Cost-Effective Metering of Energy Use in an Ascending Pipes Distribution System

Description and Rationale

We propose to meter energy use by hot water heaters in an ascending pipes system by establishing an independent, solar-powered, horizontal loop-like system containing a special but inexpensive liquid.  It is a liquid that “freezes” upon heating, blocking the flow of the liquid through each unit-specific horizontal loop of the system.  The length of time heaters are on in the unit will correspond with the length of time the flow is blocked.  The flow for each unit is metered by a flow counter at each fluid pipe branch that translates the flow into electronic pulses.  When the pulse counts are tabulated at the meter box for all units, the unit with the lowest number of counts will have the highest energy use.

The Heat-Freezing Liquid

There are two possible liquids we found for in this application.  The first was interestingly first discovered in France about 10 years ago (2004).[1]  It is a solution of water and two organic compounds, a-cyclodextrine (alpha-CD) and 4-methylpyridine (4MP).  As discovered, the solution turned solid at temperatures of between 45-75°C, which falls within the range of hot water temperatures used in radiators.  However, the temperature that the solution becomes a solid can be customized by adjusting the concentration of alpha-CD.  As the concentration increases, the solution will freeze at lower temperatures.   Limitations of this fluid are the high concentrations required (>500 g/l), which suggest higher cost per liter.

The second fluid is likely to be far more more cost-effective since it is 99% water; it is also a more sustainable solution.  Methylcellulose is derived from cellulose, the material that makes up plant cell walls.  It is used as a laxative (an example is Citrucel), so it is safe for human contact.[2]  When a solution of methylcellulose is heated above 55°C for a 5 g/L solution, it turns into a mechanically strong gel.[3] Prices are in the range of 24 €/ 400 g, which for a 5 g/L solution means the cost will be 0.3 €/L.

Item Quantity Total Cost
Methylcellulose solution, 5 g/L 73.2 L (calculated on page 4) 21,96 (5,49 per unit)

The Flow Sensors

We propose the use of DC-powered water flow sensor counters that convert flow rate into a DC square pulse whose frequency is directly proportional to the flow rate and which have an accuracy of +/- 2%.  While there is a very low cost flow sensor, we will include the higher-priced unit in our cost estimate since it is more of a known quantity.  Such flow sensors with pulse output are compatible with a wide variety of existing metering products, and it is likely that the building owner has a metering system in place that can accept these pulses as input.

Name Cost Notes
Aquacomputer G1/4 Flow Sensor[4]

Flow rates: 0.67-10 LPM (liters
per minute)
Pulse rate: 169 pulses/L

Power: DC 5V 5-13 mA

Made in Germany

37,90 [5] Much information available on this
EWP-SNR2103B Water flow sensor/counter[6]

Pulse rate: 40 * Q (Q = LPM)

5,2 € / $6.50 USD Very low cost but not much information.

The Pump

Our design calls for a single pump per 4 floors.  Although the pump will be more expensive due to higher flow rate and pressure (the water must be piped to 4 different branches, up to a height of 4 floors), it will make maintenance much easier than having one pump per floor, thus saving labor costs.  It is also necessary to have one pump in order to ensure an equal flow rate to each floor.  This flow rate in turn will be responsible for increasing the number of pulses per hour coming from each floor at a rate directly proportional to the amount of flow, which as we will see later is inversely proportional to the amount of energy use.

The pump is literally the heart of the system, pumping the working fluid at the minimum flow rate required to maintain 2% accuracy (approximately 1 liter per minute per floor, or a minimum of 4 LPM). It is DC-powered, designed to be charged using solar power.  It should be located at least 50 m from any heater (part of the length can be in a coil that is in a different room from a heater) to give the fluid plenty of time to completely re-liquify before reaching the pump.

The Heat Exchanger

The flow rate of 1 LPM per floor is much too fast a flow rate for a system in which the fluid needs some time to gel upon exposure to a heater.  The required wait time is accomplished by creating a net of small-diameter tubing behind each heater.  Such a net can be created from two 1 to 10-way air splitters[7] (2,64 € together) connected by 4 mm inner diameter plastic tubing to fit the outputs of the air splittters and of an appropriate length to fit behind the radiator, but ideally not less than 15 cm in length.  The width will be the distance across each 1 to 10 air splitter, which was estimated from 1 to 8-way air splitter dimensions to be 15 cm[8].   This assembly should be enclosed within a protective, thin-walled plastic case that is resistant to being heated from radiator contact, such as high-density polyethylene, polystyrene, or polymethylmethacrylate (PMMA).  The resulting heat exchanger will act as a set of capillaries in the fluid circulatory system, enabling a factor of 10 reduction in flow rate per splitter tube.

There should be a minimum 1 cm thick thermal barrier on all sides of the heat exchanger except the side in contact with the radiator.  This is for tamper resistance as well as for improving the ability of the heat exchanger to “freeze” its working fluid when its corresponding heater is on.  Such a conductive and radiative thermal barrier is sold as brand name Reflectix;[9] a lower-cost version is available for 0,64-1,52 € / sq m with 0.034 W/m*K thermal conductivity and 96-97% thermal reflectivity.[10]  This barrier should be placed inside the plastic case for improved appearance and durability.  If this is done, the plastic case will have to have an inner dimension of 2 cm thick; the other dimensions should be 15 x 25 cm.

Such a polystyrene case that will meet the dimensional requirements is sold by MCS in the form of a box frame for photographs.  It is 10.9 x 8.7 x 1.7 inches (27,7 x 22 x 4,3 cm), offering ample space for double insulation on the back and sides.  A quantity of 30 is available for $97.20 USD,[11] making the unit price 2,6 €.

Clear plastic tubing with a 4 mm inner diameter is available at bulk prices of £0. 42/m (0,53 €/m) for 1020 m.[12]

Item Quantity Total Cost
1 to 10-way air splitters 2 2,64
Plastic case for containment 1 2,6
Reflective insulation, double
0,20 sq m 0,13-0,3
Clear tubing, 4 mm I.D. 10 lengths of 15 cm (1.5 m) 0,8
Total cost per heater 6,17-6,34

Sizing the Tubing Network

Assuming a height of 3 m per floor, a 4-floor building will need 12 m of up-flowing pipe and 12 m of down-flowing pipe.  For the amount of tubing needed per floor, we take the average home size in France of 113 sq m[13] and assume a roughly square floor plan.  A pipe transecting such a typical unit would be 10.6 m in length, meaning the perimeter would be 42.5 m in length.  We assume all heaters will be located along the perimeter of the unit.  Each floor thus requires at most 42.5 m, for a total of 194 m for one complete loop.

However, the system must have two complete loops of 194 m for the reason that the heaters must be connected in parallel.  In a series arrangement, any one heater can turn on and solidify its working fluid, blocking the flow.  However,  another heater can do the same, resulting in no additional flow blockage with which to determine energy use.  Thus, each heater must be fed by two lengths of pipe, with the heat exchanger being the locations where the pipes meet.

This can be visualized in the following diagram.  On the left is a standard parallel arrangement of heaters.  In the center we have moved the right set of pipes to the left.  To the far right, we have consolidated the pipes into a long conduit-like stretch.

Thus for this parallel arrangement we will need (194 m x 2) – 24 m = 364 m of piping.  The volume of the methylcellulose solution necessary to fill 364 m of 8 mm tubing is 0.0732 m3 or 73.2 L.

The bulk cost of 8 mm inner diameter silicone tubing is £0.94/m (1,18 €/m) for 1020 m.[14]  The price per unit is given below.

Item Quantity Total Cost
Clear tubing 8 mm I.D. 364 m 429,52 € (107,38 € per

Sizing the Pump

A pump must work to overcome frictional losses in the system as well as to pump across any elevation difference that might be present.  Since this system is a closed fluid system, there is no elevation difference, and thus the pump only has to overcome frictional losses.[15]

To know the pressure required to supply the minimum flow rate of 1 LPM (0.0167 liters per second) through each flow counter at a minimum reasonable water speed of 0.33 meters/second,[16] we use the Darcy-Weisbach equation, which is the most accurate model for estimating frictional head loss in steady pipe flow.[17]  This equation is as follows:

where v = flow velocity, L = pipe length, D = pipe diameter, r = density of the fluid, and f = the Moody friction factor, which accounts for the effects of the Reynolds number.[18]

For the density of methylcellulose solution we use 1,000 kg/m3 which is the density of cold water since the solution is 99% water and will be mostly at the temperature of cold water throughout the length of the pipe.

For the pipe diameter we use the 8 mm inner diameter of the pipe which will connect to the heat exchanger.

Lastly, to find the Moody friction factor f we must first find the Reynolds number.  This number is calculated as follows:

Re = v x D x (r / m)

where m = fluid viscosity.

The quantity p/u = 753,000 at room temperature of 20°C,[19] rising to 3,090,000 at 60°C.  This makes the Reynolds number = 0.33 m/s * 0.004 m * 753,000 = 6024 at the low end; a similar calculation gives 24720 at the high end of this temperature range.  Since most of the liquid will be at or near room temperature throughout the system, we use Re = 6024 to find the friction factor of about 0.035.[20]

Now the Darcy-Weisbach equation can at last be employed:

P = 0.035 * (0.33 m/s)2 * (1000 kg/m3)/2 * (388 m / 0.008 m)

The pressure drop required is equal to 86711 N/m2, equivalent to 8.84 mH2O or 12.6 psi.  This pressure is a safe factor of 2.5 times lower than the bursting strength of the weakest component in the system, the silicone tubing.[21]

For 5-year, 50,000-hour maintenance cycles, a pump that has a warranty over this time period should be used.  Such relatively low-pressure, low flow, low power consumption pumps can be found in computer liquid cooling systems.  One pump that will work for this application is the Swiftech MCP35X, able to put out a flow rate of 1 liter/minute at the necessary pressure while at as low as 70% output.[22]

Item Quantity Total Cost
Swiftech MCP35X 1 160,6 € (40,15 € per unit)

Sizing the Solar Power System

The MCP35X is designed to work a nominal 12VDC within a range of 9-13.4 VDC.  At the nominal voltage, the maximum nominal power draw is 36W while the maximum amperage is 3 A.  The pump will need to run at most 24 hours a day, for a solar energy use requirement of 36W x 24h = 864 Wh.  We will next see how this determines the size of the solar power system.

Determining Panels

Sunlight is variable in parts of Europe, but for this estimation we will assume an average of 4 peak sun hours per day.  We must try to generate 864 Wh within that timeframe.  To generate this energy entirely within this timeframe, the amount per hour that should be generated is 864 Wh / 4h = 216 W.  Thus we chose a 220 W, 33.8 V panel such as the Heckert Solar NeMo, manufactured in Germany, having an 11-year product warranty and 25-year guarantee of 80% of the rated power.[23]

The Charge Controller and DC-DC Stepdown Transformer

This component connects the panels to the batteries and keeps them optimally charged.  The best charge controllers are maximum power point tracking varieties, though these are more expensive than pulse width modulated types which will be suitable for this job.  The amperage rating of the charge controller should be greater than the panel wattage divided by the system voltage.  For a 220 W panel at 33.7 V this means a minimum of a 10 A charge controller.  However, charge controllers come in only 12, 24, and 48VDC varieties, sized according to the battery banks they will charge.  A 33.7 V panel cannot charge a 48V battery bank, so we will need to use a 24V charge controller such as the CE listed[24] Morningstar ProStar PS-15M controller that is rated at 15 A.[25]

Determining Batteries

To allow the system to remain autonomous for 3 straight cloudy days, the solar power system will require an energy storage capacity of 864 Wh * 3 = 2592 Wh.  At 12V the amp-hour rating of the batteries must be 2592 Wh / 12 = 216 Ah.  This can be supplied with four 110 Ah sealed lead-acid batteries (SLA batteries should not be drawn down more than 50% to avoid prematurely shortening battery life).  If suitable batteries cannot be obtained locally, we recommend a manufacturer such as PowerSonic which meets EU regulations.[26]

For the charge controller to charge the four 12V batteries, they must be wired two in parallel, then each parallel pair must be wired in series.

Item Quantity Total Cost
110 Ah sealed lead acid battery 4 639,36 € (159,84 € per
Solar panel 1 159,38 € (39,85 € per unit)
Charge controller 1 64,08 € (16,02 € per unit)
Total for solar power system 862,82 € (215,71 € per

Additional Components, Labor, Maintenance, and Cost Total

Item Estimated Cost
Expansion Tank

Allows the fluid in a closed loop
system to expand and contract upon temperature changes

30 € (7,5 € per unit)

To connect the solar batteries to the pump and flow

160 € (40 € per unit)
Assembly and Installation

Based on 2 people taking 5
business days to install at a labor rate of 25
€ / hr

2000 € (500 € per unit)

System is very simple; one person could spend one day
maintaining it every year.

200 € / yr
Total cost of all components,
including labor, not including maintenance
3841 (960,3 per

Pulse Rate to Energy Use Conversion

To measure the thermal energy used from each housing unit relative to the total energy used for the building, we must translate the pulse counts from each unit’s flow sensor into energy use.

We know that the number of pulse counts is inversely proportional to the amount of time the fluid flow was blocked by each heater.  The time that the fluid flow is blocked is proportional to the amount of heat released by the heater (watts) over a period of time (seconds), and energy use is equal to power times time.  The time can be obtained from the pulse count record, and the heat can be obtained from the temperature difference required to solidify the working fluid.

Measuring Time

The unit with the least energy use will have the highest pulse count, and all other units with higher energy use will have successively lower pulse counts.  The inverse ratio of each unit’s pulse counts to the total number of counts for all units recorded at the meter box will provide an indication of how much more energy one unit consumed compared to another.  In this way, the energy use can be individualized by unit.

Measuring Heat

The heat released by the radiator and that goes into freezing the working fluid can be given as follows:[27]

q = 2 π k (ti – to) / ln(r/ri)


q = heat transferred per unit time per unit length of cylinder or pipe (W/m, Btu/hr ft)

k = thermal conductivity of the material (W/m.K or W/m oC, Btu/(hr oF ft2/ft))

to = temperature outside pipe or cylinder (K or oC, oF)

ti = temperature inside pipe or cylinder (K or oC, oF)

ln = the natural logarithm

ro = cylinder or pipe outside radius (m, ft)

ri = cylinder or pipe inside radius(m, ft)

For all units in a building, these terms will be constant except for the temperature outside the piping, so they bear no relevance to our problem other than adding a constant term.  As for the temperature outside the piping, some rooms will be colder than others and some warmer, and on first glance it may seem that we do not know which would be which without measuring the indoor temperature.  However, we do have a measure of indoor temperature – the pulse counts – and so the pulse count record can inform this missing variable.

Summary of the Solution

The amount of total energy used for the building is reflected in the building owner’s energy bills.  The amount of thermal energy used by each housing unit can only be measured by system components that respond proportionately to the heat given off by those units.  What this system measures at each unit’s flow sensor can be subtracted from the building owner’s energy bill in kWh in order to obtain the proportion of energy used to heat that unit (#1).

This method of using a heat-freezing working fluid to indirectly measure the amount of heat energy used by a unit is compatible with any type of distribution system (not limited to ascending pipes), and will absorb heat from any type of heat source a heat exchanger is placed behind (#2).

The solution is fully automated, being driven entirely by solar energy (#3).

Care was taken to select a flow sensor and flow rates which would yield high accuracy counts (+/- 2%) of the duration of blockages, which would indicate the length of time a heater was on (#4).

No 3rd party data was used in this solution (#5), and it is very unobtrusive (#6), sitting behind radiators and connected only by small diameter conduit running along the floor.  If desired, wooden trim can be installed over the conduit to remove it from sight.

Tamper Resistance

The most tamper-prone part of the system is the heat exchanger, which although hidden behind each heater, is still exposed to residents who may want to reduce their billing (#7).  If the resident prevents the flow of fluid in any way, the system will treat this as a flow blockage which will cause the resident to be charged more for the tampering.  The only way a flow blockage can occur is if the fluid is heated, or heat exchanger pipes are deliberately disconnected by a resident believing that the fluid flow rate is directly proportional to the amount they will be billed, when in fact it is inversely proportional.

The correct way to tamper with the system is to increase the flow rate, which would be possible if the resident were to place ice directly onto the heat exchanger to counteract the heating from the radiator.  However, due to the thermal insulation on all sides of the heat exchanger except the side in contact with the radiator, such an attempt at cooling would not be possible since the warm side would continue to heat the heat exchanger, and the insulation on the warm side would further serve to trap heat against the pipes.

Durability and Cost

Effort was taken to find system components with a minimum 5 year / 50,000 hour warranty (#8).  Some components such as the solar panel should last well beyond a 10-year timeframe.

We attempted to provide a full picture of cost, of which 52% of that cost estimate went to labor and is likely to be an overestimate (#8). However, any new system will likely cost more than estimated when first installed due to having to figure out the installation procedure.  Despite that, we believe that the simplicity of the solution would lend itself to being implemented within a very short time frame, perhaps a matter of months from the initial sourcing of system components to the actual installation within a building (#10).  We have pointed out where each piece of equipment necessary for the system has a CE label (#11).

Since the system is entirely solar-powered, there is no reliance on existing building infrastructures (#12).

Finally, to our knowledge, there is no third party patent art preventing the use of a methylcellulose solution as the active fluid in a hot water energy use metering system (#13).

[1] Background information:; abstract available here:!divAbstract
[3], page 5
[16] – solved for velocity in meters per second; diameter = 8 mm, flow rate = 1 liter/minute
[18]; another such Moody diagram is available here:
[20] – see graph under “Pressure difference calculation”
[21], table on page 2

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