3 dimensional stream function

In summary, the conversation is about the equation for a 3-dimensional stream function and how to express the flow properties in terms of it. The participants also mention that while stream functions exist in three dimensions, they are only applicable in certain cases and can be complex to work with.
  • #1
stan
18
0
hi

does anyone know the equation for a 3-dimensional stream function?

for a 2 dimensional case, u=d(stream function)/dy and
v=-d(stream function)/dx..


so does anyone knows how to express u, v and w in terms of the stream function for a 3-dimensional case...

thanks.



stan
 
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  • #2
stan said:
hi

does anyone know the equation for a 3-dimensional stream function?

for a 2 dimensional case, u=d(stream function)/dy and
v=-d(stream function)/dx..


so does anyone knows how to express u, v and w in terms of the stream function for a 3-dimensional case...

thanks.
stan

I have never seen a tridimensional stream function, although it exists. In words of Anderson in his book of Computational Fluid Dynamics and Heat Transfer:

"For the case of 3-d flows, it is possible to use two stream functions to replace the continuity equation. However, the complexity of this approach usually makes it less atractive than using the continuity equation in its original form".

Try to derivate it using two stream functions.
 
  • #3
stream function for three dimensional flow also exists but only for axisymmetric flow i.e the flow properties in the third direction(say z axis) is same or in other words the derivative w.r.t (d/dx)that, will be zero.
 
  • #4
devrana01 said:
stream function for three dimensional flow also exists but only for axisymmetric flow i.e the flow properties in the third direction(say z axis) is same or in other words the derivative w.r.t (d/dx)that, will be zero.

I agree. Stream functions in general do not exist in three dimensions, but only in a special case. Of course 3D stream functions exist physically but can not be represented mathematically.
 

1. What is a 3 dimensional stream function?

A 3 dimensional stream function is a mathematical function used to describe the flow of a fluid in three-dimensional space. It is often used in fluid dynamics to represent the velocity field of a fluid flow.

2. How is a 3 dimensional stream function different from a 2 dimensional stream function?

In a 3 dimensional stream function, the fluid flow is described in three dimensions, while a 2 dimensional stream function only describes the flow in two dimensions. This means that a 3 dimensional stream function takes into account the velocity components in all three directions, while a 2 dimensional stream function only considers the velocity components in two directions.

3. What are the applications of a 3 dimensional stream function?

A 3 dimensional stream function has various applications in fluid dynamics, such as in the study of air and water currents, weather patterns, and ocean currents. It is also used in the design and analysis of aircrafts, ships, and other structures that interact with fluids.

4. How is a 3 dimensional stream function calculated?

A 3 dimensional stream function is typically calculated using vector calculus, specifically the curl and divergence operations. It involves solving a set of partial differential equations that describe the fluid flow in three dimensions.

5. Can a 3 dimensional stream function be used to predict the behavior of a fluid?

Yes, a 3 dimensional stream function can be used to predict the behavior of a fluid, such as its flow patterns and velocity distribution. However, it is important to note that a 3 dimensional stream function is an idealized representation of a fluid flow and may not fully capture all the complexities and variations of a real-world fluid system.

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