$1\mathrm{.}1gm$ of a powder of particle density $1800k\frac{g}{m^3}$ are charged into the cell of an apparatus for measurement of particle size and specific surface area by permeability. The cylindrical cell has a diameter of $1\mathrm{.}14cm$ and the powder forms a bed of depth $1cm.$ Dry air of density $1\mathrm{.}2k\frac{g}{m^3}$ and viscosity $18\mathrm{.}4{10}^{-6}$ Pas flows at a rate of $36c\frac{m^3}{m}in$ through the powder. The measured variation in pressure difference across the bed with changing air flow rate is given in Table Q$2$ below:

Table Q$1$

$\backslash$table$[[$Air velocity $(c\frac{m}{s}),0\mathrm{.}3266,0\mathrm{.}4899,0\mathrm{.}6531,0\mathrm{.}8164,0\mathrm{.}9797],[\backslash$table$[[$Pressure difference across$],[$the bed $(Pa)$