Determine the minimum work per unit of heat transfer from the source reservoir that is required to drive a heat pump with thermal energy reservoirs at 460 K and 540 K. The minimum work per unit of heat transfer from the source reservoir that is required to drive a heat pump is:

Water flows at the rate of 200 i/s upwards through a tapered vertical pipe. the diameter at marks(3) clo5) the bottom is 240 mm and at the top 200 mm and the length is 5m. the pressure at the bottom is 8 bar, and the pressure at the topside is 7.3 bar. determine the head loss through the pipe. express it as a function of exit velocity head.