Fluid mechanics navier stokes flow around geometry

In summary, the conversation was about fluid mechanics and specifically, the flow around certain geometries such as a 2-D fluid flowing around a circle. The person was wondering if anyone had experience with this type of flow and how to model it using the Navier-Stokes equations. They mentioned using a book by White, but were unable to find examples of 2-D flow around geometry. After receiving a helpful link, the conversation shifted to discussing the difficulty in finding analytical solutions to the Navier-Stokes equations, particularly for external flows. They also discussed the concept of "very low Reynolds number" and its relevance to different situations.
  • #1
member 428835
hey pf!

i am studying fluid mechanics and was wondering if any of you are familiar with a flow around some geometry? for example, perhaps a 2-D fluid flowing around a circle?

if so please reply, as i am wondering how to model the navier-stokes equations. i'll be happy to post the equations and my thoughts if you would like me to?

for the record, i am using white's book, and while it is great, i have not seen any examples dealing with 2-D flow around geometry. so far it's been flow in between plates and against a wall.

thanks so much for your support and interset!

josh
 
Engineering news on Phys.org
  • #3
The problem is that in general you can't find a solution to the Navier-Stokes equations analytically, especially external flows. There are some that are possible, like laminar flow over a flat plate (the Blasius solution), but these are relatively few and far between.

Except at very low Reynolds number, the 2-D flow around a circle (or cylinder, for example) is one such flow where an analytical solution is not possible for a viscous flow. You have to deal with flow separation and an unsteady wake (for example, try Googling von Kármán vortex street).
 
  • #4
thanks you guys! hey bonehead, what do we consider "very low Re number"? would it be possible to model, say, syrup sliding over a plate with a slight angle as a low reynolds number, or is this too fast?
 
  • #5
That depends on the context. With a cylinder in a viscous flow, very low Reynolds number in regards to whether Stokes flow is valid is typically considered to be [itex]Re \ll 1[/itex]. It doesn't really make sense to just ask what constitutes very low Reynolds number in a random situation since you aren't really specifying in that case what physical phenomenon you are hoping to capture or avoid. For example, in Stokes flow, very low Reynolds number represents the region where the assumptions used in deriving it are valid.
 

1. What is Fluid Mechanics?

Fluid mechanics is a branch of physics that studies the mechanics of fluids, which includes liquids, gases, and plasmas. It involves the study of how these fluids move and interact with their surroundings.

2. What is Navier-Stokes Equation?

The Navier-Stokes equation is a set of partial differential equations that describes the flow of a fluid. It takes into account factors such as fluid viscosity, density, and velocity to predict the behavior of fluid flow.

3. What is the significance of Navier-Stokes equation in fluid mechanics?

The Navier-Stokes equation is considered a fundamental equation in fluid mechanics as it allows for the accurate prediction of fluid flow behavior in various scenarios. It is used in the design and analysis of many engineering systems, such as pumps, turbines, and aircraft wings.

4. How does Navier-Stokes equation apply to flow around geometry?

The Navier-Stokes equation is used to study the flow of fluids around objects or obstacles, also known as flow around geometry. By solving the equation, scientists and engineers can understand the forces acting on the object and predict its motion and behavior in the fluid flow.

5. What are some real-world applications of fluid mechanics and Navier-Stokes equation?

Fluid mechanics and the Navier-Stokes equation have many practical applications in daily life, such as designing efficient car engines, predicting weather patterns, and understanding blood flow in the human body. They are also crucial in industries such as aerospace, energy, and manufacturing.

Similar threads

Replies
18
Views
938
  • STEM Academic Advising
Replies
6
Views
990
Replies
9
Views
2K
Replies
5
Views
2K
Replies
9
Views
3K
  • Classical Physics
Replies
7
Views
1K
Replies
7
Views
1K
Replies
1
Views
1K
Replies
3
Views
2K
  • Mechanics
Replies
5
Views
3K
Back
Top