a) Write the mathematical expression for one-dimensional flux for advection and diffusion. Do not derive it. Just write it. (b) Derive the following mass balance equation on dissolved oxygen (c) for a one-dimensional water system (e.g., a river or a long bioreactor). ??/?? = −?(subscript x)*??/?? − ? ??(subscript x)/?? + D ?^2?/??^2 − ?(subscript d)? + ?(subscript L) ?(?(subscript s) − ?) Start your answer by sketching one dimensional model domain and defining a control volume. (c) Rewrite the mass balance equation if the rate of the DO consumption is the first order reaction with respect to c as well as L. You can replace kd by kD in the new kinetic expression. Do not derive the equation. Just write your answer. (d) Write the assumptions that we made to derive the Streeter-Phelps equation. Apply the assumptions to the equation given in Part (b) and simplify the equation.
a) Write the mathematical expression for one-dimensional flux for advection and diffusion. Do not derive it.
Just write it.
(b) Derive the following mass balance equation on dissolved oxygen (c) for a one-dimensional water system (e.g., a
river or a long bioreactor).
??/?? = −?(subscript x)*??/?? − ? ??(subscript x)/?? + D ?^2?/??^2 − ?(subscript d)? + ?(subscript L) ?(?(subscript s) − ?)
Start your answer by sketching one dimensional model domain and defining a control volume.
(c) Rewrite the mass balance equation if the rate of the DO consumption is the first order reaction with respect to c as
well as L. You can replace kd by kD in the new kinetic expression. Do not derive the equation. Just write your answer.
(d) Write the assumptions that we made to derive the Streeter-Phelps equation. Apply the assumptions to the equation
given in Part (b) and simplify the equation.
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