- #1
Trenthan
- 54
- 0
Hey Guys/Girls and thanks in advance
Not quite sure this is in the correct forum since its not a homework question, more private study and curiosity lolz!
Im trying to evaluate the curvature along the streamline within a hydrodynamic potential field (fluid flow). I have no issue calculating the streamline and plotting it along with several others within the flow field. Now the problem is determining the curvature along it!
Lets assume I am trying to calculate the curvature at two points very close together on the streamline for starters. All i know about point 1 is:
"u and v" components of velocity
"x and y" position
"tangential direction"
Now using some of the information at point 1, i can find the location of point 2 (Using EULERS method with a step size of 1/128) and determine its tangential direction using the velocity components at point 1point (using arctan(v/u) )
I thought calculating the curvature would be quite straight forward however when searching the web and my shelf of textbooks, every method involves the use of the second derivative of the line segment, (streamline in my case) which i don't know.
Most methods seems to be similar to what is presented on Wolfram MAthWorld
http://mathworld.wolfram.com/Curvature.html"
Equations (1) - (7) are perfectly fine. However equation (8) is redundant in my case since the second derivative of my x and y position's at point 1 is unknown!
I'm just curious to know if anyone knows of any methods, or suggestions to determine the curvature knowing the information i know at point 1, above**
Cheers Trent
Not quite sure this is in the correct forum since its not a homework question, more private study and curiosity lolz!
Im trying to evaluate the curvature along the streamline within a hydrodynamic potential field (fluid flow). I have no issue calculating the streamline and plotting it along with several others within the flow field. Now the problem is determining the curvature along it!
Lets assume I am trying to calculate the curvature at two points very close together on the streamline for starters. All i know about point 1 is:
"u and v" components of velocity
"x and y" position
"tangential direction"
Now using some of the information at point 1, i can find the location of point 2 (Using EULERS method with a step size of 1/128) and determine its tangential direction using the velocity components at point 1point (using arctan(v/u) )
I thought calculating the curvature would be quite straight forward however when searching the web and my shelf of textbooks, every method involves the use of the second derivative of the line segment, (streamline in my case) which i don't know.
Most methods seems to be similar to what is presented on Wolfram MAthWorld
http://mathworld.wolfram.com/Curvature.html"
Equations (1) - (7) are perfectly fine. However equation (8) is redundant in my case since the second derivative of my x and y position's at point 1 is unknown!
I'm just curious to know if anyone knows of any methods, or suggestions to determine the curvature knowing the information i know at point 1, above**
Cheers Trent
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