Where 5,303 comes from
Hydraulic power is one line of physics: P = ρgQH. Density times gravity times volume flow times head. In SI that is kilograms per cubic metre, 9.80665 metres per second squared, cubic metres per second and metres, and it lands in watts with nothing left over.
Carrying it into the units people actually measure with: a gallon per minute is 6.30902 × 10-5 cubic metres per second, and a foot is 0.3048 metres. So one GPM falling one foot is 1000 × 9.80665 × 6.30902×10-5 × 0.3048 = 0.18858 watts. Turn that over and you get the shortcut worth memorising:
kW = GPM × head in feet ÷ 5,303
You will see 5,310 quoted, which is the same constant worked out with slightly different values for water density and gravity. The difference is a little over a tenth of a per cent and it is nowhere near the biggest uncertainty on the page — that will be your efficiency figure, or your flow measurement.
Everything after that is subtraction. The pipe takes head, the turbine takes a cut, the generator takes another. Nothing on this page adds anything to ρgQH, because nothing can.
Head and flow are not interchangeable, even though the formula multiplies them
The product says 60 GPM at 120 feet is the same power as 120 GPM at 60 feet, and in hydraulic terms it is. In equipment terms they are different jobs. High head and low flow is a small pipe, a small nozzle and a machine spinning fast on a thin jet. Low head and high flow is a large pipe, a large wheel and a machine that has to swallow a lot of water slowly. The same 1,358 watts arrives through completely different hardware.
Head is also the half you can survey once and rely on. Flow moves through the year, often by a factor of ten between the spring melt and the end of a dry August, and the low month is what actually sizes an off-grid system. Measure the flow in the driest month you can reach, not the one you happened to be standing there in.
Why the penstock diameter is usually the real decision
Friction loss in the Hazen-Williams form goes as diameter to the power of 4.8655 in the denominator. That exponent is the whole story: going from a 3 inch pipe to a 4 inch pipe at the same flow cuts the loss by a factor of about 3.8, and going to 6 inch cuts it by a factor of about 27.
| Penstock | Loss over 840 ft at 60 GPM | Net head from 120 ft | Output at 55% |
|---|---|---|---|
| 2 in | 47.39 ft | 72.61 ft | 452 W |
| 3 in | 6.94 ft | 113.06 ft | 704 W |
| 4 in | 1.85 ft | 118.15 ft | 735 W |
| 6 in | 0.25 ft | 119.75 ft | 745 W |
Two things fall out of that table. The first is that the 2 inch pipe spends 39 per cent of the head on friction and gives up 39 per cent of the output, permanently, every hour it runs. The second is that above 4 inch there is almost nothing left to recover — the remaining loss is under two feet and no pipe you can buy will get it much below that. The interesting decision is nearly always between the two sizes at the knee, and it is a straight trade between pipe cost once and lost watts for the life of the plant.
The same relation drives household plumbing, where it shows up as pressure rather than head. The water flow pressure drop calculator works it in psi with a full fitting take-off, which is the form you want indoors.
Hydro against solar, honestly
A 700 watt hydro plant sounds trivial next to a 5 kW array. It is not, because the array only produces during a fraction of the day and only in proportion to what the sky is doing. Seven hundred watts running all day is 16.8 kWh. A 5 kW array at four and a half sun-hours is 22.5 kWh nameplate before any system loss, and it delivers none of it at four in the morning in February.
What that changes is the battery. A generator that never stops needs storage for hours, not days, so the bank is usually far smaller than the same house would need on solar alone — the battery bank sizing calculator shows how sharply days of autonomy drive the cost. It also changes the failure mode: hydro fails when the intake screen blocks, which happens at exactly the moment the stream is highest and worst to walk to.
Start from the loads either way. The off-grid load audit calculator gives the daily kWh this page has to beat.
The legal half, which comes first
Taking water out of a stream, spring or ditch is regulated almost everywhere in the United States, and the rules are not the same in any two states. Depending on where you are it can involve a water right, a diversion permit, a fish passage or screening requirement, a minimum flow you must leave in the channel, and a separate review if the stream is navigable or carries listed species. Some of this is federal, most of it is state, and a little is local. Start with your state water resources or environmental quality agency before you move a shovel or a length of pipe. This page does arithmetic on numbers you measured and states no rule of any kind.
Beyond the legal side there is a practical one. Screening keeps fish and debris out of the intake, a minimum flow left in the channel is what keeps the reach below the intake alive, and both are things a regulator will ask about before anything else. Neither is designed here.
A penstock is a pressure pipe. A hundred feet of head puts more than forty pounds per square inch behind every joint, and a full pipe carries a great deal of stored energy that goes somewhere the moment it lets go. A pipe that fails at the bottom of the run, a valve closed quickly enough to slam the column, and an intake that a person can be pulled into are all real. Pipe rating, thrust blocking, air release and the design of the intake are a job for someone who does this work, and none of it is described here.
Anything that ties into house wiring is a licensed electrician job with a permit behind it. Back-feeding a line that the utility believes is dead can kill a lineman working on it, which is why the transfer arrangement is not a detail you improvise. Battery banks store real energy and can vent hydrogen. This page produces a number of watts and gives no wiring guidance whatsoever.
Questions people ask
How do I measure head accurately enough?
Head is the vertical drop between the water surface at the intake and the turbine, and it is worth measuring properly because everything scales linearly with it. A surveyor level and a rod is the clean way. A long clear hose filled with water works too, since the water finds its own level at both ends and you can leapfrog down the hill in stages. What does not work is a barometric altimeter or a phone, because the errors are commonly larger than the head on a small site. Do not use the length of the pipe or the length of the slope; a 900 foot run down a gentle hillside might only be 120 feet of drop, and it is the drop that makes power.
Why does my efficiency figure matter so much?
Because it multiplies everything else, and because it is the input people are least able to pin down. The hydraulic side is settled physics, but what fraction of it comes out as electricity depends on the specific machine, the drive, the generator and how far the flow is from the point the manufacturer measured. A unit quoted at a good number at its design flow can be dramatically worse at a third of that flow, which is where a lot of sites live for most of the year. Get the figure for the machine you are actually looking at, at the flow you will actually run, and treat any single number as a range.
Is a bigger penstock always worth it?
No, but the point at which it stops being worth it comes later than most people expect. Friction goes as roughly the fifth power of diameter, so the first size up is transformative and the third is nearly pointless. The table on this page runs your own numbers through every common size so you can see where the curve flattens for your flow and your length. The trade is pipe cost paid once against watts lost continuously for as long as the plant runs, so a long run with a marginal pipe is an expensive way to save money. Above the knee, spend the money on the intake instead.
Can I just divert water from the creek behind my house?
That is a legal question before it is an engineering one, and the answer differs by state and sometimes by watershed. Depending on where you are it can involve a water right, a diversion permit, screening or fish passage requirements, a minimum flow that has to stay in the channel, and additional review if the water is navigable or carries listed species. Some of these are administered by a state water resources agency, some by an environmental quality department, some by a local district. This page will not tell you what applies to you because nobody can from a distance. Ask the state agency first; it is a much cheaper conversation before the pipe is bought than after.
What flow should I design around?
The low one. A stream that runs 200 GPM in April and 25 GPM in September gives you a plant that produces at 25 GPM for the part of the year you most need it, unless you have storage or a second source. Measure the flow more than once, and get at least one measurement in the driest stretch you can. The stream flow measurement page covers the float and bucket methods for getting an honest number rather than an impression. It is also worth writing down what the channel looked like when you measured, because a figure with no context is very hard to interpret a year later.