fluid dynamics question Watch

the living legend
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#1
Report Thread starter 10 years ago
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hi,

i'm doing a module in fluid dynamics this year and i'm trying to work through some examples. i've got this question and i'm not sure how to go about tackling it, any help would b appricated. thanks

position vector x the stress tensor  \sigma (x) takes the form

 \begin{matrix}  

0  &  1  &  2      \\  

1  &  n  &  1      \\  

2  &  1  &  2      \end{matrix}

and n is an unknown constant.

(question a) determine the value of n which ensures the existance of a plane passing through x on which the stress tensor s(t,x) is equal to 0.
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div curl F = 0
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I am unsure of the correct method to use but most of the time when you have a matrix with one unknown value then you usually work it out by requiring the determinant to be zero. So in this case that makes:

 2(1-2n) = 0 \to n = \frac{1}{2}
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MC REN
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^what he said, set the determinant to zero

This would mean that at least one of the eigenvalues is zero*, i.e. there is a direction in which the stress tensor vanishes which I think is what the question is asking (the plane bit is confusing me though)

EDIT/ Actually I guess a plane would require that 2 of the directions had eigenvalue 0, so that would put a condition on the characteristic equation

*detA = product of eigenvalues
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