A steady, incompressible, two-dimensional velocity field is given by the following components in the x-y plane: u=1.85+2.05x+0.656y v=0.754−2.18x−2.05y . Calculate the acceleration field (find expressions for acceleration components ax and ay), and calculate the acceleration at the point (x, y) = (-1, 5).

1)

2) 8.418

Explanation:

1)

The two components of the velocity field in x and y for the field in this problem are:

The x-component and y-component of the acceleration field can be found using the following equations:

The derivatives in this problem are:

Substituting, we find:

And

2)

In this part of the problem, we want to find the acceleration at the point

(x,y) = (-1,5)

So we have

x = -1

y = 5

First of all, we substitute these values of x and y into the expression for the components of the acceleration field:

And so we find:

And finally, we find the magnitude of the acceleration simply by applying Pythagorean's theorem:

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explanation: