Pump will be installed next to the turbine unit at the bottom of the hill. Centrifugal pump will be used for pumping the water from the sea to the upper reservoir during the period when excess electrical power is available. It is important to carefully consider the total volume of water that should be pumped to the upper reservoir. (Note: This is a complex task of matching the under supply and the size of the solar PV panels and performance of Hydro turbine and Pump). Hint: Sizing of the total area of solar PV panels will have to be done in multiple iterations.

Variety of centrifugal pumps are available commercially, but for the purpose of this assignment you are expected to design a centrifugal pump impeller. Assume that the water enters the centrifugal pump axially at the inlet with zero whirl. And the inlet and outlet flow velocities are equal.

The inlet diameter of the impeller is (245 + 0.1*B)mm (here B is the second last digit of your student number) and the slip factor is 1. The outer diameter of the impeller is twice the inlet diameter. Electric motor that drives the pump has motor electric efficiency (ratio of shaft power output to electrical power input) of (80 + 0.1*B)% (here B is the second last digit of your student number) over a wide range of rotational speed. Use rotational speed of 1500 rpm for the design of the pump impeller. Initially assume that the pump has manometric efficiency of (77 + 0.1*B) % (here B is the second last digit of your student number). Also assume that the pump has mechanical efficiency of (75 0.1*B) % (here B is the second last digit of your student number).

Design the centrifugal pump impeller that can utilise the peak surplus electrical power (over supply). For this develop and present the inlet and outlet velocity triangles for the centrifugal pump impeller that you design. Estimate the dimensions of the centrifugal pump impeller, i.e. inlet and outlet blade angles, diameters, outlet width and theoretical head for the peak electrical power supply and draw velocity triangle diagrams for inlet and outlet.

Now use the pump impeller that you have designed in the earlier point (i.e. use the impeller geometry such as inlet and outlet blade angles, diameters and the outlet flow area) to estimate the performance of this impeller under part load conditions (i.e. for every hour when there is excess electrical power available it will run). Assuming constant net pumping head equal to that you have used to design the impeller and variable rotational speed (i.e. impeller blade velocity can vary), estimate the achievable flow rate (m³/s and kg/s), inlet and outlet flow velocities (m/s), inlet and outlet blade velocities (m/s), angular velocity (rad/s) and rotational speed (rpm) of the impeller for the part load operation for every hour. Present all the hourly values (Part load) in a tabular format. And at least one sample calculation for every parameter that you determine.

Hint: First find the flow rate based on the part load power available assuming constant electrical motor efficiency, manometric efficiency and mechanical efficiency for the entire range of part load operation. Using this flow rate and impeller geometry that you have already fixed, estimate the flow velocity and the blade velocity. From the blade velocities estimate the rotational speed at which the pump should be operated at part loads for every hour.

Now estimate the total volume (in m³) of water that can be pumped to the upper reservoir during the day using the excess electrical power available (over supply). Compare this volume with the total volume of storage that you estimated in earlier step and if needed adjust the size (area) of the solar PV panels such that the pumping can handle 5% extra volume as compared to minimum storage requirement to compensate for losses such as leakage, evaporation and degradation of overall system performance over the life of the system.