Question

A pumped-storage hydroelectric plant generates high value electricity during peak demand times, by allowing water (density 1,000 kg/m3) to run through a pipe from an elevated reservoir through a bank of turbines and then into a lower level reservoir. It then uses low-cost, off-peak electricity to pump the water back up into the upper reservoir The water surface in the very large upper reservoir (A) is 600 m above datum whilst that in the very large lower reservoir (B) is 100 m above datum. When generating power, water discharges from A to B through the turbines at a total rate of 200 m'/s through a 3 m diameter concrete pipe (which has a roughness value of e 0.4 mm). The pipe is 1,000 m in length. Considering only major losses, what is the electrical power output from the turbine generator? Later, the water is then pumped back up to the upper reservoir at a rate of 100m'/s through a 1,000 m long, 2 m diameter concrete pipe of roughness 0.4 mm. Considering only major losses what is the required electrical power into the pump system? Notes: The efficiency of the turbine generators in converting fluid power into electricity is 80% whilst the efficiency of the pump system in converting electricity into fluid power is 78%. A Moody chart for pipe friction is given at the end of the exam paper. Take the kinematic viscosity of water to be v-10" m?/s atm Total pipe length 1,000 m Pumps oir turbines r_ *tm 600 100m ELEVATION Pump Pipe diameter-2m system Pipe diameter -3m Turbines PLAN

Answer 1

Goom -Area (A) 1:02 Vec (Y - 1076 From mooty chart d30oo Re 8.488시07

2 9 Iolentp634.oq mk power Achnd power developed Cee): or 0.8% 634.08 507-275 MW 60/ att Pr

enath Pat Goon 0om pump -Area 먹 pipe l'a'.. .rd.2 discharge (A) 00 ros} sea CAC 3-146 bom가 A 3 1416 eynoldz . Number(k) 2 10 "2 29 足、31:8309x3 To (06 From Moly chart 29 d 4282

0 - 861.49 m too+ hp 361-49 600 Lam 100ox 100x181 x 861.49 CtUel power requîre 84S.12 alt part- 1083.489 Mkl