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Zarathuztra

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## Homework Statement

A velocity field is given by [itex]\vec{V}[/itex]= [Ax[itex]^{3}[/itex] + Bxy[itex]^{2}[/itex]][itex]\hat{i}[/itex] + [Ay[itex]^{3}[/itex] + Bx[itex]^{2}[/itex]y][itex]\hat{j}[/itex]; A=0.2 m[itex]^{-2}[/itex]s[itex]^{-1}[/itex], B is a constant, and the

coordinates are measured in meters. Determine the value and

units for B if this velocity field is to represent an incompressible

flow. Calculate the acceleration of a fluid particle at point

(x, y)=(2, 1). Evaluate the component of particle acceleration

normal to the velocity vector at this point.

## Homework Equations

u=[itex]\frac{\partial\Psi}{\partial y}[/itex] v=-[itex]\frac{\partial\Psi}{\partial x}[/itex]

## The Attempt at a Solution

I used the above equation to get value equations u and v, there is something I'm missing, a bit of reasoning that has to be made using the given information to determine a constraint that exists since the fluid is incompressible. This should link the rates of change to each other. But that's where I get stuck, having trouble hanging on to all the concepts..

u = [2Bxy][itex]\hat{i}[/itex] + [.6y[itex]^{2}[/itex] + Bx[itex]^{2}[/itex]][itex]\hat{j}[/itex]

v = -[.6x[itex]^{2}[/itex] + By[itex]^{2}[/itex]][itex]\hat{i}[/itex] - [2Bxy][itex]\hat{j}[/itex]

*Assumptions:*

1. Incompressible flow

2. B is constant

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