A lead pipe has $2$ cm inner diameter, $2\mathrm{.}8$ cm outer diameter, length of $5$ m$.$ Liquid water at $80$ oC flows through the pipe with velocity of $0\mathrm{.}5$ m$/$s$.$ Air is blown around the outside of the pipe at $25$oC$,$ with h$=150$ W$/$m$2$ K$.$ The system is at steady state.$$ Show calculations in SI units, using temperatures in Celsius, wherever possible.

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a$.$ Calculate h for the liquid water.

b$.$ Calculate the overall heat transfer coefficient.

c$.$ Calculate the total rate of heat transfer through the wall of the pipe.

d$.$ Calculate the actual temperature of the water leaving the pipe, and compare to the assumption in part $($a$).$