Here is a collection of definitions for Sankey diagrams:

“Sankey diagrams are a specific type of flow diagram, in which the width of the arrows is shown proportionally to the flow quantity. They are typically used to visualize energy or material transfers between processes.”
(source: Wikipedia, article ‘Sankey diagram’)

“Sankey diagrams feature directed arrows that have a width proportional to the flow quantity visualized: if a flow is twice as wide it represents double the quantity. Flows in the diagram can show e.g. energy, materials, water or costs.”
(source: ifu.com / What is a Sankey diagram?)

“A Sankey diagram is a directional flow chart where the width of the streams is proportional to the quantity of flow, and where the flows can be combined, split and traced through a series of events or stages.”
(source: defunct Chemical Engineering Blog)

“Sankey Diagrams are attention grabbing flowcharts that help in quick visualisation of the distribution and losses of material and energy in a process. The width of the lines used in drawing the flowchart is proportional to the quantum of material or energy.”
(source: http://www.sankeydiagrams.com)

And some more in languages other than English:

“SANKEY, DIAGRAMA DE. SANKEY’S DIAGRAM. Representación gráfica del consumo de energía en un ecosistema natural o artificial, a manera de franjas que representan, según su anchura, la cantidad de energía correspondiente, según su dirección, al destino final de esa energía.”
(source: Fausto O. Sarmiento: Diccionario de Ecología)

“Un diagrama-Sankey es la representación gráfica de los caudales (cantidad por tiempo) de p.e. energía, material o dinero a través de un sistema. Normalmente los caudales son representados por flechas, en los cuales el ancho es proporcional al tamaño del caudal mostrado. Mejor que números o descripciones el diagrama le explica cuales caudales benefician y cuales constituyen residuos o emisiones.”
(source: STENUM Spanish webpage)

“Un diagrama de Sankey es un diagrama en que la anchuras de las flechas son proporcional a las cantidades de flujos. Sankey diagramas son una manera útil de visualizar los flujos de materiales, energía o costes.”
(source: duh? don’t remember where I took that from)

“Ширина стрел обозначает количество энергии. Вход энергии (топливо, электричество) обычно вливается в процесс слева, а полезный выход энергии (обогрев, освещение, механическая мощность, химическая энергия) и потери (тепло, шум и т.д.) показываются выходящими справа.”
(source: TACIS dissemination project webpage)

“Een Sankey-diagram is een diagram van het type stroomdiagram. Het wordt met name gebruikt in de procestechnologie en voor het weergeven van energiestromen. Typisch voor een dergelijk diagram is dat de breedte van de pijl, dat de energie- of materiaalstroom aangeeft, proportioneel is met de grootte van de stroming. Een Sankey-diagram is een prima middel om de energie- of materiaalstromen te visualiseren en daarmee het spaarpotentiaal te bepalen of de inefficiënte positie(s) in het proces vast te stellen.” (source: Wikipedia in Dutch)

“Le diagramme de Sankey (ou diagramme des flux d’énergie) représente, par des flèches de largeur correspondant à leur amplitude, les flux d’énergie traversant une frontière donnée.” (source: Morel/Gnansounou: Énergétique du Bâtiment, EPFL, p. 85)

“Il diagramma Sankey è uno specifico diagramma di flusso, nel quale viene mostrata la larghezza delle frecce in proporzione alla quantità di flusso. Generalmente sono utilizzati per visualizzare le quantità di energia o materiali o costi tra i processi.” (steppen-wolf.eu)

Sankey Diagram in Japanese: サンキーダイアグラム
(※サンキーダイアグラムとは、特定の種類のフローチャートのこと)

Sankey Diagram in Chinese: 桑基图 (see here)

Sankey Diagram in Korean: 생키 다이어그램

Sankey Diagram in Arabic: مخطط سانكي

Sankey Diagram in Russian: диаграммы Сэнкей

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