Quantification of Advective Transport

The bulk motion of fluid is common throughout the environment this advective motion is described mathematically by the direction and the magnitude of its velocity. If a chemical is introduced into flowing air or water, the chemical is transported at the same velocity as the fluid. While spreading due to Fickian transport may occur at the same time, as described in the next section, the center of mass of the chemical moves by advection at the average fluid velocity. 

The rate at which a chemical is transported per unit area is often expressed in terms of flux density. Flux density is the mass of chemical transported across an imaginary surface of unit area per unit of time (Fig. 1-5) and is often given the symbol J. Note that the imaginary surface may be one of the boundaries of a control volume. Flux density due to advection is equal to the product of a chemical s concentration in the fluid and the velocity of the air or water, 

The velocities of air and water frequently vary with time, as is evident to anyone who has stood in a gusty wind or swum in a turbulent river. Consequently, any estimate of flux density due to advection by a turbulent fluid flow must involve a time period over which flow variations and corresponding fluctuations of chemical concentration are averaged. Often the fluctuations in time are faster than the instruments for determining velocity and chemical concentration can follow, and the instruments inherently provide averaged values. In other situations, instruments can easily detect and measure the 

FIGURE 1-5 Advective transport of a smoke plume as shown in Fig. 1-4. The imaginary square frame is oriented perpendicular ( L) to fluid flow and for convenience has an area of one (in whatever units we prefer—m2, ft2, etc.). The flux density of smoke, J, is the product of the wind velocity V and the concentration of smoke in the air, C. 

If the salt concentration in a river is 20 mg/liter and the average river velocity is 100 cm/sec, what is the average flux density J of salt in the downstream direction  

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