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Water (density (ρ)=1000 kg/m3, kinematic viscosity (v)=1.30×10−6 m2/sec ) flows downwards from Tank 1 to Tank 2 through a new 4-in schedule 40 steel pipe line (ε= 4.6×10−5 m). Tank 2 is exposed to the atmospheric pressure. The desired flow rate is 0.015 m3/s when the difference in fluid level elevation (Δz) is 75 m, as shown below. Note: Inner diameter and the flow area of the 4-in schedule 40 steel pipe are 0.1023 m and 8.213×10−3 m2, respectively. Tanks are sufficiently large. (20 pts) (a) Write the energy equation for this problem, list all the reasonable assumptions, and eliminate unnecessary terms. Make sure to select the most appropriate end points so you end up with the simplest equation possible. (b) Determine the head loss due to the piping system in [m]. (c) Determine the required gage pressure in the tank (Ptank, gage ) in [kPa] in order to have the desired flow rate for the given conditions.