An air pump is a device for pushing air. Examples include a bicycle pump, pumps that are used to aerate an aquarium or a pond via an airstone; a gas compressor used to power a pneumatic tool, air horn or pipe organ; a bellows used to encourage a fire; a vacuum cleaner and a vacuum pump. All air pumps contain a part that moves (vane, piston, impeller, diaphragm etc.) which drives the flow of air. When the air gets moved, an area of low pressure gets created which fills up with more air. 
Pumps and compressors use very similar mechanisms, and basically perform the same action, but in different fluid regimes. At some point there is a crossover point in terminology, but here are some stereotypes:
• Compressors operate on compressible fluids, typically gases. Pumps operate on fluids, typically liquids, approximated as in-compressible.
• Compressors are intended to develop a very high pressure rise against a closed system; pumps are designed to develop relatively little pressure against a free-flowing system with minimal back-pressure.
• Pumps are often used in continuous-flow operation, while many lower-end compressors must have intermittent duty cycles.
• Compressors usually have a feedback sensor to shut off when they reach a desired pressure; pumps have a fixed design and operate freely across their performance curve as conditions change
In 1649, Otto von Guericke invented the spool vacuum air pump. This pump was called air pump in 19th century lexicons. Additionally, Guericke's air pump decreased any potential leaks between the piston and the cylinder by utilizing washers made from leather.
In 1705, an English scientist by the name of Francis Hauksbee, developed a style of a double-barrelled air pump. Hauksbee's double-barrelled air pump was used primarily for scientific research, and had the ability to create a vacuum.
In the case of air pumps, diaphragm pumps are considered to be a type of pump that utilizes positive displacement. A simple diaphragm pump contains a chamber that acts like a springy diaphragm. When compressed, the air within the diaphragm gets expelled. When the diaphragm is decompressed, the chamber refills with air. A simple example for a diaphragm pump is a foot pump that requires the user to constantly step up and down on the pump to inflate something.
A simple reciprocating pump is commonly made up of a cylinder with an inlet, an outlet, and a piston within. The inlet and the outlet are used to direct the flow of air, while the piston is used to generate the flow of air. When the piston is pulled up, air gets sucked into the pump through the inlet. The pump chamber depressurizes as it fills with air. When the piston is forced down, the air becomes compressed and closes the inlet. Then the air flows out from the outlet.
- "Pump Theory - Principles". powerequipment.honda.com. Retrieved 2018-11-26.
- Brockhaus 1809 Luftpumpe
- "The History of Pumps: Through the Years". Pumps & Systems. 2011-12-22. Retrieved 2018-11-26.
- George Wilson (Jan 15, 1849), "On the Early History of the Air-pump in England", Proceedings of the Royal Society of Edinburgh
- Brundtland, Terje. "Francis Hauksbee and his air pump". http://rsnr.royalsocietypublishing.org. Retrieved 26 November 2018. External link in
- Hansen, Tom. "How Does a Diaphragm Pump Work?". www.dultmeier.com. Retrieved 19 November 2018.
- "Understanding How Reciprocating Pumps Work | Designs & Types of Reciprocating Pumps". www.powerzone.com. Retrieved 19 November 2018.
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