An economiser of a modern steam generator is to be designed which receives feed water at its inlet header from the high pressure feed heater at the rate of $650$ kg$/$s and at $150$ bar and $180$C$.$ The hot flue gases pass over the economiser and as a result of heating the feed water becomes saturated liquid at that pressure and leaves the outlet header to flow into the drum. The mass flow rate of flue gases passing over the economiser coils is $1350$ kg$/$s$.$ The flue gases leave the economiser at $450$C$.$ In order to restrict the erosion rate by fly ash, its velocity is restricted to $12$ m$/$s while the optimum velocity of water leaving the economiser coil is $1\mathrm{.}2$ m$/$s$.$ The tubes are of $70$ mm OD and $60$ mm ID$.$ The overall heat transfer coefficient may be taken as $70$ W$/$mK$.$ The specific heat of the gases may be taken as $1\mathrm{.}2$ kJ$/$kgK$.$ The vertical pitch of the coil is $80$ mm and the clearance on the two sides of the duct of width $4\mathrm{.}8$ m is $5$ mm$.$ Calculate the following:

$($i$)$ The number of coils needed in the economiser and the length of one coil

$($ii$)$ The vertical height of economiser coils.