Hi, Just having trouble defining gravity in cylindrical coordinates (r,theta,z).
I have a pipe on an incline so without posting a diagram assume gravity is acting at an angle of (90-beta) to the z axis. Trying to derive a momentum balance and am having trouble finding g_r and g_theta
Do i assume that g_r and g_theta are 0 and gravity is only acting in the z direction?
any help is appreciated cheers

use trig , like in xyz, gx= gsin(alpha)
tilt your coordinate system but keep gravity down. z will be parallel with flow
use trig

This post was edited by saber_x3 on Mar 29 2014 09:56am

sorry i was unclear i know the z component i was just wondering is there corresponding r and theta components of the gravity as these terms come up in the momentum balance or are they 0
thanks though

yes, those components exist
when you tilt your cylindrical coordinate system, gravity will still act up and down
those components exist because you tilt the coordinate system
the g component parallel with the flow will be gsin(alpha) , alpha is angle of incline
then you have g_radius which is the other side of the triangle (gcos(alpha))
g_radius is perpendicular to the pipe

This post was edited by saber_x3 on Mar 29 2014 11:33am

"the g component parallel with the flow will be gsin(alpha) , alpha is angle of incline"

g_z component

i understand that g_r will be gcos(alpha) but in which direction is it acting because doesnt that depend on theta so it all depends on initial setting up of the coordinates?
so if ive assume gravity acts in the -ve z direction making the self weight act against the flow how do i define the gravity in terms of the radius as the radius is constant for all values of theta however will change at pi/2. Would the two halves cancel each other out and then hence same with the theta so gravity in terms of theta and r is 0 over the full system?

i read my notes, and i think i was over thinking it

the only thing needed to be added is the additional force due to weight in the flow direction
Wsin(alpha)
others are 0
so your velocity profile v_z =f(r) , is still a parabolic velocity distribution