Calculating Fluid Friction in a Spiraling Tube of Varying Diameter and Shape

[Ameriu]

Well, yes, this is my first post here, and I do hope I got it into the right section (And no, this is not homework, and although I was thinking of posting it there; I also considered posting it in the engineering forum, but I believe it would fit better in general physics forum).

Would it be possible to calculate fluid friction against the walls of the tube, if it is moving within a narrowing pipe/tube, which is laid in a fashion that resembles Archimedean Spiral?

I've been looking for the solution for past few days, yet most of the fluid friction topics describe drag friction, or contain very vague formulas for "water friction against pipes", but none of the really let me take into the account the decreasing diameter and increasing angle of piping.
Additionally, how would that friction change according to the cross-section of the tube/piping (square/oval etc.)

Any directions on where to look for the solution of this problem would be appreciated!

 

[scienceteacher]

My first post too! I think you are more interested in the relationship between the pressure of the fluid and the speed of the fluid as the volume of the conatainer changes. I would check out the Navier-Stokes equation.

 

[GT1]

If the changes in the diameter and angle are not too steep you can solve it by diving the pipe length to few (the more the better) segments with diameter of the average diameter in that segment, and then find the pressure drop for this segment and after that sum the pressure drops of all the segments.
If the changes in the diameter and angle are abrupt you can try solving it as a series of minor losses of bends and gradual contraction. Check this link for example for the minor losses - http://udel.edu/~inamdar/EGTE215/Minor_loss.pdf

 

[Bob S]

The Hazen-Williams empirical formula for turbulent flow in pipes (tubes) can be used for calculating the pressure drop in a continuously decreasing pipe diameter (using an iterative program like FORTRAN):

http://en.wikipedia.org/wiki/Hazen–Williams_equation

This is probably a reasonable approximation for an Archimedes spiral, as long as the radius of the bend is large compared to the pipe diameter a any point.

The roughness (friction) coefficient depends on the Reynolds number of the flow. See

http://www.google.com/url?sa=t&source=web&cd=54&ved=0CCgQFjADODI&url=http%3A%2F%2Fudel.edu%2F~inamdar%2FEGTE215%2FLaminar_turbulent.pdf&ei=5rZuTL71Do-isAOc6qmiCw&usg=AFQjCNGighgb2ILl0zNI-EzgHnGsc5zWww&sig2=HBiWDv42IUVNv9vX-Fo2GA

Bob S

 

[Ameriu]

Thank you, this seems like the right piece of information I needed!