# Q: Stokes paradox (flow around a cylinder)

• A
• Andy Resnick

#### Andy Resnick

Can anyone recommend a good (peer reviewed) reference that discusses low Reynolds number flow around a cylinder? I'm specifically looking for derivations of the drag coefficient. The usual 'gold standard' references:

http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=367164
Lamb (Hydrodynamics)

are fairly difficult to parse, and these:

http://www.lmm.jussieu.fr/~lagree/COURS/M2MHP/petitRe.pdf
http://arxiv.org/pdf/0901.3621.pdf

are not peer-reviewed. Thanks in advance...

Last edited by a moderator:
Thanks!

## 1. What is Stokes paradox?

Stokes paradox is a phenomenon in fluid dynamics where the drag force on a cylinder in a viscous fluid decreases with increasing Reynolds number (Re). This is contrary to the expected behavior, as the drag force should increase with Re. This paradox can be explained by the presence of a separation point on the cylinder, causing the flow to transition from laminar to turbulent, resulting in a decrease in drag force.

## 2. How does the Reynolds number affect Stokes paradox?

The Reynolds number (Re) is a dimensionless quantity that represents the ratio of inertial forces to viscous forces in a fluid flow. In the case of Stokes paradox, as Re increases, the flow around the cylinder transitions from laminar to turbulent, causing a decrease in the drag force. This is due to the formation of a separation point on the cylinder at higher Re values, which alters the flow behavior and decreases the drag force.

## 3. What is the significance of Stokes paradox in fluid dynamics?

Stokes paradox highlights the complex behavior of fluid flows, where the expected relationship between drag force and Reynolds number does not hold. This paradox has implications in various fields, such as aerodynamics and marine engineering, where understanding and predicting drag forces is crucial for design and performance optimization.

## 4. Can Stokes paradox be observed in real-world situations?

Yes, Stokes paradox has been observed in various real-world situations, such as flow around cylinders in wind tunnels, flow around ships and submarines, and flow around buildings. In fact, this paradox was first observed by Sir George Gabriel Stokes in his experiments with viscous flows in the 19th century.

## 5. How is Stokes paradox related to the Navier-Stokes equations?

The Navier-Stokes equations are a set of equations that describe the behavior of fluid flows. These equations consider both viscous and inertial forces, and they can be used to calculate the drag force on a cylinder. However, the Navier-Stokes equations do not fully capture the complex behavior of fluid flows, and they cannot explain Stokes paradox. This highlights the need for further research and development in the field of fluid dynamics.