Press 1 to start. Each button plays one step on the machine.
Inside the turbine
still
One gallon of diesel's worth
A small hydro power plant, one step at a time. Press the steps in order and watch the machine do each one. The numbers come from one unit of a real plant at the foot of a dam in Utah[1], with sources at the bottom.
Inside the turbine
still
One gallon of diesel's worth
The big idea: a gallon of lake falling 270 feet makes only a tiny bit of electricity, so it takes about 18,100 gallons to make what one gallon of diesel makes. The lake does it with no fuel at all.
How the falling water's power is worked out: the 270 feet is the plant's net head[1], the fall the turbine actually gets once the water's losses on the way down are taken off. 300 cubic feet a second falling 270 feet carries 300 × 270 ÷ 8.8 = 9,205 horsepower[1][4], which is 6,867 kW[4]. The turbine is rated at 8,651 horsepower in the article's text[1], so it catches about 94% of it (95% with the 8,700 horsepower in the same article's spec box). One unit makes 6,300 kW (the plant's 12.6 MW over its 2 units[1]), so about 92% leaves as electricity. Each generator makes it at 12,470 volts, and a line carries it 3 miles at that voltage to a substation that steps it up to 46,000 volts for the long wires[1].
Where "about 18,100 gallons" comes from: 300 cubic feet a second is 2,244 gallons a second[6]. 6,300 kW from 2,244 gallons a second is one kWh for every 1,282 gallons. One gallon of diesel makes 14.1 kWh in Diesel to Light: its 500 kW generator burns 133.9 litres an hour[8], which is 35.4 gallons an hour[6], and 500 ÷ 35.4 = 14.1 kWh a gallon. Then 14.1 × 1,282 is about 18,100 gallons, which runs through the turbine in 8.1 seconds. The lake can let out about 102 billion gallons (314,000 acre-feet of active storage[1][7]), enough to do that about 5.6 million times.
Where "about 4,860 homes" comes from: 6,300 kW, less the 5% lost in the wires on the way[9], leaves 5,985 kW. An average US home used 10,791 kWh in 2022[10], which is 1.232 kW over the 8,760 hours of a year. 5,985 ÷ 1.232 is about 4,860 homes. That is while the unit runs at full power. The plant only runs on water already being let out of the dam for people downstream[3], and the 2009 article estimates the whole plant makes about 39,000 MWh a year[1]: less the same 5%, that covers about 3,400 average homes over a year. The Central Utah Water Conservancy District says the whole plant makes enough for 9,000 homes[3], counted its own way.
The turbine runs at 360 rpm, the speed given in a 2009 article about the plant, which went into commercial operation on July 1, 2008[1]; a 2007 review, written while the plant was still being built, expected 600 rpm and about 6 MW from each unit[2]. The 2009 article gives the plant's installed capacity as 12.6 MW in its text, while its spec box lists each turbine at 6.5 MW and 8,700 horsepower[1], and the water district's page says the plant can generate 13 MW[3]: this page uses 12.6 MW, so one unit makes 6,300 kW. The drawing is not the real dam, which is 300 feet high (299 in the article's spec box)[1]: it shows the parts a plant like it has[5], with one unit's numbers. In the real plant the step-up to 46,000 volts happens at the substation 3 miles away[1]; the drawing puts that transformer next to the powerhouse. How full the drawn lake looks, the three houses and how fast the turbine panel turns are this drawing's own choices. The panel turns 0.3 times a second and the real runner 6 times a second (360 rpm[1]), so the panel plays 20× slower. Steps 1 to 5 are not timed to real life. The flow between standing still and full output is not given by the source, so the chip says it in words.