What does it mean when divergence is zero?

zero divergence means that the amount going into a region equals the amount coming out. in other words, nothing is lost. so for example the divergence of the density of a fluid is (usually) zero because you can’t (unless there’s a “source” or “sink”) create (or destroy) mass.

What is the nature of the field if the divergence is zero and curl is also zero?

Explanation: Since the vector field does not diverge (moves in a straight path), the divergence is zero. Also, the path does not possess any curls, so the field is irrotational.

What does it mean when curl is zero?

If the curl is zero, then the leaf doesn’t rotate as it moves through the fluid. Note that the curl of a vector field is a vector field, in contrast to divergence.

What is the divergence of a vector?

The divergence of a vector field simply measures how much the flow is expanding at a given point. It does not indicate in which direction the expansion is occuring. Hence (in contrast to the curl of a vector field), the divergence is a scalar.

What is divergence in fluid mechanics?

Divergence measures the change in density of a fluid flowing according to a given vector field.

What is divergence and curl of a vector field?

The divergence and curl of a vector field are two vector operators whose basic properties can be understood geometrically by viewing a vector field as the flow of a fluid or gas. The curl of a vector field captures the idea of how a fluid may rotate. Imagine that the below vector field F represents fluid flow.

What is divergence and curl of a vector?

Roughly speaking, divergence measures the tendency of the fluid to collect or disperse at a point, and curl measures the tendency of the fluid to swirl around the point. Divergence is a scalar, that is, a single number, while curl is itself a vector.

What is the divergence of the vector field f where f XI YJ ZK *?

3. Compute the divergence of the vector xi + yj + zk. Explanation: The vector given is a position vector. The divergence of any position vector is always 3.

What is divergence curl?

What happens when the divergence of a vector field is zero?

Imagine taking an elastic circle (a circle with a shape that can be changed by the vector field) and dropping it into a fluid. If the circle maintains its exact area as it flows through the fluid, then the divergence is zero. This would occur for both vector fields in (Figure).

What is the divergence of incompressible fluid?

Divergence. Consider an incompressible fluid whose velocity field is . It is clear that for any closed surface, since what flows into the surface must flow out again. Thus, according to the divergence theorem, for any volume. The only way in which this is possible is if is everywhere zero.

Can an incompressible fluid have a velocity field of zero?

Consider an incompressible fluid whose velocity field is . It is clear that for any closed surface, since what flows into the surface must flow out again. Thus, according to the divergence theorem, for any volume. The only way in which this is possible is if is everywhere zero.

How do you know if the divergence is zero or not?

If the circle maintains its exact area as it flows through the fluid, then the divergence is zero. This would occur for both vector fields in (Figure). On the other hand, if the circle’s shape is distorted so that its area shrinks or expands, then the divergence is not zero.