Divergence of a Vector

The divergence of a vector field u, written div u, is given in Cartesian coordinates by... 

Alternatively, one may attempt to estimate the integral over the derivative of the displacement field that entered in the expression for the coupling constant g= pc Jy cPr du/2. Since da is the divergence of a vector, the integral is reduced to that over a surface within the droplet s boundary ... 

It is now necessary to derive analogous relations for the divergence of a vector, viz. V - A. The calculation can be carried out in at least two ways. The direct analytic approach is long, but does not involve any methods other than those of vector algebra. Otherwise, it is necessary to develop the diver-geoce (Gauss s) theorem, after which the desired result is easily obtained (see Appendix VI). In either case it is given by... 

The divergence of a vector v with components vt,v2. .., v is the scalar number noted either dive or, with the nabla notation V t, defined as ... 

In cylindrical coordinates write a general expression for the the divergence of a vector V = uez + ver -(- we. Take care with inclusion and evaluation of unit vectors where appropriate. 

Another type of derivative, the divergence of a vector field, is defined in Section 1.3.5. 

When the gradient operator is dotted with a vector or a tensor, the divergence of the vector or tensor is obtained. The divergence of a vector produces a scalar... 

When contraction is performed once (summation over repeated indices), the divergence is obtained instead of the gradient. The divergence of a vector field v is a scalar... 

Alternatively we can say that the divergence of a vector v is the number of vector lines originating in an infinitely small volume or, which is the same thing, the flux of the vector held through the surface of this volume. 

We note that the divergence of a tensor is a vector, whereas the divergence of a vector is a scalar... 

C Trondheim Bubble Column Model Divergence of a vector... 

According to this equation the divergence of a vector is given by the scalar product of the vector operator V and the vector. The other operator defining a vector derivative is curl. It is defined as follows ... 

EXAMPLE 7.28 (a) Write the expression for the divergence of a vector function F expressed in terms of spherical polar coordinates. 

As with the gradient of a scalar, the divergence of a vector is invariant under a transformation from one set of rectangular coordinates to another. 

Hence, temperature profiles in pure isotropic solids, the scalar velocity potential for ideal fluid flow, and dynamic pressure profiles for flow through porous media are all based on the solution of Laplace s equation. Whenever the divergence of a vector vanishes and the vector is expressed as the gradient of a scalar, Laplace s equation is required to calculate the scalar profile. 

The divergence of a vector field u(x, y,z) is a scalar field which for each point of the vector field gives the inflow or outflow per unit volume in the immediate vicinity of this point ... 

In defining the divergence of a vector field A(r, t), we have transformed an integration over sxuface area into an integration over volume, as shown... 

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