What is divergence free flow?

If F represents the velocity of a fluid, then the divergence of F at P measures the net rate of change with respect to time of the amount of fluid flowing away from P (the tendency of the fluid to flow “out of” P). …

Why is divergence velocity zero?

The gas may be moving, but the volume rate of gas flowing into any closed surface must equal the volume rate flowing out, so the net flux is zero. Thus the gas velocity has zero divergence everywhere.

How is the velocity field defined for a flow?

When we describe the flow of a fluid like water, we may think of the movement of individual particles. These particles interact with each other through forces. This represents the velocity of the fluid at the point (x, y, z) at the instant t . The quantity v(x, y,z,t) is called the velocity vector field.

What is the physical meaning of divergence of velocity?

Explanation: Divergence of velocity of a moving fluid model physically means that “time rate of change of the volume of a moving fluid element per unit volume”.

What is divergence of velocity field?

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 meant by velocity field?

Figure 3.1 : Velocity Field. Velocity field implies a distribution of velocity in a given region say R (Fig.3.1). It is denoted in a functional form as V(x,y,z,t) meaning that velocity is a function of the spatial and time coordinates.

Is flow velocity same as flow rate?

Flow rate Q is defined to be the volume V flowing past a point in time t, or Q=Vt where V is volume and t is time. Flow rate and velocity are related by Q=A¯v where A is the cross-sectional area of the flow and v is its average velocity.

What is a condition for this velocity field to be irrotational?

Flow is said to be irrotational when the vorticity has the magnitude zero everywhere. It immediately follows, from Equation (4.77), that the circulation around any arbitrary loop in an irrotational flow pattern is zero (provided that the loop can be spanned by a surface that lies entirely within the fluid).

How do you interpret the velocity field diverge?

In the case of a velocity field, its diverge can be interpreted as the negative of the fractional rate of change of the density of the fluid element (this can be proved by wiriting the continuity equation in velocity diverge form). See for instance Fundamentals of Atmospheric Modeling, by Jacobson, Chapter 3.

What happens to the velocity field when air is heated?

While air is heated in a region, it expands in all directions, and thus the velocity field points outward from that region.” If we have a vector field which represents a force, I interpret the divergence as representing the strengthof the field at whatever point it’s taken at.

What is the meaning of divergence in physics?

The wikipedia article on divergencedescribes one interpretation of divergence: “The velocity of the air at each point defines a vector field. While air is heated in a region, it expands in all directions, and thus the velocity field points outward from that region.”

What is the divergence of the acceleration field at a point?

The reason behind that is the fact that the term in question comes in by taking the divergence of the convective term of acceleration in the NS equation. The divergence of the acceleration field at a point, if non-zero, indicated the presence of a source or sink of acceleration.