Question

Consider the velocity field $\vec{V}=A\left(x^{4}-6 x^{2} y^{2}+y^{4}\right) \hat{i}+$ $A\left(4 x y^{3}-4 x^{3} y\right) \hat{j}$ in the $x y$ plane, where $A=0.25 \mathrm{m}^{-3} \cdot \mathrm{s}^{-1}$, and the coordinates are measured in meters. Is this a possible incompressible flow field? Calculate the acceleration of a fluid particle at point $(x, y)=(2,1)$.

          Consider the velocity field $\vec{V}=A\left(x^{4}-6 x^{2} y^{2}+y^{4}\right) \hat{i}+$
$A\left(4 x y^{3}-4 x^{3} y\right) \hat{j}$ in the $x y$ plane, where $A=0.25 \mathrm{m}^{-3} \cdot \mathrm{s}^{-1}$,
and the coordinates are measured in meters. Is this a possible incompressible flow field? Calculate the acceleration of a fluid particle at point $(x, y)=(2,1)$.

Added by Daniel B.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Madhur L

04/16/2023

Step 1

First, we need to check if the flow is incompressible. For a flow to be incompressible, its divergence must be zero. The divergence of a vector field $\vec{V}$ is given by: $$\nabla \cdot \vec{V} = \frac{\partial V_x}{\partial x} + \frac{\partial V_y}{\partial Show more…

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Consider the velocity field $\vec{V}=A\left(x^{4}-6 x^{2} y^{2}+y^{4}\right) \hat{i}+$ $A\left(4 x y^{3}-4 x^{3} y\right) \hat{j}$ in the $x y$ plane, where $A=0.25 \mathrm{m}^{-3} \cdot \mathrm{s}^{-1}$, and the coordinates are measured in meters. Is this a possible incompressible flow field? Calculate the acceleration of a fluid particle at point $(x, y)=(2,1)$.