- #1
Wildcat04
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Homework Statement
Find vz(r)
Boundary Conditions:
1. vz(Ro) = 0
2. vz(Ri) = W
Homework Equations
(1/r) d/dr [r dvz/dr] = 0 (from previous problem)
Let v = dvz / dr
d/dr [r v] = 0
r v = c1
v = c1 / r
vz = c1 ln r + c2
BC 1:
0 = c1 ln Ro + c2
c2 = - c1 ln Ro
BC 2:
W = c1 ln Ri - c1 ln Ro
W = c1 (ln Ri - ln Ro)
W = c1 ln(Ri/Ro)
c1 = W / ln(Ri/Ro)
My Soultion:
vz = (W ln r) / (ln(Ri/Ro) - (W ln Ro)/ln(Ri/Ro)
vz = W[ln (r / Ro) / ln(Ri/Ro)]
Unfortunately, the answer key says it should be:
vz = W [ln (Ro / r) / ln(Ro/Ri)]
So I am close but no cigar. I have recompleted this problem several times and keep arriving at the same solution. Can anyone point out my mistake?