Design a downdraft gasifier with a required syngas output of $2\mathrm{.}5\frac{m^3}{\text{m}\text{i}\text{n}}($standard conditions$)$ using a cylindrical cross section. The A$/$F ratio should be used $70\%$ of the stoichiometric requirements and sawdust will be used as fuel. The superficial velocity should be $0\mathrm{.}03\frac{m}{s}.$ The

air density at standard conditions is $1\mathrm{.}2\frac{kg}{m^3}.$ About $25kg$ of biomass is used every hour.

Ultimate analysis of sawdust

Biomass Sawdust

$C\%49\mathrm{.}7$

$H\%6\mathrm{.}2$

$O\%42\mathrm{.}53$

$N\%0\mathrm{.}7$

$S\%0\mathrm{.}17$

Ash$\%0\mathrm{.}7$

a$)$ Determine the $\frac{A}{F}$ ratio and volume flow rate of air needed $(\frac{m^3}{\text{m}\text{i}\text{n}}).$

b$)$ Determine the minimum diameter of the gasifier reactor $(m).$