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Gill Function

Fish use the process of ventilation, moving the respitory medium over the respitory surface, to exchange gases through its gills. Fish breathe oxygen gas that is dissolved in the water, not the oxygen in the water itself. Most fish use the motion of swimming and moving their mouth and gill covers to ventilate thier gills. During this a current of water will flow in the mouth, pass through the slits of the pharynx, flows over the gills and lastly leaves the fishes body.
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Every gill arch has two rows of gill filaments. These are made up of flattened plates called lamellae. Capillaries in the lamellae have blood flowing which picks up oxygen from water. The capillaries are arranged so that countercurrent exchange can occur. Countercurrent exchange is the exchange of a substance or heat between two fluids flowing in opposite directions.
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The countercurrent flow of water and blood makes a partial pressure gradient where O2 diffuses from the water to blood along the entire capillarie length. This process is efficient since fish pick up about 80% of the dissolved O2 from the water it allows to enter it.
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Sources:

Biology textbook Eighth Edition
http://science.howstuffworks.com/question386.htm
http://www.daviddarling.info/encyclopedia/G/gill.html
http://www.cnr.vt.edu
http://image.tutorvista.com/content/respiration/gill-filaments.jpeg
http://www.cartage.org