Reaeration of a River

Consider a river that has, at a point we refer to as 2 = 0, an oxygen content C , which is below the saturation solubility of oxygen. This means thaf oxygen concenfrafion will steadily increase in the direction of flow due to upfake from fhe afmosphere and will ultimately, as 2 — o°, attain the equilibrium solubility of oxygen, C. Application of Equation 2.2 yields, in the first instance 

If we assume the liquid-phase resistance to be controlling, will be of the form 

A second question concerns the definition of the interfacial area A. It is relatively rare to find that this quantity coincides with the area of a flat surface. More commonly, the river has surface ripples and waves of an unknown interfacial area. The value becomes particularly uncertain in the case of rapids in which air is entrained into the water phase in tire form of bubbles or foam, again, of an unknown interfacial area. It has become common practice in these cases to lump this unknown factor into the mass transfer coefficient in the form of an average specific area a with units of m2 interfacial area/m river volume. We write 

Dividing by A Az, and letting Az go to zero, tire difference quotient AC/ Az is converted into a derivative and we obtain 

Equivalently, since Q/A equals the river flow velocity v, we can write 

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Two environmental models (a) evaporation from a basin (b) reaeration of a river. 

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