Saturated steam that is pure and free from air & other noncondensate at a temperature of $110C$ corresponding to a given pressure condenses in steam condenser comprising a single vertcal tube of outside diameter $2\mathrm{.}54cm$ on its outer surface. The surface temperature of the condenser tube is maintained at $90C.$ Calculate the design height of the tube of condenser if it is required to condense $20k\frac{g}{h}r$ of steam. Take thermo$-$physical properties as: ${}_l=974k\frac{g}{m^3}$;${}_v=0\mathrm{.}598k\frac{g}{m^3}$;$h_{fg}=2307\mathrm{.}3k\frac{J}{k}g$;$k_l=0\mathrm{.}6687\frac{W}{m}K$;$v_l=0\mathrm{.}364{10}^{-6}\frac{m^2}{s}.$