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Continuity equation question 
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#1
Jul1404, 10:01 AM

Sci Advisor
PF Gold
P: 1,479

Hi guys. I am solving the axisymmetric free jet of an incompressible fluid. But I have troubles at r=0. Continuty equation can be written in cylindrical coordinates as:
1/r*d(rv)/dr + du/dz=0 v=radial velocity (v=0 at r=0) u=axial velocity. hz=delta(z) hr=delta(r) What happens at r=0?. I have to obtain a finite difference scheme in order to integrate the problem, so I have created a grid that has "i" index for "z" coordinate and "j" index for "r" coordinate. j=1 corresponds to the simmetry axe. for j>1 I have no problem because r>0. But in r=0 there is a singularity point. How can I deal with this?. As you can see I know v(i,1)=0 


#2
Jul2304, 08:04 AM

P: 3

1/r*d(vr)/dr+du/dz=0 =>
1/r*(v+r*dv/dr)+du/dz = v/r + dv/dr +du/dz at r=0, v=0 > dv/dr + du/dz = 0 does this help? 


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