the total acceleration equation is a = dvdt = ∂v∂t (u∂v∂x v∂v∂y w∂v∂z) = ∂v∂t (v⋅∇)v. if the total time derivative is applied to a pressure p, dpdt = _____.



Answer :

= ∂V∂t + (V⋅∇)V

In mathematics, the complete derivative of a function f at a point is the best linear approximation near that point of the function with respect to its arguments. Unlike partial derivatives, the total derivative approximates a function with respect to all of its arguments, not just one. Pressure is defined as force/area, and the derivatives of pressure physically correspond to the rate of change of this quantity. If the derivatives are with time, the derivatives will tell you how fast the pressure is changing with time, just like any function.a = dVdt = ∂V∂t + u∂V∂x+v∂V∂y+w∂V∂z = ∂V∂t + (V⋅∇)V

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