$(20$ pts$.)$ It is known that a pump $(87\%$ efficient$)$ requires $35$ kW of power to supply water $($at a flow rate of $0\mathrm{.}02\frac{m^3}{s})$ to an open reservoir located on the roof of a high rise building from the water main in the basement $(90$ kPa gage$)$ after passing through a filtration system shown in the diagram. What is the loss coefficient through the filter system? Assume all pipes are galvanized iron $10$ cm in diameter.