Hydropower Fundamentals

Hydropower provides roughly 14% of global electricity and remains the world's largest renewable source. It also achieves turbine efficiencies above 90%, far higher than any thermal plant. The physics is simple: falling water converts gravitational potential energy to electricity with minimal thermodynamic waste.

The power available from falling water is P = rho x g x Q x h, where rho is water density (1,000 kg/m3), g is gravitational acceleration (9.81 m/s2), Q is volumetric flow rate (m3/s), and h is the height the water falls (head). Unlike heat engines, hydro turbines are not limited by the Carnot ceiling because no thermal cycle is involved. Energy goes directly from gravitational potential to kinetic to mechanical to electrical form.

Calculate power. A dam with 100 m of head and a flow of 50 m3/s. P = 1,000 x 9.81 x 50 x 100 = 49 MW (gross). At 90% turbine efficiency: 44 MW net.

Compare to thermal. A coal plant converting the same 49 MW of thermal input at 35% efficiency produces only 17 MW. Hydro's direct mechanical conversion avoids the ~65% heat rejection that thermal plants cannot escape.

If hydropower is so efficient and cheap, why hasn't it grown as fast as solar and wind?

Geography is the constraint. Good hydro sites require elevation change and reliable water flow. Most of the best sites in developed countries are already dammed. New large hydro also faces environmental opposition (river ecosystems, displacement of communities) and multi-decade construction timelines.

Hydropower's combination of high efficiency, storage capability (reservoirs), and dispatchability makes it uniquely valuable for grid stability.

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