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BE_110_HW_8 - BE 110 Homework Assignment#8 1 Practice...

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BE 110 An Introduction to Biomechanics Fall 2005 Homework Assignment #8 Due THURSDAY 12/01/05 , 8AM before class 1. Practice Problems - Show that the material derivative of a volume integral D Dt A ( x , y , z , t ) dV V ( t ) = dA dt + A v i x i dV V ( t ) where A(x,y,z,t) is a continuously differentiable function. Note that this relationship can be applied to different physical principles, such as conservation of mass (in which case A = ρ the mass density), or conservation of momentum (in which case A needs to be replaced by the vector component A i = ρ v i ). See section 10.4. on page 215-217. - The material derivative can be used to find the boundary condition for an object suspended in a fluid. This is a useful theorem for analysis of particle motions. See problem 10.7. and 10.8. - Show that the permutation symbol is an isotropic tensor, i.e. the tensor components remain the same under a permissible orthogonal transformation. A permissible transformation refers to the fact that the orientation of the axis system does not change during the transformation, i.e. a right-
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