The three-halves power, and why sheet thickness is expensive
Water flowing over a level lip is a weir, and weirs have been measured for two centuries. The Francis formula for a rectangular sharp-crested weir is:
Q (cfs) = C × L (ft) × H (ft)1.5
with C around 3.33 for a sharp crest. Q in gallons per minute is that times 448.83, since a cubic foot per second is 7.48052 gallons times 60 seconds.
The exponent is the interesting part. Flow is linear in the width of the weir and goes as the three-halves power of the depth of water over the crest. Double the width and you double the flow. Double the sheet thickness and you multiply the flow by 21.5, which is 2.83.
Then the pump power multiplies again on top of that, because friction head rises with flow to the power 1.852, so the head goes up as well as the flow, and power is the product of the two. Running the defaults through it:
| 1/2 in sheet | 1 in sheet | Ratio | |
|---|---|---|---|
| Flow | 25.4 GPM | 71.9 GPM | 2.83 x |
| Friction head, 90 ft of 2 in | 1.04 ft | 7.10 ft | 6.86 x |
| Total dynamic head | 12.0 ft | 18.1 ft | 1.50 x |
| Input power at 60% | 96 W | 409 W | 4.25 x |
Four and a quarter times the running cost for a sheet twice as thick. Whereas doubling the width of the weir at the same sheet thickness doubles the flow, and the power roughly doubles-and-a-bit with it. If the goal is a bigger looking waterfall, width is much the cheaper axis, and it is the one people reach for last.
Total dynamic head is the number pumps are sold against
Flow alone selects nothing. A pump curve is a line of flow against head, and where your system sits on it is decided by the head your plumbing imposes. Three things make it up:
- Static lift. The vertical distance from the water surface the pump draws from up to the weir crest. It does not depend on flow at all.
- Friction. Pipe and fittings, rising steeply with flow. The Hazen-Williams relation used here is head loss in feet per 100 feet = 0.2083 × (100÷C)1.852 × GPM1.852 ÷ ID4.8655, the same relation behind the water flow pressure drop calculator.
- Everything else. A filter, valves, a check valve. Enter it in feet; multiply a psi figure by 2.31 to convert.
The diameter exponent of 4.8655 is where pipe size earns its keep. Going from 1-1/2 inch to 2 inch at the same flow divides the friction by (2.067 ÷ 1.610)4.8655, which is 3.37. At 60 GPM over 90 equivalent feet, 1-1/2 inch pipe costs about 17.1 feet of head and 2 inch costs about 5.1. That difference alone is often larger than the entire static lift of a garden water feature.
From head to watts
Water horsepower is the useful work being done on the water:
WHP = GPM × head (ft) ÷ 3960
The 3960 is 33,000 foot-pounds per minute per horsepower divided by 8.33 pounds per gallon. Dividing by wire-to-water efficiency and multiplying by 745.7 gives the input watts, which is what the meter sees.
Wire-to-water efficiency is not the pump efficiency on the datasheet. It is pump efficiency multiplied by motor efficiency, and on a small circulation pump the combination is often 50 to 65 per cent rather than the 75 or 80 the hydraulic curve alone suggests. Using the hydraulic figure will make the energy estimate optimistic by a third.
Running it, and running it less
A water feature is a discretionary load. Nothing about pool circulation depends on it, so it can run on a timer for the hours anyone is outside to look at it and be off for the rest, and that decision moves the annual number far more than any efficiency choice in the hardware. A 400 watt feature at four hours a day is 584 kWh a year; the same feature running dawn to dusk is well over 2,000.
It also evaporates water. A sheet of water falling through air is doing what a cooling tower does, and a feature run continuously in dry weather is a measurable line on the water bill and on the heating bill for a heated pool. The bucket test calculator is the way to find out how much, and the pool heat loss calculator prices the heat that goes with it.
If the feature runs off the main circulation pump rather than its own, the added head has to come out of the same pump curve, and on a variable-speed pump that means a higher speed for the filtration it was already doing. Power goes with the cube of speed, so that is not a small change — the pool pump run time calculator works it through.
What this page does not settle
Any suction point in a pool can hold a swimmer against it, and children have died that way. Drain covers, split suction, safety vacuum release and everything else in that area is regulated and is work for a licensed pool professional. This page has no procedure for it and names the hazard only so it is not forgotten while the flow numbers are being admired.
Anything electrical within reach of pool water is licensed work, and the reason is that people are standing in the circuit. Bonding, grounding, receptacle placement, clearances and equipment disconnects are set by the code your jurisdiction has adopted and enforced by its inspector, and none of it appears on this page. If a pump, light, heater or panel needs more than plugging into a working receptacle, that is a job for a licensed electrician.
And the weir coefficient remains the soft spot. A real spillway lip is rarely sharp-crested, the approach channel is rarely ideal, and the sheet either clings to the face or springs clear depending on details this arithmetic knows nothing about. Size the pump with a margin and put a valve in the line, because the last adjustment always happens with water running.
Questions people ask
How many GPM does a waterfall need?
It depends on the width of the lip and how thick you want the sheet, and the two do not contribute equally. Flow is linear in the weir width and goes as the three-halves power of the depth over the crest, so a 24 inch weir with a half inch sheet is about 25 GPM while the same weir with a one inch sheet needs 72. Per foot of weir, a thin decorative veil might be 10 to 15 GPM, a sheet that holds together in a breeze 25 to 40, and a heavy rush considerably more. Work it from the geometry you want rather than a per-foot rule, because the sheet thickness is doing most of the work in that number.
What is total dynamic head and why does the pump need it?
It is everything the pump has to push against, expressed in feet of water. It is the static lift from the pump water level to the weir crest, plus the friction in the pipe and fittings, plus whatever a filter or valves cost. A pump curve plots flow against head, and a pump only delivers its rated flow at its rated head. Sold a pump on flow alone and installed on a system with more head than the rating assumed, you get less water than the box promised, sometimes far less. Take both numbers from this page to a curve and read the intersection.
Does the pipe size really matter that much?
More than almost anything else, because friction goes as the inside diameter to the power of about 4.87. Going from 1-1/2 inch to 2 inch Schedule 40 at the same flow divides the friction loss by 3.37. At 60 GPM through 90 equivalent feet, that is the difference between 17.1 feet of head and 5.1 feet — larger than the static lift on most garden features. The practical consequence is that a long run in undersized pipe cannot be fixed by a bigger pump in any economic sense: you pay for the extra head every hour the feature runs, forever, and the flow you gain is a fraction of the power you spend.
How much does it cost to run a pool waterfall?
Input watts times hours, at your rate, and the hours matter more than anything else. The default here, a 24 inch spillway with a half inch sheet on a modest run of 2 inch pipe, comes out near 96 watts, which at four hours a day and 15 cents a kilowatt hour is about twenty-one dollars a year. Widen and thicken it to a genuinely showy feature at 400 watts and run it twelve hours a day and you are at 1,750 kWh a year. Since a water feature does nothing for the water quality, the timer is the biggest lever available, and it is free.
Why is my waterfall thinner than the calculator says?
Several reasons, and all of them point the same way. The weir coefficient of 3.33 is for a sharp-crested weir with free discharge, and a real spillway lip is usually rounded or broad, which passes less water for the same head. The approach to the lip is rarely as clean as the formula assumes. And on the pump side, the actual flow is wherever the pump curve crosses the system curve, which is generally lower than a nameplate figure suggests once real pipe and fittings are in the way. Fit a valve on the feature line so the sheet can be trimmed with water running, and treat the calculated flow as a target rather than a prediction.