The performance of a fan in terms of pressure, volume flow and power absorbed depends on a number of factors, the most obvious of which are:-
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The design and type of fan,
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The point of operation on the volume flow/pressure characteristic,
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The size of fan,
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The speed of rotation of impeller,
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The condition of the air or gas passing through the fan.
It is customary for a manufacturer to make a range of fans of varying size to single design, thus producing a series of geometrically similar fans (homologous series). It is convenient to be able to compute the performance of each fan from the minimum test data. The pressure/volume flow relationship it is not generally capable of being expressed as a simple mathematical function. However, by considering any single point of operation on the characteristic curve (for example, the point at which the fan efficiency is a maximum), it is possible to drive some simple relationships, generally known as the fan laws.
For all fan laws: hTa = hTb and (point of rating)a = (point of rating)b