A 2000 MW dam has maximum head of 200m. What is the rate of falling water on the turbines? (Neglect losses)

Correct option is C

Introduction
· Hydroelectric power is a form of renewable energy that harnesses the kinetic and potential energy of flowing water to generate electricity through specialized mechanical turbines.
· The power generation potential of any hydroelectric dam is primarily determined by the hydraulic head, which is the vertical distance the water falls, and the volumetric flow rate, which defines the volume of water passing through the system per unit of time.
· Large-scale dams are critical components of the global energy mix, acting as a source of baseline power and providing rapid-response solutions for peak-load management in modern electrical grids.
· The sustainability and efficiency of these projects depend on maintaining a precise balance between the water stored in the reservoir and the discharge rates required to meet domestic and industrial energy demands.

Information Booster
· The rate of falling water, technically referred to as the discharge or volumetric flow rate (Q), is calculated using the fundamental hydroelectric power equation: $$P = \rho \cdot g \cdot h \cdot Q$$.
· In this specific scenario from the 2017 paper, the power capacity (P) is given as $$2000 \text{ MW}$$​ (which converts to $$2 \times 10^9 \text{ Watts}$$​ and the hydraulic head (h) is provided as $$200 \text{ meters}$$.
· To find the flow rate, the total power is divided by the product of the fluid density, the acceleration due to gravity, and the height; using standard values for water density ($$1000 \text{ kg/m}^3) and gravity (9.8 \text{ m/s}^2$$​), the calculation $$2 \times 10^9 / (1000 \times 9.8 \times 200)$$​ results in approximately 1020.41 m³/s.
· This value signifies that over one thousand cubic meters of water must strike the turbine blades every single second to maintain a $$2000 \text{ MW}$$​ output under ideal conditions.
· Neglecting losses implies a theoretical efficiency ($\eta$) of 100%, though real-world hydroelectric plants usually operate at 85–90% efficiency due to friction in penstocks and mechanical heat generated in the turbines.
· The relationship between these variables is linear, meaning that if the head were doubled to 400m, the required flow rate would be halved to achieve the same power output, illustrating why high-head dams are geographically efficient.