the drag and viscosity of air at high speeds to optimize efficiency and reduce fuel consumption. In sports, such as swimming and cycling, athletes must also consider drag and viscosity to improve their performance.

5. How do scientists study drag and viscosity at high Reynolds numbers?

Scientists use a variety of methods, including computer simulations, wind tunnels, and physical experiments, to study drag and viscosity at high Reynolds numbers. These methods allow them to observe and measure the effects of these forces on objects moving through fluids, and to make predictions and develop theories about their behavior.

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