At 8:54 you said that for the C1/r term that dividing by zero would make the term go singular, and the only way for the equation to be true is if C1 was equal to zero. I'm a little confused because 0/0 is still undefined? It may be due to the fact that at r=0, polar coordinates are not able definitively specify a location. Because at r=0 any angle theta will result in the location being at the origin. However, because we know the flow is symmetric about theta, any angle theta will result in the same value at any distance r. Therefore, we can conclude C1 must be zero at r=0.
I see your point. A solution to your 0/0 issue is to multiply both sides by r before applying the V_z symmetry boundary condition. Now, rdV_z/dr=0=0+C_1 at r=0, and it becomes totally clear the C_1=0. That's a more sound mathematical argument. Thanks for the helpful comment!
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Slowly falling in love with the Navier-Stokes Equation. Brilliantly explained, Professor. Thank you!
Thanks for the content professor. I have thoroughly enjoyed your videos.
Incredibly insightful, thank you.
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At 8:54 you said that for the C1/r term that dividing by zero would make the term go singular, and the only way for the equation to be true is if C1 was equal to zero. I'm a little confused because 0/0 is still undefined?
It may be due to the fact that at r=0, polar coordinates are not able definitively specify a location. Because at r=0 any angle theta will result in the location being at the origin. However, because we know the flow is symmetric about theta, any angle theta will result in the same value at any distance r. Therefore, we can conclude C1 must be zero at r=0.
I see your point. A solution to your 0/0 issue is to multiply both sides by r before applying the V_z symmetry boundary condition. Now, rdV_z/dr=0=0+C_1 at r=0, and it becomes totally clear the C_1=0. That's a more sound mathematical argument. Thanks for the helpful comment!