Proving the Three-Component Formula for Fluid Mechanics Forces

dopey9
Messages
31
Reaction score
0
Can someone help me with this proof
 

Attachments

  • 4.GIF
    4.GIF
    22.5 KB · Views: 502
  • 3.JPG
    3.JPG
    46 KB · Views: 466
Physics news on Phys.org
Well, Cartese away first, and we'll help you if you stumble! :smile:
 
I would recommend starting by supposing F is made up by three components, F_1 , F_2 ,F_3 then just expand out the left hand side!

It is tidous but you will see it will fall out

 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

Similar threads

Back
Top