These laws assume that the pump / fan efficiency remains constant i . e . \ eta _ 1 = \ eta _ 2, which is rarely exactly true, but can be a good approximation when used over appropriate frequency or diameter ranges ( i . e ., a fan will not move anywhere near 1000 times as much air when spun at 1000 times its designed operating speed, but the air movement may be increased by 99 % when the operating speed is only doubled ).
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