Page 256 - Modelling in Transport Phenomena A Conceptual Approach
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236 CHAPTER 7. UNSTEADY-STATE MACROSCOPIC BALANCES
the sediment layer gains phosphorous by settling and loses phosphorous by recycle
and burial.
Settling Recycle
SEDIMENT LAYER
Figure 7.6 Schematic diagram for Problem 7.25
Show that the governing equations for the phosphorous concentrations in the
lake, PI, and in the sediment layer, P2, are given as
where
min = loading rate = 2000 kg/year
e,, = outflow volumetric flow rate = 80 x 106m3/year
us = settling velocity of phosphorous = 40 m/year
A2 = surface area of the sediment layer = 4.8 x lo6 m2
(kc),. = recycle mass transfer coefficient = 2.5 x loF2 m/year
(kc)b = burial mass transfer coefficient = 1 x m/year
VI = volume of the lake = 53 x 106 rn3
& = volume of the sediment layer = 4.8 x lo5 m3
and determine the variation of PI in mg/m3 as a function of time if the initial
concentrations are given as PI = 60 mg/ m3 and P2 = 500,000 mg/ m3.
(Answer: PI = 22.9 - 165.4e-5.311t + 202.5e-0.081t)
