Fundamentals of Turbines in Fluid Mechanics

Turbines convert the kinetic and potential energy of fluids into mechanical work through rotational motion of rotor blades, playing a crucial role in power generation and fluid machinery. They are mainly classified as impulse or reaction turbines. Impulse turbines use high-velocity fluid jets striking the blades, causing motion with negligible pressure change. Reaction turbines rely on pressure drops and fluid expansion through the blades, producing rotation by reactive and impulse forces. The power output of a turbine is calculated by $P = \rho Q g H \eta$, where $\rho$ is fluid density, $Q$ is flow rate, $g$ is gravitational acceleration, is head or height, and is efficiency. Blade design and angle are vital for maximizing energy transfer, determined from velocity triangles and flow dynamics. Common turbine types include Pelton (impulse, high head, low flow), Francis (reaction, medium head and flow), and Kaplan (reaction, low head, high flow). Turbines enable renewable hydroelectric energy and are applied more broadly in jet engines and propulsion systems, linking fluid flow to mechanical energy output. Optimizing turbine design increases efficiency and reduces environmental impact in energy conversion.