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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).
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 affinity laws (also known as the "Fan Laws" or "Pump Laws") for pumps/fans are used in hydraulics, hydronics and/or HVAC to express the relationship between variables involved in pump or fan performance (such as head, volumetric flow rate, shaft speed) and power. They apply to pumps, fans, and hydraulic turbines. In these rotary implements ...
The specific speed value for a turbine is the speed of a geometrically similar turbine which would produce unit power (one kilowatt) under unit head (one meter). [6] The specific speed of a turbine is given by the manufacturer (along with other ratings) and will always refer to the point of maximum efficiency.
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 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: