calc_tutorial_17_3_005

 
Problem Statement

{2,3,4,5}
{2,3,4,5}
{5,6,7}
{2,3,4,5}
{3,5,7}
{2,4,6,8}
5+2
round(5/7,3)

Find a constant c for which the velocity field

v = (5cx − 4y)i + (5y − 5z)j + (5x + 2cz)k

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

 
Step 1

Question Sequence

Question 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 = (5cx − 4y)i + (5y − 5z)j + (5x + 2cz)k.

div(v) = (∂ / ∂x)(5cx − 4y) + (∂ / ∂y)(5y − 5z) + (∂ / ∂z)(5x + 2cz)

= c +

Correct.
Incorrect.

 
Step 2

Question Sequence

Question 2

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

div(v) = 0

7c + 5 = 0

c =

Correct.
Incorrect.