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These equations govern the power, efficiencies and other factors that contribute to the design of turbomachines. With the help of these equations the head developed by a pump and the head utilised by a turbine can be easily determined. As the name suggests these equations were formulated by Leonhard Euler in the eighteenth century. [1]
The runner of the small water turbine. A water turbine is a rotary machine that converts kinetic energy and potential energy of water into mechanical work. Water turbines were developed in the 19th century and were widely used for industrial power prior to electrical grids. Now, they are mostly used for electric power generation.
A wheel power divided by the initial jet power, is the turbine efficiency, η = 4u(V i − u)/V i 2. It is zero for u = 0 and for u = V i. As the equations indicate, when a real Pelton wheel is working close to maximum efficiency, the fluid flows off the wheel with very little residual velocity. [11]
The power coefficient [9] C P (= P/P wind) is the dimensionless ratio of the extractable power P to the kinetic power P wind available in the undistributed stream. [ citation needed ] It has a maximum value C P max = 16/27 = 0.593 (or 59.3%; however, coefficients of performance are usually expressed as a decimal, not a percentage).
The volume of water that enters an Archimedes screw turbine depends on the inlet water depth and the screw's rotation speed. To estimates the total flow rate passing through an Archimedes screw turbine for different rotation speeds (ω) and inlet water levels the following equation could be used:
A Bonneville Dam Kaplan turbine after 61 years of service. The Kaplan turbine is a propeller-type water turbine which has adjustable blades. It was developed in 1913 by Austrian professor Viktor Kaplan, [1] who combined automatically adjusted propeller blades with automatically adjusted wicket gates to achieve efficiency over a wide range of flow and water level.
The Francis turbine is a type of water turbine. It is an inward-flow reaction turbine that combines radial and axial flow concepts. Francis turbines are the most common water turbine in use today, and can achieve over 95% efficiency. [1] The process of arriving at the modern Francis runner design took from 1848 to approximately 1920. [1]
The water wall turbine is a water turbine designed to utilize hydrostatic pressure differences for low head hydropower generation. It supports bidirectional inflow operation using radial blades that rotate around a horizontal axis. The water wall turbine is suitable for energy extraction from tidal and freshwater currents.