# What is the theoretical maximum energy efficiency of hydro turbines?

From what I've read it seems that hydro turbines can theoretically achieve 100% energy conversion from kinetic to electrical energy. However, I just wanted to double check if this was true.

– Fred
Sep 20, 2016 at 6:06
• Even in theory I doubt 100% is possible - because the speed of the water after the turbine is effectively carrying away some lost energy (loosely speaking). You'd need a second low pressure turbine of a different design to recover some of that, and the water would be exiting it even slower meaning there's a little more energy to reclaim, etc.
– Andy
Sep 20, 2016 at 6:39
• Further, you need to define what energy you're converting. Certainly you're not removing the heat energy (leaving the output as ice at 1mK :-) ). Sep 20, 2016 at 14:21

Something can only be 100% efficient when a lot of generous assumptions are taken into account.

If you assume:

1. No friction (turbine surface, turbulence, nozzle, or bearings)
2. Perfect cup design (100% 180degree jet reversal)
3. A dry wheel (no water is spun off)
4. Not counting the gravitational potential to drop the water away from the wheel in the efficiency calculation.

Then a Pelton wheel is 100% efficient.

I worked in alternative energy for several years and, 90% is the best is have seen (Pelton, oversized penstock, ~400ft head). 50% would probably be a good across-the-board average for currently installed microturbines in the western United States. The lower the head(upstream pressure), the larger and more expensive a turbine and supporting components have to be to achieve the same efficiency. Also, the energy to remove the water from the turbine becomes appreciable. So generally, the lower the head the lower the efficiency.

Below is a graph of different turbine efficiencies. Pelton is a common choice for variable flow streams because a single turbine has a relatively high efficiency across a wide range of flowrates. Efficiency is very design and resource dependent so use this graph for a general understanding only (image source).

A Pelton wheel is a good turbine to start learning the mechanics before you look at more complex turbines. Pelton Turbine - Working & Design Aspects

Yes, it's true in the sense that there's no other theoretical upper limit on conversion that's below 100%.

There are such theoretical limits that are strictly less than 100% for PV; one for single-junction (the Shockley Queisser limit), a higher one for two junction, and so on.

And there is a theoretical limit on heat engines - the Carnot efficiency.

Hydro has no such theoretical limit other than the standard hard 100% limit: all hydro is strictly less than 100%.

Turbine stacking anyone? My truck has dual turbo chargers. The math says that if u convert for liquid instead of gas & increase the slack space to accommodate the liquid pressure variance behind the 1st turbine using Pelton wheels, it allows for the second turbine to have enough head pressure to account for the rotational momentum & friction losses in both turbines. Diameter & length of the slack tube to provide enough head pressure to the second Pelton wheel is crucial, requiring the correct vertical length. This may also require using a reducer nozzle to increase the ram pressure to maintain the second wheels correct rpm. Adjust the flow rate to the 1st wheel to find the slack tube length & diameter to generate the correct flow rate & pressure to the second wheel. I recommend working through the engineering math first.

I guess if the design is like a wind turbine, like a propeller sat in the flow with no ducting then the betz limit would apply. See: https://energyeducation.ca/encyclopedia/Betz_limit