Water is transported to a residential area at 1.5 m^3/s using a 1500 m long concrete pipe with diameter 70 cm and surface roughness of 3 mm. to save energy, the city proposes to coat the inside of the pipe with a 2 cm thick liner with surface roughness of 0.04 mm. doing so will reduce roughness but also reduce pipe cross-sectional area.
1. will the gains be worthwhile?
2. calculate the relative change (percent increase/decrease) in needed pumping power if the lining is installed.

Liquid flows at steady state at a rate of 2 lb/'s through a pump, which operates to raise the elevation of the liquid 100 ft from control volume inlet to exit. the liquid specific enthalpy at the inlet is 40.09 btu/lb and at the exit is 40.94 btub. the pump requires 3 btu/s of power to operate. if kinetic energy effects are negligible and gravitational acceleration is 32.174 tt/s, the heat transfer rate associated with this steady state process is most closely 1)-2,02 btu/s from the liquid to the surroundings 2)-3.98 btu/s from the surroundings to the liquid. 3)-4.96 btu/s from the surroundings to the liquid. 4)-1.04 btu/s from the liquid to the surroundings.