A cylindrical tank with an internal diameter of $1$ m contains $1500$ kg of spherical particles of uniform diameter $($d$,=4$ mm$)$ and density $($Pp $=2500$ kg$/$m$^3).$Water $($p $=1000$ kg$/$m$^3,$ H $=0\mathrm{.}001$ Pa$.$s$)$ flows upward through the particle bed at a rate of $0\mathrm{.}1$ m$.$a$)$ Estimate the minimum fluidization velocity $($Vm$)$b$)$ Estimate the height of the resulting bed $($m$)$c$)$ You have noticed that the actual height of the bed is higher than that estimated in b$).$You suspect that the particle diameter and$/$or density is incorrect. $$So you measure the pressure drop across the entire bed using a U$-$tube mercury $($density $=13\mathrm{.}6)$ manometer when the bed is fluidized and fixed. $$The resulting gauge readings when the fluid flow is $0\mathrm{.}1$ and $0\mathrm{.}0005$ m$$ are $84$ and $0\mathrm{.}41$ mm respectively. $$What is the estimated density and diameter of the particles from the pressure drop measurements?