# Where is the energy loss from using flowing water for power?

Pumped storage hydroelectric is in widespread use. But it only works in certain locations.

The source of energy driving a water wheel depends a lot on the style of the wheel. Undershot wheels depend largely on the kinetic energy (velocity) of the water flowing past the paddles, as the water is not falling in altitude (much) from the moment it enters the wheel until it exits.

Overshot wheels don’t depend much on the kinetic energy of the water entering the wheel. They do depend on the rate of flow – the volume of water entering the wheel per unit time, and of course a faster-flowing stream can contribute to this, but a slower stream with a deeper or wider race can do this too.

The potential energy recovered in an overshot wheel is primarily in the weight of water falling into the buckets at the top of the wheel to the exit at the bottom of the wheel. A faster-flowing input stream, of course, will fill the buckets faster.

The distance the water falls from the point where it enters the wheel to the point where it exits is called the “head”. An undershot wheel has very little head. An overshot wheel has a head about equal to the diameter of the wheel.

There are also “breastshot” wheels, where the water enters the wheel about midway up (that is, at about the height of the axle). These have about half the head of an overshot wheel.

There is also the pitchback wheel, which is something like an overshot wheel, but can get a little extra energy from the flow of water after it exits the bucket at the bottom, thus getting a bit of undershot wheel effect too.

I just learned all this from this page I just found, giving a tutorial on water wheel designs and discussing their energy flows:

Note the illustrations of the various kinds of wheels in this article, several of which show the distance of the “head” labeled.

The water moving past the paddles is caused by a fall or drop in altitude over distance; however small. No drop in altitude = a lake = no turning paddles. Check out drawings of a Poncelet wheel; about the most efficient type of undershot wheel and not the elevation difference induced by the design. Cruder undershot DIY paddle wheels you just drop in the river do turn but are very inefficient and may only capture a fraction of a mm in drop.

This is not quite correct. Stream wheels (wheels without elevation changes - note that the undershot wheels others have mentioned do involve an elevation difference) certainly exist. They are not very efficient. One type is the ship mill:

It’s still causing a very slight buildup of water behind it. Even if you argue that it’s purely extracting the kinetic energy of the water, there’s no way to actually do that without changing the water level since water is (basically) incompressible, so to slow the water you need to increase the cross-section. It’s just not a very large difference because it’s extracting so little power. It would be more noticeable if it was as wide as the river.

No doubt, but there’s no change in the stream elevation, which is what I think everyone understands by “an elevation drop”. There isn’t even a small weir, like undershot wheels have.

Maybe so, but regardless, there is going to be an elevation drop, even if it is hidden somehow. An overshot wheel is almost purely driven by potential energy; i.e., by the gravitational force pulling the water down over a distance. Other types, like an undershot wheel, or the turbines in a typical dam, use at least some of the drop to give the water kinetic energy. A turbine uses the geometry of the design to let the outflowing water have a larger cross-section (and thus lower speed) than the inflow. For an open design like an undershot wheel, you pretty much need to also have some local elevation change (even if it is only directly behind the wheel).

For a stream wheel, the elevation change is just the normal streambed (since no river is flat). That’s why they’re so very inefficient.

There will still be some buildup just behind the wheel, in the same way that a canoe paddle will have a mound of water behind and a depression ahead. No way to extract kinetic energy otherwise in a design like that. Overall, yes, the energy is coming from the elevation change of the river. But there must be a difference between the normal flow of the river and the one where the wheel extracts energy. A slow moving river (i.e. not rapids) has streambed friction and perhaps viscosity. If the wheel is extracting energy, it must lower those effects somehow. And pretty much the only way for that to happen is for the water to be moving more slowly, and assuming constant flow that means a larger cross-section, which means a larger height (even if it’s only for a portion of the river).

I think the point there is that the river bottom can be flat or even back-sloped yet the water can still flow. That flow comes from gravity upstream where the river bottom is not flat, but can be far upstream. The energy is in the moving water propelled from upstream, the slight build up behind the water wheel may be insignificant with a practical flow rate.

Sunlight, I thought. I mean, the water usually ends up at the higher elevations via the hydrologic cycle, which is pushed by sunlight-driven evaporation and the consequent rainfall/snowfall at higher elevations.

In other words, the water gets to the higher elevations by evaporating and then raining/snowing at higher elevations. From there, it flows downhill and converts potential energy into kinetic energy as it flows (if I remember my physics right).

Yes, except that in practice, it’s mostly converting the potential energy into heat, with only a little ending up in kinetic energy. Consider a cliff a mile high, and dumping something over the edge of the cliff: It’s going to be going really, really fast when it hits the bottom (most of the energy converted to kinetic energy). Now consider a river with its head at a mile elevation, and how fast that river is flowing when it reaches the sea: It’s going to be much, much slower than something dropped a mile straight down.

I can’t remember my physics right because I hardly know any, so excuse my ignorance for asking how momentum plays into this. Once the water is moving isn’t momentum an expression of the kinetic energy available?

This, which I came here to mention. Does gravity make water power a renewable energy source?

Dan

This isn’t really true either. Over a drop distance of a mile, straight potential → kinetic energy transfer (in a hypothetical frictionless environment) would mean that the water would have accelerated constantly to a final velocity of about 178 meters/sec by the time it hit the bottom. Terminal velocity of a raindrop (~10 meters/sec) in air is far, far less than this.

Hydroelectric is generally considered a renewable source of energy, yes.

Though, the current condition of Lake Meade kind of tells us reliability can be a concern sometimes. Also there’s only so much possible hydroelectric capacity, which is itself not uniformly distributed geographically.

The Mississippi River has its headwaters at 1475 feet above sea level, a little over a 1/4-mile. It has 2300 miles of length over which to dissipate that energy. By the time it gets down to New Orleans, I’d guess the water is moving 5 MPH or less, versus the frictionless 1/4-mile freefall velocity of ~200 MPH. The missing energy manifests as heat in the river water due to viscous dissipation over the course of those many miles (though the actual temp of the river water at any point will probably be more strongly influenced by ambient conditions/weather).

Yes, because the raindrop has significant air resistance, which (like the drag on the river) converts most of its energy to heat.

With the quibble that that’s the head by name only: By most standards, it’d make more sense to call the Missouri and the lower Mississippi the same river, with the river coming in from Wisconsin a mere tributary, and the Missouri’s headwaters are close to or above a mile high.

Regardless, though, the conclusion is the same: Most of the potential energy the water initially had does not end up as kinetic energy.

Sure, but the energy that powers any sort of water power scheme is from the sun, which is what ultimately moves the water into position up into the higher elevations for it to flow downward.

Gravity is just there; it’s not actually adding or removing energy from the system.

Right, I think we’re in full agreement on that. Gravity isn’t a source of energy; it’s just something that facilitates some ways in which energy can change form.