PLEASE DO NOT USE ANY AI

A well$-$mixed lagoon is connected to the sea by a channel as shown in Figure.

The Lagoon and Channel have the following characteristics;

At $\backslash (\backslash$mathrm$\{$t$\}=0,100\backslash$mathrm$\{$~kg$\}\backslash )$ of a conservative dye is instantaneously released and distributed across the Lagoon. The exchanged discharge rate is $\backslash (10000\backslash$mathrm$\{$~m$\}^\{3\}/\backslash )$ day through the channel. The following measurements of the dye concentration in the Lagoon are made over the time.

a$)$ What is the mass transfer coefficient$(\backslash (\backslash$mathrm$\{$m$\}/\backslash )$ day$)$ and diffusion coefficient $($E$)(\backslash (\backslash$mathrm$\{$m$\}^\{2\}/\backslash )$ day$)$ for exchange between the Lagoon and the Sea?

b$)$ What mass loading of a nonconservative $($reactive$)$ pollutant with $\backslash (\backslash$mathrm$\{$k$\}=0\mathrm{.}01\backslash )$ day $\backslash (\{\}^\{-1\}\backslash )$ could be input to this system under steady$-$state conditions if the allowable concentration in the system were $\backslash (1\backslash$mathrm$\{$~g$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ).$ Express your result in $\backslash (\backslash$mathrm$\{$g$\}/\backslash )$ day. Note that both the conservative dye and reactive pollutant have negligible concentration in the sea, and neglect the residence time in the channel.