• Pixel-art sticker of Hydrel, personifying Hydroelectric Power, with the caption “Fall Farther, Make More Power.”

IndexHeat & EntropySticker

Hydrel

Hydroelectric Power Physics

\[P = \eta\,\rho\,g\,Q\,h\]
Regular price $4.99 USD
Regular price Sale price $4.99 USD
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Meet Hydrel, a concrete dam who turns falling water into electricity. Power depends on flow, drop height and efficiency: a 50 m drop with 20 m³/s at 90 percent efficiency gives about 8.8 MW, enough for several thousand homes. Three Gorges reaches about 22 GW. Pixel-art kiss-cut sticker in 2, 3, 4 and 6 inches; equation, symbols and sources in the physics panel below.

Size
Surface

Flat $6 shipping worldwideMade to order, ships in 2–5 business days

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Shipping

Flat $6 shipping on every order, worldwide, whatever's in it.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Meet Hydrel, a concrete dam who turns falling water into electricity.

Water held behind a dam has gravitational potential energy. When it falls through the turbines, that energy becomes motion, and generators turn it into electricity. The power depends on how much water flows each second and how far it falls.

The power is P = ηρgQh. Here ρ is the density of water, Q is the flow in cubic metres per second, h is the height the water falls, and η is the efficiency of the turbines and generators, often around 90 percent.

A small dam with a 50 m drop and a flow of 20 m³/s produces about 0.9 × 1000 × 9.8 × 20 × 50 ≈ 8.8 MW, enough for several thousand homes.

The Three Gorges Dam in China has a capacity of about 22 GW, the largest in the world. Pumped hydro stations run the idea in reverse, pumping water uphill when power is cheap and letting it fall again when it is needed.

Equations

\[P = \eta\,\rho\,g\,Q\,h\]
Symbols
SymbolMeaningUnit
\(P\) electric power \(\mathrm{W}\)
\(\eta\) efficiency \(\mathrm{dimensionless}\)
\(\rho\) water density \(\mathrm{kg/m³}\)
\(g\) gravitational acceleration \(\mathrm{m/s²}\)
\(Q\) volume flow rate \(\mathrm{m³/s}\)
\(h\) height of fall \(\mathrm{m}\)