‘Dubbel’s Handbook of Mechanical Engineering’ could be considered a bible for mechanical engineering students in Germany. Despite its 900 pages it is still called a pocket book (‘Dubbel – Taschenbuch für den Maschinenbau’) in German quite euphemistically. Since it was first published in 1914 by Heinrich Dubbel it has seen some 24 editions and roughly 920,000 copies sold. Since 1994 it is also available in an English translation from Springer Publishers.


Someone challenged me, if I could do the above figure from Dubbel’s book (“Wärmestrom in einer Kesselanlage”, heat flow in a boiler system). I did various copies and here are the two I like best:

In this version losses are shown in grey with a gradient to dark grey.

The other one sticks closer to the original with the hatch pattern on the arrows representing losses. I had to fill the nodes since the contrast between the colored arrows and the hatched arrows was just too harsh.

I confess I couldn’t do the labels with prime marks and subscript directly in e!Sankey. So I did them in Word, created tiny images and rotated them as work around. Later I found out that the whole image was probably originally intended to be displayed vertically, but rotated to the left only to save space in the book.

Anyway … a fun challenge. I hope you like the result. Let me know your opinion.

A rather simple Sankey diagram. It can be found on p. 195 of a study on Food Waste in Germany by ISWA, Stuttgart University comissioned by the Federal Ministry of Food and Agrriculture (BMEL). Flows are in million tons per year (averaged for the five-year period 2003 to 2007).


The yellow streams represent food delivered to individual housholds (“Haushalte”) as well as to commercial (large scale) users (“Grossverbraucher”) such as restaurants. The orange arrows show food waste (10 mo. tons p.a.). Note that individual households have a higher reject rate.

Just another quick Sankey diagram before the weekend. This beautifully crafted black&white diagram is from a scientific article ‘Exergy assessment of a cogeneration system with micro-turbine and absorption chiller’ by Martínez Reyes et.al. published in Proceedings of COBEM 2005 (18th International Congress of Mechanical Engineering).

This is for a cogeneration system with a 30 kWe gas micro-turbine and a 35 kWt absorption chiller. Flows are in kW with a scale of 1 cm = 100 kW in the original size. Good handling of the loop flow.

Following up to my two previous posts on Iran’s Energy Flows and Iran’s Energy production and consumption, here is the third Sankey diagram I could find in the report ‘Iran and World Energy Facts and Figures, 2012’ published by Ministry of Energy (MOE) of the Islamic Republic of Iran.

It is on greenhouse gas (GHG) emissions caused by the energy sector in the country


This is interesting, as the setup is reversed in comparison to the typical energy flow diagrams we all know. Here, the consuming sectors are on the left, alongside the energy generation sector itself. The middle section of the diagram sorts the arrows by energy carrier that causes the GHG emissions: natural gas contributes 53% (orange) and petroleum products 45.6% (blue). The third column shows a breakdown into the gases CO2, CH4 and N20.

No absolute values are given in the diagram, the magnitude of the flow amount to 100%. However the detailed values can be found in the accompanying tables in the report: carbon dioxide with 556,866,000 tons, methane 57,000 tons and nitrous oxide 11,600 tons (all values for 2012). Mind that these are absolute values, so in order to understand the impact on climate change one would have to multiply with the respective emission factors for methane and laughing gas and normalize them to kg CO2-equivalents.

Just a quick post before the weekend: Visualization of the water cycle in the Netherlands by Gunjan Singh. See initial sketch and some comments here.


Quantities are in billion kg (=million tons). “The weight of the arrows depict the proportions most of the time”, exceptions are in the thin arrows at the right which would otherwise be fine hair lines only and almost invisible.

South China Sea has recently garnered increased media attention due to China reclaiming land and building an airfield on Fiery Cross Reef. The territorial dispute regarding Spratly Islands has been simmering since the 1970ies when oil was discovered in the region. South China Sea is also “one of the busiest shipping lanes in the world” with “more than half of the world’s supertanker traffic, by tonnage, pass[ing] through the region’s waters every year” (Wikipedia).

The Department of Energy has two interesting maps on their beta website showing LNG and crude oil transport for 2011.

Transport of liquefied natual gas (LNG) in trillions of cubic feet in the South China Sea:

Transport of petroleum in millions of barrels per day in the South China Sea in 2011:


(both maps from eia.gov website)

These are ‘Sankey-inspired maps’ rather than exact Sankey diagrams. Arrow widths are not maintained where the shipping routes pass through narrow straits. Nevertheless, transport volumes are generally on a correct scale.

German Fraunhofer IKTS research institute features a Sankey diagram for a SOFC fuel cell system in this PowerPoint presentation (held 2012 at the Lucerne Fuel Cell Forum).

Flows are in J/s, the power output has been converted to Watt. Some volume flows and parameters are given as additional information on the flows.

After posting on Australian Metals Flows yesterday I realized I had never presented a Sankey diagram for energy flows in Australia.

Well, here it is. From the Government of Australia, Clean Energy Regulator, Renewable Energy Target program website comes this beauty (CC-BY license Commonwealth of Australia):


One can really say that Australia is mainly exporting its energy. Flows in Petajoule (PJ) for the year 2012/13. Older energy flow diagrams available in the Australian Atlas of Minerals, Resources and Processing Centres here.