Consider the shown two$-$pipe reverse return hot water heating system. The longest equivalent length is $70$ m $.$ The heating load in kW for each radiator is shown on the figure.

Calculate the followings:

$($a$)$ Boiler heating capacity.

$($b$)$ Pump capacity, its model number and its pressure head if an iron and bronze pump is to be used.

$($c$)$ Diameter of all supply and return pipe sections if steel pipes are to be used. Assume that the hot water temperature drop across the radiators is $10C$ and the domestic hot water used is $300\frac{L}{?}$ day with temperature difference of $55C.$

$($d$)$ Diameter of supply and return pipe sections if copper tubes pipes are used instead of steel pipes.

$($e$)$ Repeat the solution if the hot water temperature drop across the radiators is $20C$ instead of $10C.$ Comment on the obtained results.