T$-$W$3$

A hydropower plant is designed to generate electricity using water flowing from a height. The flow rate of water is $200$ cubic meters per second, and the height $($head$)$ from which the waterfalls is $50$ meters. Assuming the efficiency of the hydropower plant is $90\%,$ calculate the electrical power generated by the plant.

A solar thermal plant uses a field of parabolic trough collectors to generate electricity. The plant operates with a solar field that receives an average solar irradiance of $800\frac{W}{m^2}$ and has a total collector area of $10,000m^2.$ The plant's thermal efficiency is $50\%,$ and the power block efficiency $($conversion of thermal to electrical energy$)$ is $30\%.$ Calculate the electrical power output of the plant.

A solar hydrogen production system uses photovoltaic $($PV$)$ panels to generate electricity that powers an electrolyzer. The system has a PV array with a total area of $200m^2,$ and the average solar irradiance on the panels is $600\frac{W}{m^2}.$ The overall efficiency of the PV panels is $20\%,$ and the electrolyzer efficiency is $70\%.$ Calculate the amount of hydrogen produced per hour.