Most hydraulic designers in America still use the British system of measurements when evaluating hydro-power; so there are some concepts to keep in mind:
- Water weighs 62.4 pounds per cubic foot.
- 8.8 cubic feet of water weights 550 pounds.
- There are about 7.5 gallons in one cubic foot.
- One cubic foot per second (cfs) is equal to approximately 7.5 gallons-per-second, or about 450 gallons-per-minute (gpm).
- Energy is measured as (distance) times (force); with units of foot-pounds (ft-lbs).
- Power is measured as (Energy) divided by (time); with units of (ft-lbs)/second. 550 ft-lbs/seconds is one horsepower (hp, British units). One horsepower is 746 Watts (SI units, W); therefore, one hp = 0.746kW
Notice the three components of the power equation: (feet), (pounds), and (seconds). If (feet) is increased, power is increased. If (pounds) is increased, power is increased.
Conceptualizing the power of flowing water
Try imagining 7.5 one-gallon jugs, or a one-cubic-ft barrel of water hanging from a cliff tied by a rope; imagine the rope wound around the axle of a generator like a string on a yo-yo. As the water falls from top of the cliff to the bottom, the rope spins the axle of the generator as it unwinds. The potential energy of the water at the top of the cliff is converted to electric energy as it falls and spins the generator. The same amount of energy will be converted whether it falls quickly, or takes a long time. But if it falls quickly, more power is generated for a short amount of time; if it falls slowly, less power is created for a long period of time.
Instead of a single barrel, now imagine a series of barrels, falling continuously, one after the other. The barrels would provide a transfer of energy, from top to bottom, continually, one after the other. This continual falling of water is a stream.
Instead of being tied to a rope on a generator at the top of the cliff, now imagine the first barrel pushing against a gate at the bottom of the cliff. The more barrels there are stacked up against one another, the more force is exerted on the gate. The concept of hydraulic head is just that, a way to measure how many units of water are “stacked up” on top of one another, in the vertical direction only. The greater the hydraulic head, the greater the force exerted on the “gate”.
Instead of a gate, imagine a paddle on a wheel. The hydraulic head exerts a force on the paddle of the wheel; the paddle is pushed to the side, and the wheel spins. Imagine a series of paddles around the wheel, and imagine the wheel being on the axle of a generator. Flowing water spins the wheel, which spins the generator, producing electricity. The system you’ve just imagined is a hydro-turbine. There are a handful of “Paddle” wheels that are used in hydro-turbines, the most common are: Francis, Turgo, Pelton. The difference among the various wheels or runners is basically due to the different shapes of paddles. Site conditions, such as available head and quantity of flow usually determine which type of wheel is most suitable. See my article for more information about turbine runners.
Two necessary measurements
It is important to know the hydraulic head, or head, that is available, because it will tell how much force will be exerted on the turbine; and therefore, how much energy is available per unit of flow. For a piped system, head is measured as the vertical difference from where the water enters the pipe, to where it exits the turbine. The length of pipe between entering and exiting is not a factor in determining head. The longer the pipe, the greater the pipe cost and friction loss, but the available head will not change. For a dammed system, head is measured as the vertical difference between the surface of the water, and where the water exists the turbine.
It is also important to know the flow rate, or quantity of water that is available. As common sense will tell, a trickle of water produces less power than a torrent of water.
Basic hydropower equation
As stated above, power is measured as ft-lbs/s. Sparing the details of unit cancelation, it is easy to remember that (quantity) times (head) equals power, or ft-lbs/s. Pay attention to units, because flow units in cfs is very different than in gpm.
For every foot of head, 62.4 pounds is added to the cumulative force on the turbine. Many times, turbine charts use pressure instead of head. Since water weighs 62.4 pounds per cubic foot, or 62.4 pounds (per square foot) times one foot vertical, it is easy to convert available head to available pressure. Each one foot cube of water exert 62.4 pounds on the (square foot) surface below it; this is converted to 0.43 pounds on every square inch (psi) below it. So one foot of head equals 0.43 psi. Alternatively, 2.3 feet of head results in one psi.
Although Americans use the British system to measure hydro-power, we use the SI system when discussing electric energy and power. Watt is the SI unit of power. So the power equation must contain a conversion factor from British (horsepower) to SI units (Watt). For more discussion on energy verses power, see my related article.
For estimating, the basic hydropower equation is:
- kW = (H x Q x (62.4) x 0.746 x e) / (550)
- where kW is kilowatts
- H is head, measured in feet
- Q is quantity, measured in cfs
- 62.4 is the weight of water per foot of head
- 0.746 is the conversion factor from hp to Watts
- e = efficiency factor (usually 0.5 for small micro-hydro systems)
The equation can be further simplified when using cfs, and e = 0.5:
kW = (H x Q) / 24
If the available head is 120-ft, and flow quantity is 0.1-cfs; estimated continuous power production would be 0.5-kW; or 12-kW-hours of energy per day.