In the tank illustrated below, there are two inlets and one outlet, with volumetric flowrates $F_1,F_2,$ and

$F_3.$ The outlet flowrate $(F_3)$ is equal to $(h{)}^{0\mathrm{.}5},$ where $$ is a constant and $h$ is the fluid height. The total

tank volume is tank diameter $=D,$ 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 ${}_3($and these values are constant$).$ The

density of inlet stream $2({}_2)$ is twice the value of inlet stream $1.$ What is the correct expression for the

height of fluid in the tank $($h$)$ at steady$-$state? You can assume that the tank is well$-$mixed and that the

temperature is constant. $($circle answer$)$

a$)h=[\frac{(F_1+2F_2){}_1}{{}_3}{]}^2$

d$)h=[\frac{4(F_1+F_2-F_3){}_1}{D^2}{]}^2$

b$)h=[\frac{2(F_1+F_2){}_1}{({}_1+{}_2)}{]}^2$

e$)h=[\frac{4(F_1+F_2-F_3)}{D^2}\frac{({}_1+{}_2)}{{}_3}{]}^2$

c$)h=[\frac{(F_1+2F_2){}_2}{D^2}{]}^2$

f$)h=[\frac{2(F_1+F_2-F_3){}_3}{({}_1+{}_2)}{]}^2$

g$)$ None of the above