Graph function help - fluid mechanics/streamlines related

In summary, the conversation is about finding the streamfunction in a fluid mechanics problem and plotting the stream lines. The person is unsure if they have completed the question correctly and asks for help. The conversation also touches on the difference between stream function and velocity potential. The summary concludes with the solution of the conversation being to set the solution for the velocity potential equal to a constant in order to graph the stream lines.
  • #1
elle
91
0
Graph function help please - fluid mechanics/streamlines related

I'm not too sure whether I should have posted this in the Physics section or in the maths :confused: Please move this topic if its in the wrong place!

this probably seems like a silly question but is it possible to plot x*y + c on a graph where c = a constant? :confused: I'm working on a question on fluid mechanics where I have to find the streamfunction and plot the stream lines. However I'm in doubt whether i have done the question correctly in the first place.

Please help!

Homework Statement



For the 2D velocity field u = xi - yj find the streamfunction 'psi' (apologises, I'm not too familiar with Latex)


Homework Equations



given above

The Attempt at a Solution



After partially differentiating and using formulas from my notes, i got psi = x*y + c :confused:
 
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  • #2
elle said:
I'm not too sure whether I should have posted this in the Physics section or in the maths :confused: Please move this topic if its in the wrong place!

this probably seems like a silly question but is it possible to plot x*y + c on a graph where c = a constant? :confused: I'm working on a question on fluid mechanics where I have to find the streamfunction and plot the stream lines. However I'm in doubt whether i have done the question correctly in the first place.
What do you mean by "plot x*y+ c". That's neither a function nor an equation. If you mean xy= c or xy+ c= 0, then, yes, of course, you can plot it- it's a family of hyperbolas.

Please help!

Homework Statement



For the 2D velocity field u = xi - yj find the streamfunction 'psi' (apologises, I'm not too familiar with Latex)
Then [itex]\nabla \psi= x\vec{i}- y\vec{j}[/itex], right?
So
[tex]\frac{\partial \psi}{\partial x}= x[/tex]
and
[tex]\frac{\partial \psi}{\partial y}= -y[/itex]
That should be easy to integrate.

Homework Equations



given above

The Attempt at a Solution



After partially differentiating and using formulas from my notes, i got psi = x*y + c :confused:
Perhaps I am misunderstanding your "stream function". I get the orthogonal family to xy= C which would be the potential function.
 
  • #3
You are confusing "stream function" with "velocity potential", HallsofIvy!

A stream function may always be defined if the velocity field is solenoidal, i.e, [tex]\nabla\cdot{\vec{v}}=0[/tex]
In the 2-D case, we may define: [tex]\vec{v}=\nabla\times\psi\vec{k}[/tex], where [itex]\psi[/itex] is the scalar stream function.

The analogue in electro-magnetism is called the magnetic vector potential, I believe..
 
Last edited:
  • #4
Very likely- it's been a long time since I have looked at fluid dynamics.

So the equations are
[tex]\frac{\partial \phi}{\partial x}= y[/tex]
and
[tex]\frac{\partial \phi}{\partial x}= x[/tex]

Yes, that tells us that [itex]\phi(x,y)= xy+ c[/itex].
Since the stream lines (again, if I remember correctly!) are the lines on which [itex]\phi[/itex] is a constant they are given by xy+ c= c' or xy= C, the hyperbolas that my family, [itex]x^2- y^2= c[/itex] are orthogonal to.

elle, perhaps your only problem was not realizing that you get an equation to graph by setting your solution for [itex]\phi[/itex] equal to a constant.
 
  • #5
HallsofIvy said:
Very likely- it's been a long time since I have looked at fluid dynamics.

So the equations are
[tex]\frac{\partial \phi}{\partial x}= y[/tex]
and
[tex]\frac{\partial \phi}{\partial x}= x[/tex]

Yes, that tells us that [itex]\phi(x,y)= xy+ c[/itex].
Since the stream lines (again, if I remember correctly!) are the lines on which [itex]\phi[/itex] is a constant they are given by xy+ c= c' or xy= C, the hyperbolas that my family, [itex]x^2- y^2= c[/itex] are orthogonal to.

elle, perhaps your only problem was not realizing that you get an equation to graph by setting your solution for [itex]\phi[/itex] equal to a constant.


ohh yeah! I forgot that its equal to a constant :redface: Thanks guys for the help :smile:
 

1. What is a graph function in fluid mechanics?

A graph function in fluid mechanics is a graphical representation of a mathematical function that describes the behavior of a fluid. It is commonly used to visualize fluid flow and study its properties, such as velocity, pressure, and streamlines.

2. How do I plot a graph function for fluid mechanics?

To plot a graph function in fluid mechanics, you will need to have a mathematical function that describes the behavior of the fluid. You can then use software such as MATLAB or Python to input the function and generate a graph. Alternatively, you can plot the function manually by calculating and plotting points on a graph.

3. What information can I obtain from a graph function in fluid mechanics?

A graph function in fluid mechanics can provide valuable information about the behavior of a fluid, such as the velocity profile, pressure distribution, and streamlines. It can also help in identifying areas of turbulence or stagnation and understanding the effects of different parameters on the fluid flow.

4. What are streamlines in fluid mechanics?

Streamlines in fluid mechanics are imaginary lines that represent the path of a fluid particle in a flow. They are tangent to the velocity vector at every point and do not cross each other. Streamlines can help visualize the direction and speed of fluid flow and are useful in analyzing flow patterns and identifying areas of recirculation or separation.

5. How can I use a graph function to analyze fluid flow?

A graph function can be used to analyze fluid flow by providing a visual representation of the fluid behavior. It can help in identifying areas of high or low velocity, pressure variations, and regions of turbulence. By manipulating the function, one can also study the effects of different parameters on the fluid flow and make predictions about the behavior of the fluid in different scenarios.

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