Advanced Fluid Mechanics - Video #2 - Cartesian Tensors
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YouTubeProf. Brendan MacDonald
Advanced Fluid Mechanics - Video #2 - Cartesian Tensors
This video covers: 1. Cartesian tensors 1.1 Scalars, vectors, and notation - Einstein summation convention 1.2 Second-order tensors 1.3 More on vectors 1.4 Vector vs. index notation 1.5 Force on a surface - Example of force on an angled surface in 2D flow through a channel 1.6 Gauss' Theorem 1.7 Stokes' Theorem
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Cartesian Tensor Definition
Use the basic definition of a Cartesian tensor to show the following. (a) That for any general, but fixed, ϕ, (u1, u2)=(x1 cosϕ-x2 sinϕ, x1 sinϕ x2 cosϕ) are the components of a first-order tensor in two dimensions. (b) That ( x2^2 x1 x2 x1 x2 x1^2) is not a tensor of order 2. To establish that a single element does not transform correctly is sufficient. | Numerade
Use the basic definition of a Cartesian tensor to show the following. (a) That for any general, but fixed, ϕ, (u1, u2)=(x1 cosϕ-x2 sinϕ, x1 sinϕ x2 cosϕ) are the components of a first-order tensor in two dimensions. (b) That ( x2^2 x1 x2 x1 x2 x1^2) is not a tensor of order 2. To establish that a single element does not transform correctly is sufficient. | Numerade
numerade.com
Jan 19, 2022
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