As part of a feasibility study for a new pumped-storage hydropower scheme, you are tasked to prov…

As part of a feasibility study for a new pumped-storage hydropower scheme, you are tasked to provide some rough guidance on the operation of the system. The pumped-storage hydropower scheme consists of two reservoirs with different elevations and a pipe connecting the two reservoirs. The pipe has a constant diameter D and a length L. Along this pipe line a convertible pump-turbine is installed (i.e. the pumpturbine can work as pump or turbine depending upon flow direction). In a section close to reservoir 2, a redundancy pipe is designed as a backup option to discharge water from reservoir 1 to reservoir 2 when the pump-turbine machinery requires maintenance. Valves are installed to allow a diversion of flows into the maintenance pipe (Valve 1 & Valve 2). The figure below illustrates the pumped-storage hydropower scheme including the elevations of the reservoirs, the pipe length and the positioning of valves and the pump in side view and top view. You can assume that the total length of the pipe L is the same for maintenance and the main pipes. In your calculations, both friction losses and local losses need to be taken into account; the local loss coefficient for the bend is kbend = 0.2, for the T-junction kT-junction = 0.2 and for a fully open valve kValve = 0.2; for all other local losses make useful assumptions for the local loss coefficients.

Water level in Reservoir 1, H1 [mAHD]: 159
Water level in Reservoir 2, H2 [mAHD]: 45
Flow rate, Q [m3/s]: 24
Water volume in Reservoir 1, V1 [ML]: 9670
Pipe length, L [m]: 1370
Pipe diameter D1 [m]: 0.6
Pipe diameter D2 [m]: 0.65
Pipe diameter D3 [m]: 0.7
Pipe roughness ks1 [mm]: 0.0876395
Pipe roughness ks2 [mm]: 0.220998
Pipe roughness ks3 [mm]: 0.23625

The pipe dimensions you determined in previous part(pipe2 is the optimum pipe which has 0.65m diameter and 64.13m^3/s flow rate) are selected for the design of the whole pipe system (i.e. main and maintenance pipes). For a case with closed Valve 1 and open Valve 2, water is pumped from Reservoir 2 to Reservoir 1. For design purposes, assume constant water levels in the reservoirs H1 and H2. What is the required pump head to maintain the constant flow rate Qopt?