Chapter 1. calc_tutorial_17_3_005

1.1 Problem Statement

{2,3,4,5}
{2,3,4,5}
{5,6,7}
{2,3,4,5}
{3,5,7}
{2,4,6,8}
$a+$f
round($c/$g,3)

Find a constant c for which the velocity field

v = ($acx − $by)i + ($cy − $dz)j + ($ex + $fcz)k

of a fluid is incompressible [meaning that div(v) = 0].

1.2 Step 1

Question Sequence

Question 1.1

Recall how to find the divergence of a vector field F = <F1, F2, F3>.

div(F) = (∂F1 / ∂x) + (∂F2 / ∂y) + (∂F3 / ∂z)

We need to find a constant c such that div(v) = 0.

Calculate div(v) for v = ($acx − $by)i + ($cy − $dz)j + ($ex + $fcz)k.

div(v) = (∂ / ∂x)($acx − $by) + (∂ / ∂y)($cy − $dz) + (∂ / ∂z)($ex + $fcz)

= mpgA8Zi4UKU=c + SFgqQUkJGdg=

Correct.
Incorrect.

1.3 Step 2

Question Sequence

Question 1.2

Find c for which the given velocity field of a fluid is incompressible. Round your answer to three decimal places.

div(v) = 0

$gc + $c = 0

c = zBNzILz/DvM=

Correct.
Incorrect.