Hi All,(adsbygoogle = window.adsbygoogle || []).push({});

I have been trying to understand some fluid mechanics in a research paper and have been wrestling with the mathematics for quite some time now without success.

I want to derive gradient operator with following coordinate system in R^3 space

Let and arbitrary curve C be locus of centroid of a cylindrical (non circular) jet in space.

Let sigma is the arclength along this curve. let rho be perpendicular distance from the locus of centroids. Let theta be the angle between the line drawn from a particular point in jet to the locus of the centroids and the normal to C at that point.

What would be the gradient operator in the cordinate system in terms of

tau (torsion)

K (curvature)

sigma, rho, theta (coordinates)

isigma, irho, itheta (unit vectors along the direction of increasing sigma, rho and theta respectively)

If you could forward me to any manterial or help me derive the gradient operator, I would really appreciate.

Thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Gradient operator in Natural Curvilinear Coordinates

**Physics Forums | Science Articles, Homework Help, Discussion**