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In statistics, efficiency is a measure of quality of an estimator, of an experimental design, [1] or of a hypothesis testing procedure. [2] Essentially, a more efficient estimator needs fewer input data or observations than a less efficient one to achieve the Cramér–Rao bound .
Rolls-Royce Avon early jet engine showing 1 of 2 sets of 3 valves at the top and 1 of 2 valves at the bottom which release some air from the compressor, pressure ratio 7.45:1, for starting and low speed running. Also visible at the front is the row of bearings for the variable inlet guide vanes.
The GGS model predicts that peak efficiency is achieved when the flow through the turbine is approximately 61% of the total flow which is very similar to the Betz result of 2 ⁄ 3 for a flow resulting in peak efficiency, but the GGS predicted that the peak efficiency itself is much smaller: 30.1%.
Mathematically, it is represented as =, [1] where is the cycle efficiency and is the propulsive efficiency. The cycle efficiency is expressed as the percentage of the heat energy in the fuel that is converted to mechanical energy in the engine, and the propulsive efficiency is expressed as the proportion of the mechanical energy actually used ...
Because kinetic energy equals mv 2 /2, this change in velocity imparts a greater increase in kinetic energy at a high velocity than it would at a low velocity. For example, considering a 2 kg rocket: at 1 m/s, the rocket starts with 1 2 = 1 J of kinetic energy. Adding 1 m/s increases the kinetic energy to 2 2 = 4 J, for a gain of 3 J;
Efficiency is often measured as the ratio of useful output to total input, which can be expressed with the mathematical formula r=P/C, where P is the amount of useful output ("product") produced per the amount C ("cost") of resources consumed.
A rocket's required mass ratio as a function of effective exhaust velocity ratio. The classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself using thrust by expelling part of its mass with high velocity and can thereby move due to the ...
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] These equations can be derived from the moment of momentum equation when applied for a pump or a turbine.