Consider the following Cartesian velocity field u = A(t)(f(x), g(y), h(z)) where A, f, g, and h are non-constant functions of only one independent variable. a) Determine ∂u/∂t and (u ∙ ∇)u in terms of...


Consider the following Cartesian velocity field u = A(t)(f(x), g(y), h(z)) where A, f, g, and h are non-constant functions of only one independent variable.


a) Determine ∂u/∂t and (u ∙ ∇)u in terms of A, f, g, and h, and their derivatives.


b) Determine A, f, g, and h when Du/Dt = 0, u = 0 at x = 0, and u is finite for t > 0.


c) For the conditions in part b), determine the equation for the path line that passes through xoat time to, and show directly that the acceleration a of the fluid particle that follows this path is zero.



Sep 21, 2022
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