In the tank illustrated below, there are two inlets and one outlet, with volumetric flowrates $F_1,F_2,$ and $F_3.$ Flowrate $F_2$ is twice that of $F_1.$ The total tank volume is $V($tank dimensions $=LWH),$ and the initial liquid volume in the tank is $V_i.$ The density in the inlet streams is ${}_1$ and ${}_2,$ and the density of the outlet stream is ${}_3.$ The density of inlet stream $2({}_2)$ is twice the value of inlet stream $1.$ What is the correct expression for the derivative of the height of fluid in the tank $($h$)$ as a function of time $($i$.$e$.,d\frac{h}{d}t)?$ You can assume that the tank is well$-$mixed, the temperature is constant, and the outlet density $({}_3)$ is equal to $(\frac{1}{3})({}_1+2{}_2).$

a$)\frac{dh}{dt}=(\frac{3}{LW})[F_1+4F_2-3F_3]$

e$)\frac{dh}{dt}=(\frac{4}{LW})[F_1+0\mathrm{.}50F_2-0\mathrm{.}75F_3]$

b$)\frac{dh}{dt}=(\frac{LW}{{}_1})[F_1+4F_2-F_3]$

f$)\frac{dh}{dt}=(LW)[1\mathrm{.}33F_1+0\mathrm{.}67F_2-F_3]$

c$)\frac{dh}{dt}=(\frac{3F_1-F_3}{LW})$

g$)\frac{dh}{dt}=(LW)[F_1+0\mathrm{.}50F_2-0\mathrm{.}75F_3]$

d$)$ None of the above

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