Fluid Streamline Vector Problem

[danong]

I have a question regarding fluid streamline vector,
why is it different from the usual position vector when you take the partial derivative of it in order to obtain the grad of it?

For position vector you take partial derivative and obtain the vector along (for say) a curve.
But in fluid dynamics,
instead of taking partial derivative directly with respect to x, to obtain U(i-vector),
you take the equipotential derivative with respect to x, which is so different from the previous case,
why is it?Thanks in advance.

 

[arildno]

I have a question regarding fluid streamline vector,
why is it different from the usual position vector when you take the partial derivative of it in order to obtain the grad of it?

For position vector you take partial derivative and obtain the vector along (for say) a curve.
But in fluid dynamics,
instead of taking partial derivative directly with respect to x, to obtain U(i-vector),
you take the equipotential derivative with respect to x, which is so different from the previous case,
why is it?


Thanks in advance.

Well streamlines, particle paths (and for that matter, dye lines), are entirely different concepts.

The streamlines is an instantaneous, geometric feature of the velocity FIELD, i.e, the set of curves that can be traced out by regarding the local velocities as tangent vectors to those curves. The particle path is the path a particular particle traces out OVER time.

Only if the velocity field is STATIONARY (i.e, does not locally change over time) will the streamlines and particle paths coincide.

 

[danong]

arildno : Thanks for the clear explanation, i'd finally understood the concept with your help!

 

[arildno]

arildno : Thanks for the clear explanation, i'd finally understood the concept with your help!

My pleasure!