Volume 3

A study of the pollution and natural purification of the Ohio river / Prepared by direction of the surgeon general.

  • United States. Public Health Service
Date:
1924-
Catalogue details

Licence: Public Domain Mark

Credit: A study of the pollution and natural purification of the Ohio river / Prepared by direction of the surgeon general. Source: Wellcome Collection.

    20/94 (page 12)
    in which— D=the required average concentration of dieblved oxygen ex- pressed in per cent of saturation, aiter time, t. B=the uniformly distributed initial iicaiesaie expressed in the same units. e=2;718. Tester k= rial Ee t—the elapsed time since concentration (B) existed. L=the linear depth of the column. athe diffusion coefficient, a constant for pure water, and a given gas (oxygen) at constant temperature. This equation applies primarily to quiescent water, but it has already been indicated that the effect of mixing is virtually to decrease the effective depth through which diffusion acts, so that the applica- tion to turbulent waters is permissible, the depth term being then indeterminate. | For the purposes of the present discussion it is desired to determine - the rate of solution of oxygen under any stated conditions. This rate is derivable from the equation of condition by differentiation with respect to a variable time. The actual operation need not be per- formed, for it is obvious that the result will be a complex expression containing the factor (1 ey 00) the initial saturation deficit, together with a complex time function. The rate of solution, therefore, is proportional, among other things, to the initial saturation deficit, and the proportionality factor is itself a time function—i. e., it varies with the time. At zero time—i. e., at the start— the rate is strictly proportional to the deficit. In any stream having sufficient turbulence to make reaeration a real factor in self-purification, there is sufficient mixing to bring about a fairly uniform condition throughout the vertical cross- section, so that at no time is there material vertical stratification. Such a condition may be regarded as being made up of short periods of quiescence followed by complete mixing, so that the final dissolved oxygen value at the end of any short period of quiescence becomes the initial, uniformly distributed value at the beginning of the next period. Since the rate of solution at the beginning of any period is strictly proportional to the deficit at that time, it follows that under the assumed conditions—and these are approximately the conditions met with—the rate of solution is proportional] to the existing satura- tion deficit. This is the law of the velocity of solution of solids in water, derived experimentally by Noyes and Whitney.” 14 Noyes, A. A., and Whitney, W. R., Zeit, f. physik. Chem., 23, 1897, p. 689.