Please answer the following questions and show solutions completely. Thanks!

$1.)$ A steam boiler produces $31$ English ton of steam from $1$ a$.$m to $7$ p$.$m

continuous operation per day. The steam enters the turbine at $31$ bar and $310$

degrees Celsius. The pump feeds the boiler with water that has a temperature of

$91$ degrees Celsius. If the burner in the boiler uses bunker diesel fuel with $37\mathrm{.}1$

degrees API, calculate the volume of diesel that must be burned in gallons$/$minute

if the efficiency of the boiler is $91\mathrm{.}7\%$ The temperature of the Diesel is supplied to

the boiler at $31\mathrm{.}7$ degrees Celsius.

$2.)$ Four boilers operating steadily on $400$ metric tons of high$-$grade bituminous

coal contained in a bunker. Boiler $1$ produces $2\mathrm{.}4$ metric tons$/$hr of steam at $42$

mpa and $420$ degrees Celsius and feedwater temperature of $94$ degrees Celsius

with an efficiency of $842\%.$ Boiler $2$ produces $\frac{3}{4}$ of the Boiler $1$ steaming

capacity at saturated steam at $2\mathrm{.}4$mpa and the feedwater temperature of $92$

degrees Celsius with $82\%$ efficiency. The third boiler produces $\frac{2}{3}$ steaming

capacity of Boiler $2$ at $250$ degrees Celsius saturated with $82\mathrm{.}5\%$ efficiency. Boiler

$4$ produces $\frac{5}{4}$ of Boiler $3$ steaming capacity with factor of evaporation of $1\mathrm{.}3$ and

boiler efficiency of $95\mathrm{.}4\%.$ Compute the number of days the coal in the bunker

runs the four boilers if the coal has a heating value of $44,250$ KJ$/$kg$.$ Assume

$20-$bour operation per day.

$3.)$ The following coal has the following ultimate dry analysis by weight. $C=75\%,$

$H=15\%,O=0\mathrm{.}5\%,N=0\mathrm{.}5\%,S=8\%$ and Ash $=1\mathrm{.}5\%.$ The steaming capacity of

the boiler using this coal is $75$ short ton covering a period of $1$ a$.$m to $7$ p$.$m$.$

Calculate the volume of air needed in $f{t}^{{?}^{{?}^{?}}}\frac{3}{sec}$ at $100\mathrm{.}2$kpa and $32C$ with a excess

air of $32\%$ The boiler efficiency is $92\%$ The stream leaves the boiler at $82$ bar and

$530$ degrees Celsius while the feedwater enters the boiler at $92$ degrees Celsius.