The focus of the article is for climates that have warm weather year round, but I kept expanding the scope and effort is made to include cold weather options.
For the sake of simplicity and effectiveness I moved to a reasonable climate.
I've seen placing a black tank inside of an insulated box with a vacuum glass on the side facing the sun.
I've heard placing a hose underneath composting mulch exposed to the sun is very effective as well, and will keep the hose from busting during freezing weather.
More freezing weather options ->
But for the sake of cheapness and less work, given there's already planned to be a water tank above the house for other reasons, I'm going to circulate water through a black hose connected to the tank at each end.
For supa-cheap, you can make due with thermosiphon circulation. No pump needed.
For supa-supa cheap, you can skip the tank and use the volume of your huge diameter hose, connected straight to the tap. 100 meters of 1 inch HDPE holds 87 liters. 100 meters of 2 inch tubing will have 286 liters. Although you won't conserve your hot water supply overnight.
The storage tank we are getting is supposed to be for cold water, but who needs cold water anyway? Hell we need to boil the water to drink it anyway. And all the faucets don't have cold-hot mixers. So we can do without cold water, and instead have warm water.
Except for my cat. The plan for her proximity sensing water faucet would be ruined. What if I want to put a drinking water filter so we don't have to boil water? Cold water is overrated. We can adapt.
For showering, feed the water into the inlet of your hot water tank, or your cheap $15 electric showerhead. They can provide hot water when needed after a number of cloudy days.
I will test run 3.3m^2 of collector aperture on an 1100 liter tank, both being uninsulated. Will the huge tank maintain the heat absorbed over many days, reaching an average of 30 to 35 Celsius?
An 1100 liter tank can be had for USD $160. A 250 liter tank can be had for $85. 100 meters of 1“ HDPE tubing costs $30. Connectors cost around $15. You'll need a drill and hole saw to make holes in the tank. A low price of $130 is much lower than the low of $500 mentioned on sustainability sites I've visited.
The following is a guide you shouldn't follow: ecoonline.com.au. They complicate needlessly, and in so doing, sell you more stuff.
New Finds with similar designs!
Related web pages:
https://hadzy.com or https://ytcomment.kmcat.uk, for searching through comments in a YouTube video.
Aperture is the most important aspect of collecting solar energy. Aperture is the effective area exposed to the sun.
The solar zenith angle is the angle between the sun’s rays and the vertical direction. Even at the equator, the variation of the solar zenith angle varies between positive and negative 23.5 degrees.
Aperture can be reduced if there is a zenith angle. If the panel is immobile, reducing its angle relative to the sun will have to be averaged over the year. Perhaps tilted more towards the winter sun.
The direction to position a solar panel depends on your latitude. The closer to the equator, the more the panel faces straight up. The closer to the poles, the more the panel tilts towards the equator.
A household's hot water usage, and the efficiency of the system, determines the aperture needed. In my case, I will need more aperture to make up for the lack of tank and tubing insulation.
Although a larger tank will cool more slowly, it will also heat up more slowly, so additional aperture may also be needed to have hot water in less time in the morning.
Solar water heaters are usually sized at 80 liters of water storage for every square meter of collector aperture or area. This ratio of 80:1 will provide hot water (55°C or 130°F) in the afternoon of sunny, warm days if the tank is filled with cold water (15°C or 60°F) in the morning.
If this ratio is changed to 40 liters of water for every square meter of collector (40:1), then the water will heat up faster but will also cool off faster in the afternoon or at night if the tanks are not insulated.
If this ratio is changed to 120:1, the water will barely get warm (38°C or 100°F) but will retain its heat for many hours. This ratio is best used to pre-heat water which will be heated to a higher degree with another heat source. Human Development Library 2.0, Peace Corps, nzdl.org
In response to this peace corps method for scaling a solar water heater:
In one of your calc/estimates, you conclude that because you have a lot of tankage, you need a lot of absorber area. That’s backwards. Hot water demand determines collector area. Collector area then drives tank size (so you can store an entire day’s worth of solar input). Having a tank larger than that is all good, no downside and let you store enough warm/hot water to get through a cloudy day or two. It doesn’t dictate more collector area if you don’t need any more warm/hot water to meet your needs. David Thomas on Quora
I think David may be referring to an insulated tank, when peace corps was working with uninsulated tanks.
What a larger tank will do, is average out the water temperature (reduce the lows and highs), by providing a larger thermal mass.
If the average temperature is not shower worthy, then a smaller tank may be beneficial because it would allow a shower at certain hours of a sunny day, which is better than no warm shower. Although anything is better than freezing cold showers, which is the norm in this area.
Sizing a Solar Water Heating System
Sizing your solar water heating system basically involves determining the total collector area and the storage volume you'll need to meet 90%–100% of your household's hot water needs during the summer. Solar system contractors use worksheets and computer programs to help determine system requirements and collector sizing.
Contractors usually follow a guideline of around 20 square feet (2 square meters) of collector area for each of the first two family members. For every additional person, add 8 square feet (0.7 square meters) if you live in the U.S. Sun Belt area or 12–14 square feet if you live in the northern United States.
A small (50- to 60-gallon) storage tank is usually sufficient for one to two three people. A medium (80-gallon) storage tank works well for three to four people. A large tank is appropriate for four to six people.
For active systems, the size of the solar storage tank increases with the size of the collector – typically 1.5 gallons per square foot of collector. This helps prevent the system from overheating when the demand for hot water is low. In very warm, sunny climates, some experts suggest that the ratio should be increased to as much as 2 gallons of storage to 1 square foot of collector area (100 liters per meter squared). energy.gov
The power of the Sun at the Earth, per square metre is called the solar constant and is approximately 1370 watts per square metre (W/m2). sws.bom.gov.au
Only 56% of the solar radiation that reaches the atmosphere makes it through to earths surface. fondriest.com
To optimize cheapness and laziness, I choose black hose because I don't have to paint it black. I don't have to worry about freezing, because it never freezes around here.
PE pipe is fine with UV and heat to 140-180°F (60-82°C)
I am lazy and want to spend less time making spirals, so want to choose the largest diameter hose so that I get the same aperture with the lesser amount of loops in a spiral coil.
1” HDPE black hose is the largest diameter which still allows bending into a small inner spiral. 1.5“ HDPE hose is sold as a roll that's twice the diameter of 1”, taller than most women.
1“, 1.5”, and 2“ HDPE is sold in 100 meter rolls. Big cheap aperture. As a bonus, water flow in larger diameter tubing has less viscous friction.
100 meters of 1” with an inner diameter coil of 0.5 meters will make a coil 2 meters in outer diameter. If you have more roof space to work with, you can add 1.5“ or 2” tubing to the outer diameter of the 1“ tubing, assuming the roof can support the added load.
For thermosiphon flow with a tank, instead of running the two tubes in series, connected by an adapter, the superior method is to attach the two hoses in parallel, with each having it's own circulatory loop. Running in parallel reduces the temperature at the return to the tank, thus reducing heat loss to ambience along hotter tubing. I could use shorter lengths than 100 meters, but I want lazy, simplicity, and would rather make less holes in the tank.
Running in parallel also increases flow because each line has less dynamic head than the two in series. If you want to increase flow with a pump, you can still use a single pump by having a fork-in-the-road after the pump where the water flows out of the tank.
With thermosiphon flow, flow rate is driven by the height of the tank relative to the hose spiral, and the temperature difference between the cooler water flowing into the hose, and the warmer water returning to the tank.
Choose the thinnest wall HDPE pipe available, as a thicker wall represents more of a barrier for heat transfer.
Class-125 and drainage piping from agricultural irrigation suppliers is thinner than Schedule 40, with DVW piping being in between. More wall thickness in such a low-pressure application only adds weight, cost and reduces heat transfer to the fluid inside. David Thomas on Quora
100 meters of 1.5” tubing surrounding a 1“ spiral will yield an outer diameter of 3.3 meters.
100 meters of 2” tubing surrounding a 1“ spiral will yield an outer diameter of 3.5 meters.
Surface area for 100m of 1” HDPE is 3.34 m^2
Surface area for 100m of 1.5“ HDPE is 4.83 m°2
Surface area for 100m of 2” HDPE is 6.03 m^2
You can use zip ties to hold all the spiral loops together.
More expensive but easier to set up, is a pre-built black hose pad. There will be more resistance to thermosiphon flow compared to a 1“ hose spiral because water makes right angle turns and flows through small diameter 0.25” pipes. They are designed for use with a pool pump.
If you live in an area of affluence, where people normally have hot water and therefore electric or gas hot water heaters, then a second-hand tank could be free. These come with excellent insulation to heat loss.
Around here the tanks are put on the roof to provide water whenever municipal water is shut off. They aren't insulated. The smallest sold is 250 liters, and the most common size is 1100 liters which costs about USD $160.
Will an uninsulated tank experience temperature stratification? Will the cool walls cause internal mixing?
Stratification happens on humongous municipal tanks, but that may not be the case on smaller tanks with a greater surface to volume ratio?
Unless you have included mechanisms to mix the water, yes, stratification will occur. You usually want that and plumb it to enhance stratification so the hottest water is available for use and the coldest water flow out the bottom to the collector panels because that coldest water can gain the most heat with the smallest losses. David Thomas on Quora
One might think the heat loss at walls would cause a drop of that fluid, but unless the fluid is mechanically circulated, the colder fluid seems to just stay at the bottom. Michael New on Quora
Insulating an uninsulated tank is a simple and cost effective upgrade. Instead of a 100 liter tank decreasing by 20C overnight, a well insulated tank would decrease by 5C. See introduction in Reducing the heat loss at night from solar water heaters of the integrated collector–storage variety, Faiman et al 2001
Insulation should have the following desirable properties:
We would want insulation to have a low Thermal Diffusivity:
Thermal Diffusivity (mm2/s) = Thermal Conductivity / (Density x Specific Heat Capacity)
In addition, the surface of the insulation can also absorb energy from the sun's rays as a secondary optimization. The insulation surface could be painted: see coatings The surface of the insulation will become hot, and not transfer heat well to the tank due to heat loss from convection. However, some heat will be stored in the insulation, and reduce heat loss from the tank at night as the insulation will stay warm for a long time.
Manufactured tank insulation jackets exist but may not be available in your country. They can be adapted with a coating. See section below on coatings.
Mineral Wool is stiff and dense but can follow the curvature of the tank, held in place with rope or straps.
One could make a steel frame and glass greenhouse for a black uninsulated storage tank. A cheaper, although less effective version can be made with a PVC arched frame and clear plastic.
I think insulation would provide more energy efficiency than a hermetically sealed greenhouse.
Ideally you have hot water plumbing and a dedicated hot water storage tank. If the residence only has cold water plumbing and a cold water storage tank, the least expense towards the ideal is to add dedicated hot water piping for a single showerhead and use the following combined storage tank method.
The combined storage tank supplies all the water to the house, both hot and cold. Although in practice, warmer and cooler as allowed by the water stratification in the tank.
There are 5 tank connections. Holes are added to the tank with a hole saw. Nipple connectors with rubber gaskets keep the tank from leaking.
Of the 5 connections, 1 is for water inlet, 2 deliver water to the house, and 2 are for water circulation to the solar collector spiral.
The top connection for the spiral can lead to an internal tube with weighted endpoint attached to the float/buoy/bobber. A floating duct. If the water level lowers due to municipal water shutting off, the solar collector will continue to function.
To encourage water stratification it is best not to route the warmer water through the cooler water, or vice versa. To keep the hose of the floating duct from sinking into the cooler water, the hose of the floating duct should be slightly lighter than water. You may add small inline floats to the hose to make this true.
If you have reliable municipal water, the floating duct is really not necessary. KISS: keep it simple stupid.
The bottom connection should lead to the outer spiral loop. An optional one way check valve can be installed at this bottom connection, where the water temperature will be cooler thus prolonging the life of the valve. More details in the Thermosiphon Science section.
The connection that delivers hot water to the residence can optionally lead to a gas or electric hot water heater, or an electric showerhead. This connection can also have a floating duct. If the water level lowers due to municipal water shutting off, you continue to draw hot water from the top. Note in the diagram that the connection is mistakenly drawn low on the left.
Tanks are sold with water input at the top, but need to be altered to fill from the bottom to promote water stratification. Instead of running a pipe from the top inlet to the bottom, replace the float valve at the top with a bottom mount float valve. The float valve that comes with the tank can be used as a bottom mount float valve by connecting at the bottom and tying a line to the float. Plug the non-used inlet hole at the top.
If you use floating ducts, they are connected to a float, along with the municipal inlet valve. Connect the hoses and inlet valve line 120 degrees away from each other along the tank wall. Also tie the 3 lines to the float 120 degrees away from each other. This will offer the stability of a triangle to help keep the float from rotating and tangling the lines.
There are 4 tank connections. The difference in plumbing between a combined tank and the dedicated tank is that there is no cooler water outlet for house use.
If you are using well or stream or some other untreated water, you will want water filtration.
Have sediment filters placed before the storage tanks, to keep them clean, and to conserve water pressure to the house.
As a rule of thumb, sediment filtration stages can start with a 40 micron spin down sediment filter, followed by a 4.5“ x 20” big blue filter, either 1 micron or 0.1 micron. 0.1 micron filters are not common but available via sites like Alibaba, where you will need to talk with manufacturers. Experience will tell you if you need to choose different micron ratings for the sediment filters. Experience being that one stage is clogging too frequently for convenience.
To have clear water at the tap, you may need a UF membrane if the water is high in tannins.
See separate article on Whole House Water Filtration and section below on Microbial Control
If routing solar to a gas or electric hot water tank
The following options may be necessary if working with a combination of limited roof space, an uninsulated solar array, and an uninsulated tank. 95% of the time they aren't needed, and only add unnecessary cost and maintenance.
Gary at builditsolar.com tested 3 paints inside a case with an acrylic front. Attaching thermocouples to the back of the painted metal, he found that flat black paint was superior to a product specifically made for solar coating.
For near direct incidence of sun on the 6 by 6 samples, the flat averaged about 7.3F hotter than the gloss sample. Flat average = 155.4F, gloss average = 148.15F
For the test with the sun at an azimuth angle of about 45 degrees, the flat averaged abut 7.5 F hotter than the gloss sample. Flat average = 153.58F, gloss average = 147.13 F
The Thurmalox was intermediate between the two – perhaps closer to the flat
Best Type of Black Paint for Solar Collector Absorbers, builditsolar.com 2010
Another Thurmalux comparison at resystech.com.
However, not all flat black paints are effective. Check out Wayne Schmidt's flat black paint comparison, which shows that Gary's Rust-Oleum Flat Protective Enamel doesn't appear to be the best. By visual inspection, Stewart Semple's Black 2.0 is superior.
Appearances can be deceiving, because the infrared spectrum from about 700 nm to 1 million nm also absorbs heat from the sun. See Geistpunk Workshop's video showing little temperature differences between Stewart Semple and two other cheap flat black paints.
Light reaching the Earth's surface, by energy totals is composed of 49.4% infrared radiation, 42.4% visible light, and just over 8% ultraviolet. noaa.gov
For longer wavelengths, the surface underneath the paint is involved in absorption. Although the intensity of the radiation decreases exponentially with penetration depth due to absorption. For frequencies reaching the surface of the earth, infrared has the longest wavelength range. Note that longer wavelengths carry less power.
Some engineers discuss sources for Cat-A-Lac paint, which keeps changing ownership.
Consider the following image from Wikipedia, where there isn't a lot of room for improvement compared to Cat-A-Lac flat black paint:
Compare to the radiation incident on the earth's surface, where 1 micrometer = 1000 nanometers:
Make your own black paint
According to US patent number 401,1190 taken out by Maria Telkes … a black paint that gives 13% higher temperatures compared to normal black paints can be made from 3 easily obtainable ingredients (1) Zinc Powder (2) Copper Sulphate (3) Sodium Hydroxide. Any school lab will have these and almost any town with a chemical market will have them. solarcooking.com
It's interesting that HDPE is as effective at shielding astronauts from radiation as aluminum New Comparative Metric for Evaluating Spacecraft Radiation Shielding, Warden and Bayazitoglu 2018. Likely aluminum by reflection and HDPE by absorption.
“It has long been known that a lamp-black coating will make a body nearly black.” Wikipedia. Lamp-black is made with carbon black, which is added to HDPE to increase UV resistance.
The following chart shows that polyethylene black plastic is nearly as effective as Catalac paint:
It would be helpful to know what class of HDPE I'm using, and what additives it has that can affect absorptivity. Although I'm doubtful I have access to anything but one type of HDPE in Peru.
You can make a greenhouse to insulate your tubing aperture so you lose less heat. But you can also circulate the water more quickly through the tubing so it doesn't get as hot, and lose less heat that way. Either way works to reduce heat loss in the system.
One downside to glazing is that some of the sun's rays will be reflected at the glass. Some special glass coatings can help with transmission and internal radiation retention, but it would be more important to keep the glass clean. Adrian Mudd on Quora
While the spiral has a lot of surface area for heat loss, making a greenhouse enclosure for the tubing is lots of work.
The case I see for making an insulated greenhouse, is if you do not want to use a water tank and instead use larger diameter tubing (, such that volume of the tubing is its own storage tank. Special attention to the maximum working temperature for the tubing.
Whilst a passive solar water heater works, I was astonished how much more efficient my homemade geyser became when I added a small inexpensive pump energised by a PV panel.
Costing around $60 + a 10W PV panel of around 30 dollars that drives the solar pump only when the sun shines. For less than 100 dollars you will be well pleased with the greatly improved temperature of your shower! bernard-preston.com
Look for a circulation pump in the 100 watt range. A stronger pump will keep the flow rate high and therefore the hose temperature cooler. But any pump will assist the thermosiphon.
To simplify the overall design, the sun will power the pump. If there is enough of the sun's radiation to heat the tubing, there will be enough radiation to power the pump. No need for a controller, temperature sensors, etc.
Therefore, the pump should circulate water even when it's only getting a fraction of its rated wattage. Will it be intelligent enough to turn itself off under insufficient wattage? Would it matter if the pump has current but doesn't rotate?
A simple 12Vdc relay might work, so that when you have 12 volts, the relay turns on the power to the pump. When the voltage gets to 2.5 volts, it will disconnect the motor, as the relay will naturally drop out. Ronald Williams on Quora
Will it include a capacitor that provides the necessary multiple of running power to start? Will it perform efficiently at a wide range of RPM?
A centrifugal pump is best for circulation, with low head (only dynamic head) and high flow, but at low RPM the efficiency and durability drops. Will a positive displacement pump perform at higher average efficiency over the range of power supplied from the solar panel?
Being in Peru, my purchase options are pretty much limited to AliExpress. Are all Jebao aquarium pumps sine wave positive displacement pumps? The Jebao site is unclear, doesn't include all their models, and support lacks in knowledge. Maybe because I talked to sales.
Your best efficiency point article is correct, but does not mention that changing the pump speed changes the shape of the pump curve, so that you always operate at your best efficiency point.
Your Jebao may be centrifugal, or just as efficient as one would be. Small pumps like that are notoriously inefficient, and not worthy of a detailed examination. Just get a bigger panel if necessary. Ronald Williams on Quora
Ronald recommends an RV pump, however, an RV pump inlet and outlet diameter are 1/2 inch.
A centrifugal pump offer a constant resistance once it starts. While a positive displacement pump offers rhythmic high and low loads. This requires a much higher threshold supply, for 1 power stroke. Stephen Kao on Quora
A 300 watt panel may power your 100 watt pump.
To make best use of a solar panel, you need a device with maximum power tracking circuitry.
As the video explains, without this device, the pump determines the voltage the solar panel operates at, which may not be the most ideal intersection along the solar panel's IV curve.
Without an MPPT controller, the pump will determine the working voltage, and the wattage will be whatever area is covered in the IV curve below.
Using an MPPT controller, a 12 volt solar panel peaks around 17 volts, and a well designed 12 volt pump will handle the higher voltage. As the solar irradiance declines, the supplied current will decline faster than the voltage, until the wattage is insufficient to power the pump.
For a smaller panel or larger pump, an MPPT controller can be used to optimize power draw from the solar panel. Pricing for a controller is inexpensive on AliExpress at $10-$20. Although quality unknown.
A panel's watt rating is based on its 17 volt maximum. 17V * 5.9A = 100 watts. When connected to a 12 volt pump, 5V * 5.9A = 29.5 watts isn't being utilized. A 100 watt solar panel might be able to power a 70 watt pump for a short time, for each day with peak solar input, except that many pumps require a multiple of their running power to start.
An MPPT includes a DC to DC converter, which would convert the panel's peak 17 volts to 12 volts and increase the amperage to the pump. A 100 watt solar panel could thus power a 70 watt pump for a longer period with an MPPT controller. Be sure the controller is rated to meet the minimum requirements. Oversizing the controller isn't a problem.
However, “ The MPPT charge controller will attempt to deliver as much current to the motor as possible. It may run the motor but it might also damage the motor. The charge controller is designed to charge batteries. ” Edward Hutchinson on Quora
I think a battery should not be attached to the MPPT Controller. Although there is some stored heat on the tubing walls, it won't last long, and I wouldn't want cooled water pumped to the tank. I'd rather the pump turn off and on again, or run slowly when a cloud passes over.
Pumps require a multiple of their running power to start. A capacitor may be used to provide the initial start power in the morning when solar panels are not producing full power.
Example of a pump with built in capacitor: https://www.youtube.com/watch?v=472XLJzaq2Q
Example of a DC pump that will start near its rated wattage: https://www.youtube.com/watch?v=J_qBrdfMOg0
I see 24V dc pumps there, maybe a 24V MPPT and a timer that sets the pump to run periodically when there should be sunlight, or photocell that turns on, allowing the pump to run when it is sunny out, or both, even better. Adjust the timer so that the battery is maintained day after day. The photocell will prevent the pump from running on really overcast days, some shielding of the photocell from the daylight will be necessary. Ronald Williams on Quora
A battery, a timer, a photocell, an MPPT, a pump, a solar panel… if you have enough surface on your roof, just add another hose and use thermosiphoning. If you have limited roof space, add efficiency by any of these means.
Safety first! (inside joke)
First day is 100% cloudy. At noon there is no flow within the solar collector. Maybe a reason for using a smaller diameter tubing is that the greater temperature within the hose will overcome viscous friction to start flow! I may need to add a pump due to the lower surface to volume ratio of the tubing.
Google says solar panels get 10-25% of their normal power output on a cloudy day.
I installed colored teflon tape to see thermosiphon flow, but didn't see it afterwards. I had bunched it up into the tank connection from the outside, expecting it to stretch out and wiggle with the flow. I thought maybe the bunched up teflon may prohibit flow, so I lowered the water level and disconnected the hose at the top to see what's going on. The teflon tape was stretched out into the hose! What?! There was thermosiphon flow in the opposite direction at night?
I forgot to add colored teflon tape to the bottom hose connector, which would have confirmed unwanted backwards flow, peering in from the top of the tank with a flashlight. I can use up the water in the tank to install new tape.
The tank is not black because I didn't buy it. I plan to insulate the tank and paint the exterior black, although I am having trouble finding a source for mineral wool insulation.
Before there is flow in the hose solar collector, all the hose heats relatively uniformly in the sun. The density difference that initiates thermosiphon flow is inside the tank where the water is cooler and denser than the inside the hose. So I'm not sure what's wrong compared to other systems that achieve flow, other than the larger diameter solar collector hose.
The top connection for the solar collector deforms the tank from the weight, so I plan to make a supporting structure.
I scrapped the floating duct idea to promote flow by reducing viscous friction. Municipal water shut-off is so rare in this town that in my case simplicity of design is more beneficial.
David Thomas on Quora suggested there may be air in the hose prohibiting flow. There was. I bled the air out by releasing the top hose connection. It took like 5 minutes for the water to flow smoothly out of the hose without sputtering. The shadow in the video is my arm, with hand covering the opening in the tank.
Thermosiphon flow began not long after connecting the hose back to the tank at noon. By 2pm the water at the surface was noticeably warmer.
I tied teflon tape to the end of a stick and held the tape where water returns from the hose at the top. I thought it would wiggle, but the flow is very weak, and the only difference between non-flow is a slight tilt of the tape. It was easier to see water flow just looking at the water with sunlight. Water with flow shows flashes of light, like water that's about to boil in a pot, where water without flow is completely still.
A bucket helps a bit in holding up the hose, and as a final solution I may nail the bucket to wood of two different heights for tilt, along with a U bolt for the hose. Good enough?
Around 6pm I placed a floating bluetooth temperature recorder into the tank, of the brand Inkbird. The temperature was 30 Celsius.
The temperature reached 35 Celsius on a partially cloudy day, according to the bluetooth floating thermometer, and started falling quickly at night. Around 12:30am, the temperature had lowered to 28 Celsius.
I used an infrared thermometer on the hose, checking for reverse flow. The temperature at the top, a foot from the tank was 24C. At 6 feet the temperature was 19C. The temp for the hose at the bottom returning to the hose was 13C. So there is reverse flow, but maybe not a lot? I will be buying a one way valve.
I noticed the second floor toilet was running continuously. I woke my parents who are visiting, and told them they forgot to unstick the lever when flushing and are killing the experiment.
Newly installed toilet. Maybe it's a simple fix but the toilets here are the most cheaply made that you couldn't even imagine. It's also leaking at the base. I rent, but I end up doing all the plumbing myself after the construction crew does the plumbing.
Temperature reached 40C on a mostly clear day. However, the temperature will likely fall to 25C by morning. I sent messages to local water tank manufacturers or distributors asking if they sell custom thermal insulation for the tanks.
I thought of a DIY one way ball valve with low fluid resistance, and plan to make one. But is it even worth it? I guess if I get a higher average temperature, then yes. Though I hardly have a laboratory environment, with the tank being used for house water all the time.
I can't reproduce the sticking lever problem for the toilet. I put the float further from the lever, but don't know what else to do.
I thought of a hanging support for the hose at the tank. Maybe I don't have to invent one and they already have it for sale.
Around 10:30pm, an infrared thermometer pointed at the top of the tank showed 85F 29C, and the bottom of the tank 72F 22C. I didn't know water stratification was so pronounced!
An uninsulated storage tank does not maintain the water temperature overnight, and at best adds a couple more hours of shower worthy temperature. It's more cost effective and simpler to use the volume of water in the hose as a solar shower during the day.
If you have no cheap access to a used water heater tank, then upgrading to a thermosiphon solar water heater is a jump in expenses.
As a rare item, the cost of mineral wool insulation in Peru is about 280 soles ($65) for 1m x 4m, 50mm, 100kg/m^3. Then you will need spray foam insulation to fill the volume above the tank inside of the circumference wall of mineral wool insulation. The spray foam will harden to create a removable lid.
The simplest and cheapest of all options is connecting a black hose straight to municipal supply. Municipal water is fed through the hose directly to the cold inlet of a gas or electric hot water heater.
No gas or electric hot water heater?
Naked black tubing can be more efficient than behind glass when the temperature of incoming water is below the ambient air temperature, such as municipal water sourced from a local mountain stream.
Water will not circulate through the hose to any thermal storage tank when the sun is out. Water will only run through the hose when hot water is being used, so best results would be had from hot water usage when the hose is hot from the sun. For a 1“ hose, best results would be had with water usage from 4 hours after sunrise to an hour before sunset. Like 10am to 5pm.
You would do well to live in a desert where there is hardly a cloud in the sky, so that you have solar heated hot water available every day.
You want 1” tubing for sufficient water volume and surface area afforded by 100 meters. For a greater diameter, you would have to wait longer in the morning before water in the hose heats.
A 3“ hose will start to resemble a storage tank, and retain a shower worthy temperature until 7:30pm. This is estimated from:
Reducing the heat loss at night from solar water heaters of the integrated collector–storage variety, Faiman et al 2001
A downside to 2 or 3 inch HDPE tubing is that it will not bend to a small inner diameter for a solar collecting spiral.
100 meters of 1“ HDPE hose holds 87 liters.
100 meters of 2” HDPE hose holds 286 liters.
Since 1992, a maximum of 2.5 GPM (9.5 LPM) is the USA federally mandated flow rate for shower heads. 100 meters of 1“ HDPE hose would yield 9 minutes of hot water.
I have yet to measure temperatures, but the darling test subjects said the water was too hot to shower with during the day, and it was pleasant at 5:30pm. Even with a 50% cloudy day.
During the day the hot water was poured into a bucket to mix with cold. I offered them a hot-cold mixing faucet for 30 soles, that normally costs upward of 100 (full brass), but they chose to keep what they have.
Carlos connected the HDPE to PVC with cement instead of using the supplies I gave to glue HDPE to garden hose (a snug fit), and the garden hose clamped to a PVC threaded nipple. HDPE expands much more than PVC, so the glue didn't hold.
The HDPE hose itself also sprung a leak, and Carlos put a PVC patch over it, that didn't hold for the same reason. The hose is suspected of having a manufacturing defect because it is soft at the spot it formed a lengthwise crack.
The plumbing connections now working are shown in the images. When the shower is not in use, water to the hose is shut off to relieve pressure.
Patching the HDPE pipe worked using a section of HDPE pipe instead of PVC. Instead of PVC cement, we used silicone. The surfaces of the pipe around the crack and the inside of the patch were scoured with sandpaper and cleaned with disinfecting ethanol prior to application of the patch.
See: Expansion Coefficients for Pipes, engineeringtoolbox.com.
Water Heater Circulating to Bare Hose
The best design for a freezing climate is a black storage tank within an insulated greenhouse enclosure. The volume of water is a large thermal mass that will prevent freezing.
Even with bare/exposed 3”+ diameter HDPE tubing, the thermal mass of the water within the tubing will be sufficient to not freeze if ambient temperature reaches an overnight low of a few degrees below zero Celsius.
HDPE can withstand decades of use in freezing temperatures, but requires special preparation of joints so that the joints can also withstand freezing. An existing HDPE tubing solar collector has been in service through many freezes without a problem. Zak Vetter
HDPE pipe can tolerate freezing much better than rigid pipe, an important consideration in alpine areas. HDPE stays ductile deep in sub-zero temperatures which means less potential for failure. In fact, water can freeze and thaw repeatedly inside of HDPE pipe without causing permanent damage to the pipe. genos.com
PE pipes may be used at operating temperatures between -40°C and +80°C.peakpipesystems.com
This article analysis was focused on regions where municipal water is either unchlorinated or untreated, but likely applies generally.
Legionella bacteria are naturally occurring in fresh water sources including rivers and streams but usually in low numbers. They accumulate in warm water and can cause Legionnaires' disease. In residential homes they accumulate in water plumbing.
Read more about the life cycle of legionellae.
The possibility of disease with solar water heaters is that of warm water at temperatures not sufficient for pasteurization.
One mode of transmission is from aspiration. Aspiration occurs when accidentally swallowing towards the airway or lungs, resulting in coughing. However, water for consumption here is either boiled or filtered.
Another mode of transmission occurs by the breathing in of aerosolized water. Residential aerosolized water is mainly from showering with water of sufficient temperature to induce water vapor. Warm water is not conducive to transmission leading to disease.
Only in the case that the solar water heater is producing water of sufficient temperature for a steamy bath is there a possibility of transmission.
Yet there hasn't been much recent research regarding showering as a cause for disease (see comments). Older research dismissed showering as a means for disease.
“ Despite potentially widespread exposure, human disease is relatively uncommon, except under circumstances where pathogen concentrations are high, host immunity is low, or exposure to small-diameter aerosols occurs. ” Risk-Based Critical Concentrations of Legionella pneumophila for Indoor Residential Water Uses, Hamilton et al 2019
There have been no animal studies on transmission via aerosol because of the difficulty in getting any animal sick.
Contrary to research, policy is being formed as if showering is an important mode of transmission. There could be a financial conflict of interest in that fear increases spending.
I have outlined methods of prevention, though they are guidelines more so than requirements. The danger of Legionella affects those to weak to stand in a shower.
Management of Legionella in Water Systems, nih.gov 2019
Whole Home Water Storage Tank
The majority of families here only have cold water plumbing. For the case where a whole house water storage tank is used as the tank for the solar water heater, warm water drawn from the bottom of the tank as a cold water source may promote bacterial colonies.
Chlorine or Ozone or some other disinfectant could be used to clear the tank and house plumbing of possible legionella. Thereafter whole house water filtration/purification can reduce bacterial nutrition from reaching downstream plumbing. Ozonated water can also be supplied continuously, as it is regarded as healthy to humans.
Dedicated Hot Water Storage Tank
For the case where a dedicated hot water storage tank feeds to a gas or electric hot water heater, the latter can heat legionella to 60 °C. There is no difference between solar or regular hot water delivery in terms of legionella risk.
According to farlabs.edu.au, as long as water in the coolest part of the solar tank reaches a sterilization temperature once in a week for the required amount of time, then there is negligible risk.
If guaranteed sterilization is necessary, then my recommendation is whole home water purification and ozonation.
Hose as Solar Collector and Water Storage
For the case of a hose directly connected to a showerhead, it depends. For an electric showerhead, legionella would be electrocuted12345 unless the solar heated water was sufficiently warm to turn off the electric. Then it would be the same as a normal showerhead.
In either case, the issue is not severe since on sunny days the stagnant water in the hose will be scalding hot. Sunny days are pasteurizing. Only the limited surface area of the hose leading to the roof and returning from the roof could develop legionella biofilms. For bathrooms in Peru, bathrooms are separate from the house. The short lengths to the roof of the bathroom probably create insufficient CFU quantity to cause disease.
Note that the case studies 4 and 5 that measured legionella counts with electric showerheads had cold water in the pipes.
Occurrence of Legionella in hot water systems of single-family residences in suburbs of two German cities with special reference to solar and district heating, Mathys et al 2007
The cities in the study above do not chlorinate their municipal water supply.
The percentage of homes contaminated with legionella was most closely related to the hot water temperature from a faucet delivery point:
Most interesting is that despite dwellings with solar systems having the lowest mean hot water temperature (47.4C), only 4% were contaminated with legionella.
They also found that 17% of homes with copper plumbing were contaminated compared to 3% for plastic or steel plumbing.
This is good news, considering I'm using solar and all plastic plumbing. However, the solar water heater systems in the study were most likely of commercial type which reach much higher temperatures at the solar collectors, so more evidence is needed to conclude a comfortable margin of safety.
Attack rates in outbreaks of Legionnaires’ disease are usually low; fewer than 5% of exposed persons develop clinical symptoms. A person’s risk of developing legionellosis depends on a number of factors, including the type and intensity of exposure and the exposed person’s health status. The elderly, smokers and patients with chronic lung disease or systemic immunosuppression are more susceptible. Legionnaires’ Disease: Update on Epidemiology and Management Options, Sabria 2012
Impact of Chlorine and Chloramine on the Detection and Quantification of Legionella pneumophila and Mycobacterium Species, Christopher Elkins, CDC 2019
“ Neither chlorine nor chloramine eliminated pathogenic Legionella or Mycobacterium organisms in the water samples tested. ”
Ratios of the number of positive (pathogen) samples to the number of negative samples by concentration for TClR category. (A) Chlorine. (B) Chloramine.
How do people contract Legionella?
The most popular theory is that the organism is aerosolized in water and people inhale the droplets containing Legionella. However, new evidence suggests that another way of contracting Legionella is more common. “Aspiration” is the most common way that bacteria enter into the lungs to cause pneumonia. Aspiration means choking such that secretions in the mouth get past the choking reflexes and instead of going into the esophagus and stomach, mistakenly, enter the lung. The protective mechanisms to prevent aspiration is defective in patients who smoke or have lung disease. Aspiration now appears to be the most common mode of transmission. legionella.org
Showers are not important disseminators for Legionella. Our view has credibility since Dr. Victor L. Yu was a co-author of the article published in the Annals of Internal Medicine 1981 that suggested Legionella might be transmitted via showers. Subsequent case-control studies showed our original conclusion was erroneous, although no retraction has ever been published. Subsequent studies from Belgium, Netherlands , University of Virginia, Wadsworth VA Medical Center, University of Iowa, Lackland Air Force Base, University of Pittsburgh, and University of Arizona also showed this conclusion was erroneous. The article by Sabria in Lancet Infectious Disease 2002 gives an overview of the studies. Most (but not all) U.S. transplant centers have quietly rescinded their ban on showering and cases of Legionnaires’ disease attributed to showering have not occurred. We agree with this policy.
Studies also show that disinfection of showerheads by chemicals or cleaning is ineffective long term given the fact that Legionella recolonizes the showerheads from existing biofilms in the pipes of the plumbing system. legionella.org
Aspiration is now known to be the major mode of transmission for hospital-acquired Legionnaires’ disease.2,19–24 Colonisation of the oropharynx by legionella was suggested by one study,25but not by another.26In a prospective study of patients with head and neck cancer undergoing tumour resection with its postoperative sequelae of aspiration, 30% of postoperative pneumonias were due to L pneumophila.13
Showering is often thought, erroneously, to be a mode of transmission. We reported a link to showering in a retrospective survey of three hospitals;27 however, results of subsequent unpublished case-control studies at the three hospitals did not show a link to showering. Similarly, neither further retrospective studies28,29 nor more rigorous prospective studies designed to assess the role of showering confirmed this association with showering.2,30 Some of the latter type of study even showed that showering might be protective for Legionnaires’ disease.22,31 The presumed reason for this paradoxical finding is that patients who are able to take showers are ambulatory and less likely to aspirate. As a result, our transplant centre allows patients to shower, and we recommend that the practice of prohibiting showering for fear of acquisition of legionella should be abandoned.
Legionella has been linked to aerosol-generating devices within hospitals that used tap water,32–34 but the degree of aerosolisation was intense in each of these reports. For example, use of jet nebulisers using contaminated water delivered directly to the patients’ airways was a significant risk factor for acquisition of Legionnaires’ disease within the University of Chicago Hospital.35 Nasogastric tubes21,22,36 and intubation2,37 have been linked to hospital-acquired legionellosis in several studies; the authors presumed microaspiration of contaminated water was the means of entry. Sabria and Yu 2002
I searched for more recent studies linking showering to disease, but didn't find any.
For example, the following studies show the presence of legionella at showerheads and shower vapor, but don't say anything about transmission rates, which depend on microbe concentration.
Occurrence of Legionella in UK household showers, Colins et al 2017
“We found that the rate of viable and cultivable Legionella aerosolized from the water jet was similar between the two showerheads: the viable fraction represents 0.02% of the overall bacteria present in water, while the cultivable fraction corresponds to only 0.0005%.” Risk Exposure to Legionella pneumophila during Showering: The Difference between a Classical and a Water Saving Shower System, Niculita-Herzel et al 2022
In addition to the entries below, the following research article has a list of prevention methods:
Existence and control of Legionella bacteria in building water systems: A review, Springston and Yocavitch 2017
Bacteria need something to feed on, and cannot live in purified water. Filtration systems can reduce or eliminate bacterial growth in house plumbing.
See separate article on Whole House Water Filtration
Any length of your water system that has a temperature favorable to legionella is a risk. Prevention only by a sanitizing temperature in the water heater does not guarantee pipes downstream from the heater. Point-of-use filtering may be easier or more affordable than whole house filtering?
Underground runs of plumbing can have an ambient temperature of less than 20C (68F), where legionella will be dormant.
Temperature affects the survival of Legionella as follows:
Legionella and the prevention of legionellosis, World Health Organization 2007
Safe Hot Water Temperature, ciphe.org.uk
In the sunniest week and the hottest achieved temperature for the uninsulated storage tank, water will not go near 50 °C. Furthermore, because of water temperature stratification, the cooler bottom of the tank would continue to host legionella.
Models of insulated storage tanks exist that have a mixing cycle to ensure all the water in the tank reaches 60 °C.
The oversimplified concept of water stagnation leading to proliferation of legionella has been misleading. Research has been done showing otherwise, but no one got the memo. Growth of Legionella during COVID-19 lockdown stagnation, Rhoads and Hammes 2021
The following study shows that one particular definition for “stagnation” is false:
Aims: Stagnation is widely believed to predispose water systems to colonization by Legionella. A model plumbing system was constructed to determine the effect of flow regimes on the presence of Legionella within microbial biofilms.
Methods and results: The plumbing model contained three parallel pipes where turbulent, laminar and stagnant flow regimes were established. Four sets of experiments were carried out with Reynolds number from 10,000 to 40,000 and from 355 to 2,000 in turbulent and laminar pipes, respectively. Legionella counts recovered from biofilm and planktonic water samples of the three sampling pipes were compared with to determine the effect of flow regime on the presence of Legionella. Significantly higher colony counts of Legionella were recovered from the biofilm of the pipe with turbulent flow compared with the pipe with laminar flow. The lowest counts were in the pipe with stagnant flow.
Conclusions: We were unable to demonstrate that stagnant conditions promoted Legionella colonization.
Significance and impact of the study: Plumbing modifications to remove areas of stagnation including deadlegs are widely recommended, but these modifications are tedious and expensive to perform. Controlled studies in large buildings are needed to validate this unproved hypothesis. Effect of flow regimes on the presence of Legionella within the biofilm of a model plumbing system, Lin et al 2006
According to Dr Eason Lin: “stagnant flow” means no flow. It is also called “deadend” in America English.“
For the solar water heater, water circulation through the solar collector may be a partial remedy because the water temperature under direct sunlight is sterilizing.
aka. Water Usage to System Size Ratio
At a higher flow rate with less surface area for legionella to colonize, the CFU legionella concentration of the water will be less and less likely to cause disease.
From this perspective, it's better to have less piping length and diameter, as well as a smaller sized solar storage tank.
It's also better to run the shower for a while before entering, if the shower hasn't been used in a few days. The stagnant water in the hot water pipes will be replaced with fresh municipal water or water from the hot water heater.
Ultraviolet light can inactivate legionella. 3-log (99.9%) inactivation can be achieved with a dose of less than 7 mJ/cm2.
” UV is only effective at inactivating Legionella in the water that flows through the UV reactor. For existing facilities with Legionella present in the piping systems downstream of a UV reactor, supplemental controls such as thermal treatment or chemical disinfection will be necessary. “
Technologies for Legionella Control, epa.gov 2016, p.59-60
Microbial factors can also determine whether a particular strain of legionellae can persist in a water supply, since certain strains produce substances that inhibit growth of other legionellae strains. This ubiquity, in addition to the fact that not all legionellae strains are pathogenic for humans, is one of the added difficulties for the control of Legionnaires’ disease. Recently, the RalF protein was shown to be an essential element for L. pneumophila pathogenicity, and only some species contain it. Legionnaires’ Disease, Sabria 2012
See section in the article on water filtration.
This may be motivation for doing away with simplicity and having a more complex heat transfer system between the solar collector and the water tank.
Consideration would be given to a comparison of toxins leaching from PVC, the plastic storage tank, and to black HDPE irrigation hose used as a solar collector.
If PVC itself leaches considerable toxins, then one would question what plumbing to select for a house and what is in use by municipal water distribution.
I plan to circulate water from the storage tank using the hose's ability to act as a thermosiphon.
Water expands by 4 percent from very cold to nearly boiling. Even less than that can drive flow without a pump. For two columns of water of the same height, the column with colder water will be denser and have a higher hydrostatic pressure at the bottom.
When the sun is shining, cooler water exits the tank at the bottom, and hotter water returns to the top of the tank.
The tank outlet lower than the inlet will give a higher hydrostatic pressure on the tank outlet. So will lowering the solar collector (the black hose) below the tank.
What are the complaints forwarded for a more complex and expensive system?
” Some of the shortcomings associated with conventional solar collectors include extra expense of the forced circulation system due to the pump and its extracted power, extra space required for the natural circulation system due to the position limitations required, the night cooling due to the reverse ﬂow of cooled water, freezing of the water on cold nights, pipe corrosion due to the use of water and the limited quantity of heat transferred by the heat transfer ﬂuid. “ Experimental investigation of a two-phase closed thermosyphon solar water heater, Esen and Esen 2005
A solar water heater that anyone can make with little investment, that can be sized to meet the need despite lesser efficiency, is superior to a two phase system that needs corporate backing to be mass produced. The only concern left uncovered thus far is reverse flow at night.
A one-way check valve would allow flow in only one direction through the black hose with sunlight heated water (the solar array), and not allow flow in the opposite direction at night when the array is cooler than the tank.
” For the local weather conditions in Cyprus and for the typical configuration of the thermosyphon solar water heaters used in the island, the thermosyphonic reverse flow is rather unimportant with minimal contribution to the night heat losses of the solar collector. “ On the Night Heat Losses in Thermosyphon Solar Water Heaters, Siamas et al 2010 (download)
The pressure differential created by thermosiphon flow is small. A one way valve would be counterproductive to heat exchange by adding viscous friction and reducing flow.
A thermosiphon requires a certain amount of pressure to counteract the dynamic head from viscous friction and begin flow. At night, the warmer tank and cooler hose may not have a sufficient pressure differential to start the reversed thermosiphon flow, so a check valve may not be required.
I will test without a one way valve to begin with, by attaching a strip of teflon tape on the inside of the tank connectors. I expect them to be wiggling when there is flow. I can also measure the tubing temperatures along the inlet and outlet with an IR thermometer.
If at night there is no flow when the tubing cools to a lower temperature than the tank, then a one way valve will not be necessary.
A thermosiphon requires a sufficient pressure differential to begin flow because water has weak molecular bonds that keep it from being a gas:
A one way check valve designed for little viscous resistance would be important, especially for colder climates that would have increased possibility for reverse thermosiphon flow.
Image from gharpedia.com or appropedia.org or lowtechlab.org
Thermosiphon flow happens around a loop consisting of two columns having different densities due to the heating or cooling of one of the columns.
The two columns of water start from the very bottom of the solar collector hose, and end at the hose inlet to the tank. One column is only made of hose, the other includes the tank between the outlet and the inlet.
If the inlet and the outlet are at the same height, there would be hardly any flow. The tubing would be heated evenly by the sun and either column would have the same average density. Some mixing may occur with the cooler water in the tank, but no thermosiphon. So the “height difference” h illustrated in the diagram above isn't the critical height for thermosiphon flow.
Under sunlight, a tank inlet higher than the outlet provides a density differential as one column now includes cooler water in the tank. Water then flows from the tank to the outlet, creating a longer height of cooler water and increasing flow.
The true height that influences thermosiphon flow is height H, from bottom of the hose to the tank inlet.
If you moved the hose above the tank, the height H would have the same rule, now being the distance between the outlet and inlet. Thermosiphon flow would still be possible, although with less pressure.
Another diagram I have seen is somewhat accurate, showing the critical height H-mid from the middle of the spiral solar collector to the middle of the tank.
Part of H-mid is height h. A reasonable approximation is taken for height h where all of the hose returning from the solar collector is hotter, and all the hose leaving the tank is colder. But there is more than only height h.
Averaging happens along the heights of the tank and solar collector. Water temperature stratification along the height of the tank can be averaged as half the height hotter and half the height colder. Along the solar collector spiral, water will become increasingly hotter, so an average is taken as half the height of the collector.
If the cold outlet hose is routed as the outer spiral, then the midpoint between lowest point of the hose and the center of the spiral would be a more accurate bottom for H-mid.
But why these averaging approximations for a model, when you can give the real life model? So I repeat again: The true height that influences thermosiphon flow is height H, from bottom of the hose to the tank inlet.
The actual pressure difference between the Hose column and the Tank column would be:
Integral from 0 to H [g * (ρH(h) - ρT(h))] dh
g is the gravity constant
ρH(h) is a function of height h representing density along the Hose column
ρT(h) is a function of height h representing density along the Tank column
Energy exchange by thermal radiation incident on a body is characterized by the following equation:
α + ρ + τ = 1
α is spectral absorption
ρ is spectral reflection
τ is spectral transmission
These elements are a function of the wavelength of the electromagnetic radiation.
Kirchhoff's law of thermal radiation states that for a body at thermal equilibrium, the sum of spectral absorption is equal to the sum of spectral emissivity. At specific frequencies the absorption and emission can be different, so long as the sum is zero.
The black body concept is an idealized physical object at equilibrium, which absorbs all incident radiation, and whose emissivity is equal to absorptivity at any wavelength.
Hypothesis: The rate at which a body reaches thermal equilibrium is influenced by the ratio of emissivity to absorptivity as a function of temperature difference with environment.
Hypothesis: The rate at which a body reaches thermal equilibrium is influenced by its function of emissivity based on wavelength.
The ideal material for the solar collector would have the lowest heat capacity, and the highest conductivity.
Heat loss from the storage tank when the sun isn't shining is mostly due to convection. The worst case of radiative heat loss would be if there was no atmosphere and the surface of the tank were a blackbody emitting to the vacuum of space with no cosmic microwave background:
P = A * ε * σ * T^4
For 4 meters squared of surface area, that's 2.2 kilowatts!
However, a clear night sky from the surface of Earth has a temperature and emmits its own radiation:
A cool clear night in the desert, with a temperature of 5°C and a relative humidity of 5%. The modified Swinbank formula yields a flux of 198 w/m2, which in turn corresponds to a black body temperature of -29.9°C or a gray body temperature of -10.9°C.
A warm clear night in the countryside, with a temperature of 15°C and a relative humidity of 25%. The modified Swinbank formula in this case yields a flux of 274 w/m2, which in turn corresponds to a black body temperature of -9.5°C or a gray body temperature of 11.1°C. stackexchange.com
I'm not sure how to calculate the area A of the sky for the above equation.
Based on the flawed assumption that Desertsun02's temperature reading was taken at steady state, I was motivated to know how long a hose I could use. But it wasn't steady state. The temperature reading was really hot because he had just turned on the water after it had been stagnant in the hose under the sun. I was mistakenly worried about reaching the melting point of the tubing if the tubing was too long.
I developed a mathematical model to scale the length of the tubing so that I would stay within a safe working temperature using larger diameter tubing.
Along the way I learned how awesome larger diameter tubing is for the application of thermosiphon circulating water to a storage tank.
The aperture is the surface area of the hose that faces the sun. The temperature increase ∆T of the water in the tubing is proportional to the aperture, the volume of water in the tubing, and the time spent traveling the length of the tubing.
∆T ~ aperture * Time / Volume
The aperture / Volume coefficient K shows that, for the same Time of sunlight exposure, ∆T decreases with increasing diameter D:
K = aperture / Volume = D * L / (π * (D/2)^2 * L)
K = 4 / (π * D)
The amount of Time (t) the water is being heated as it travels the length (L) of the hose:
t = L / mean flow velocity
t = L / (flow rate / Area)
t = Volume / flow rate
∆T ~ aperture * Time / Volume
∆T ~ aperture * ( Volume / flow rate ) / Volume
∆T ~ aperture / flow rate
A thermosiphon flow rate depends on the column height, but also on the average density difference between the two columns. Perhaps the Darcy-Weisbach equation for laminar flow can be used:
(ρT - ρH) * g * h / L = 128 * μ * Q / (π * D^4)
Q = (ρT - ρH) * g * h * π * D^4 / (L * 128 * μ)
Where Q is the flow rate
ρT is the average density over the temperature variation in the Tank column
ρH is the average density over the temperature variation in the Hose column
g is the gravitational constant
h is the height of the two columns
D is the diameter of the hose
L is the length of the hose
μ is the dynamic viscosity
With a constant column height h, flow rate varies with the average density difference, diameter D, and hose length L:
Q ~ (ρT1 - ρT2) * D^4 / L
∆T ~ aperture / flow rate
∆T ~ L^2 / [(ρT1 - ρT2) * D^3]
For two hoses of the same length, L is also a constant:
∆T ~ 1 / [(ρT1 - ρT2) * D^3]
We can observe that while the density difference is a factor for flow rate Q and temperature increase ∆T, it is dwarfed by the influence of the tubing diameter.
For the same length of hose, a larger diameter hose will have a lower tank return temperature (∆T) and greater flow rate (Q), losing less heat to ambience with more aperture. A greater solar energy transfer rate to the tank.
Assuming the same start temperature, the average column densities will also be equal for two different hoses with equal ∆T.
∆T ~ L^2 / [(ρT1 - ρT2) * D^3]
∆T * (ρT1 - ρT2) can be scaled as unity leaving:
1 = L^2 / D^3
So for two hoses of different diameter, and equal ∆T imposed, hose length L can be scaled as follows:
L = √(D^3)
So a 2” hose would be 8 times as long as a 1/2“ hose to have the same temperature difference, where column heights h are equal.
The emphasis above because YouTubers are convinced that they shouldn't use more than 1/2” pipe. They must think that getting the water in the tubing hot fast is a good thing? When in reality the hotter something is the greater the rate of energy loss to ambience. You want the energy going to the tank or swimming pool, not lost to the wind.
Calculations below are for 500 meters because I remembered the length of a roll incorrectly.
Desertsun02 uses 30 meters of quarter inch poly or half inch PEX tubing to achieve 60C at a slow, unknown flow rate, supplied by partial municipal water pressure.
Update: The assumption that the temperature reading took place at steady state led me down a wrong path. I didn't figure it out until further down in trying to choose an oversized circulation pump.
Using the Hazen-Williams equation for a 1 meter gravity flow:
500m of 1" PEX (22.2mm ID) = .065 liters/s and .17 m/s
30m of 1/2“ PEX (12.3mm ID) = .063 liters/s and .53 m/s
Coincidentally, .063 liters/s is 1 gallon per minute, which looks like this. Maybe double the trickle in Desertsun02's video.
A thermosiphon won't have 1 meter of gravity pressure. Maybe 1 cm of gravity pressure:
500m of 1” PEX = .0054 liters/s and .014 m/s
30m of 1/2“ PEX = .0052 liters/s and .044 m/s
In both cases, the flow rate is about the same, but the flow velocity in 30m x 1/2” hose is 3 times faster. Viscous friction is mostly negligible at slow velocity.
mean flow velocity (S) = flow rate / area (A)
A = π(D/2)^2
For two tubes with the same flow rate, the mean flow velocity (S) varies with the square of the diameter (D):
S2/S1 = A1/A2 = (D1/D2)^2 = (22.2/12.3)^2 = 3.26
Error: A thermosiphon flow rate (f) depends on the column height. Two different diameter hoses will have the same flow rate, and will have the same temperature at the return to the tank if the aperture is the same:
∆T(f) ~ D1 * L1 = D2 * L2
With the same flow rate and aperture (a), you can compare ratios of the time water spends traveling in the tube with the diameters of the tubes.
∆T(f,a) ~ K1*t1 = K2*t2
∆T(f,a) ~ t1/D1 = t2/D2
Driven by a 1 meter column thermosiphon (Hazen-Williams example above) with 1 cm hydrostatic pressure difference, a typical water molecule spends ~682 seconds (30/.044) flowing through the 30m x 1/2“ hose.
A water molecule would spend ~35714 seconds (500/.014) in the 500m x 1” hose, receiving 29 times more solar energy.
Solar energy comparison calculation
To equalize the temperature increase, we would shorten the 500m hose to 17 meters:
500m / 29 = 17m
Sanity check using ID for solar aperture:
∆T(f) ~ D1 * L1 = D2 * L2
17 * .222 = 3.77
30 * .123 = 3.69
A function of both the temperature difference and the height between the hose outlet and inlet would drive the thermosiphon flow. In the case where the tubing and tank are both on the same level of roof, these metrics are limited and insufficient to drive the flow required for 500m of tubing.
Introducing a solar powered water pump would increase flow, reducing the temperature of the hose and heat loss to ambience.
The design specifications are sophisticated:
∆T ~ aperture / flow rate
To make sure the temperature doesn't exceed 60 C, let's assume Desertsun02's flow rate is a gallon per minute, which is 3.79 liters per minute, rounded to 4. From the temperature section above, I'll need 29 times this flow rate for the 500m x 1“ tubing, or about 4*30 = 120 liters per minute.
According to Sta-Rite Pipe Friction Loss Charts, I would have a flow velocity of 11 FPS, going over the recommended flow velocity of 5 FPS and maximum velocity of 7 FPS.
Being outside the recommended range, likely with turbulent flow instead of laminar flow, made for wacky estimates on the amount of head I would need to drive the flow rate I want. Surely the online calculators assumed laminar flow.
Wacky online calculator results
If I use 2“ tubing, and a length of 100 meters, I would have 6m^2 of aperture, and would need 13 gpm for the same ∆T as Desertsun02. The spiral aperture with 100m of 2” tubing would have a 3 meter diameter.
5.3 FPS would render 52 gpm (210 liters/min) and a cooler hose. As mentioned, a cooler hose will be more efficient at collecting solar energy.
The pump would need to handle 5 meters of dynamic head. Pumps meant to handle more head will be less efficient, as pumps are either designed for higher pressure or higher flow rate. The type of pump needed is a circulator pump.
A 100 watt water pump on Amazon is rated at a maximum of 13 gpm and 7m of head. Another model provides 50gpm and 6m of head, but requires 300 watts. AliExpress bilge pump claims 50 gpm and 8m of head, using only 120 Watts. Another AliExpress pump claims over 52gpm with 6m of head, using only 80 Watts. How do you calculate marketing hype?
The last pump comes with different nozzle sizes for attaching tubing, and largest nozzle is 38mm, which is about 1.5 inches. That's not the 2 inches I wanted for the 5.3 FPS!
When I find centrifugal pumps in the USA market that output in the range of my desired flow rate, they consume much more power to do so!
The answer is in the image below:
If I get the 12000 liters per hour AliExpress pump (53 GPM), I won't get 53 GPM unless the head is around 0.7 meters.
What does 50 GPM look like? Insane!
I will have to pick the biggest pump.
Update: I made the mistake of assuming Desertsun02's temperature readings were steady-state. I think the temperature increase would be more like 5-10 degrees Celsius for 100 meters of tubing and one GPM. Just about any cheap circulation pump would work. Even a super cheap $10 plastic one that advertises a maximum of 800 liters/hour.
“ Centrifugal pumps are the most common pump type for the transfer of low viscosity fluids in high flow rate, low pressure installations, which makes them ideal for applications that require the pump to deal with large volumes. The centrifugal pump design is often associated with the transfer of water… ” Positive Displacement vs Centrifugal Pumps, castlepumps.com
“ The most common pump types to use a centrifugal pump in a residential system are … circulation pumps (central heating pumps) which are used to circulate water in closed systems that provide heat, air conditioning and hot water. ” Positive Displacement Pumps vs Centrifugal Pumps: The Complete Guide, anchorpumps.com
Consider the Einstein model E = m * c^2, and tell me what you see wrong with the following model from messiah.edu:
I'm not going for a temperature change prediction. I want a simple model that gives an understanding of the phenomenon so that better decisions are made in the design.
Reducing the heat loss at night from solar water heaters of the integrated collector–storage variety, Faiman et al 2001
Maximum useful efficiency (MUE):
µ = Mw * Cw * (Tmax - Tsunrise) / A * int(I(dt))
This is useful if you were going to compare two systems and you could measure total irradiance and the high and low temperatures.
“solar irradiance was measured with a LiCor solid state pyranometer positioned in the plane of the aperture.”
Effect of Height Difference between Solar Thermal Collector and Storage Tank on the Entransy Destroyed, Adihou et al 2018
Aside from the nonsensical “entransy destroyed”, they have a useful plot of flow speed versus tank height, showing a logarithmic increase in speed with tank height. A higher flow rate decreases transit time, which decreases the temperature difference that drives the thermosiphon.
Raising the tank higher increases the heat transfer rate to the tank, but with diminishing returns. Best not to spend money on a SpaceX sized tower.
Another study with flawed results
People in this small town on a mountain at 1000 meters, don't really have cold weather. Coldest temperature I've experienced is 58F as an overnight low. During winter the high could be between 70-75F. Summer months are as high as 82F.
The cost of living here is very very low. Even those well off don't spend on heating water, because they don't think it's needed. They are accustomed to using cold water for showering.
In the big city along the coast 3 hours away, it's slightly warmer and the same culture applies. Although there, they have water shortages, and it's normal for municipal water to flow only during certain hours of the day, year round. Thus, they require having water tanks above the house.
Even though the small town on the mountain has a period of around 2 months with a slight lack of water, locals think it's important to have a water tank. There may be less than 10 days of the year that the municipal water inlet gets clogged during rainy season due to debris. I think because the more affluent big city (relatively) uses water tanks, the locals think they should have them too. The municipal engineer agreed with the assessment. Values are influenced by factors other than common sense.
The hot water pilot light never got turned on in this culture.
During my recent 6 weeks in Guadalajara, Mexico, I looked in vain for any solar water heaters. There were several companies which advertised in the yellow pages but, when I went to them, they were no longer in business.
This in a city which is about a mile high and which enjoys clear sun filled days much of the year. They also have flat roofs which would make the installations easy.
I mentioned this to a guy I met who is a real estate broker in California. He said that many solar water heaters were installed in his town, Chico, during the 70s when the gov’t subsidised solar installations. He says that most real estate contracts he deals with now include the instructions to the sellers from the buyers to “remove all solar water heating panels and piping” as part of the sale contract.
I had three solar water heaters (I AM persistent) that froze and broke. These were all designs that had water in small tubes. These were installed in Tempe, Arizona which rarely has freezing weather and yet one even broke when temps only reached 40 degrees. This was because the unit was a black body radiating into a clear black sky and so was colder than ambient.
“ China started SWH (solar water heater) utilization in the 1970s. By the end of 2007, the country had installed 1.08 x 10^8 m2 (collector area) of SWHs, which accounted for more than 60% of SWHs installed in the world (Luo, 2008). ” Solar water heaters in China: A new day dawning, Han et al 2010
“ China is awakening to the need to fundamentally rethink the innovation pathways by which the two industries are developed and managed, for more effectively solving development bottlenecks, such as a lack of breakthrough innovations in the SWH (solar water heater) industry and a lagging domestic market for the PV industry. ” Comparing the Technology Trajectories of Solar PV and Solar Water Heaters in China: Using a Patent Lens, Wang et al 2018
“ Chinese solar PV is predominantly produced for the export market, relies on intellectual property-intensive technology and has received much financial and political support from the central and provincial governments. On the other side, solar water heaters are an indigenous Chinese technology that is found everywhere across China, especially in rural areas. They have developed from grass-roots levels to mass products with very little central government support. Although being largely absent from high-level discussions and policies, solar water heaters could contribute a lot to China's low carbon transitions that are driven at the local level. ” Solar PV and solar water heaters in China: Different pathways to low carbon energy, Urban et al 2016
“ Without government support, poor com- munities might be left behind in a renewable energy transition. More incentives and help to deprived regions should be offered by the central government to gain the beneﬁts of adopting renew- able energy. ” China's transition to green energy systems: The economics of home solar water heaters and their popularization in Dezhou city, Li et al 2011