Following a full day with 4 workers we had the maximum 14 coils that could fit onto the two roofs laid out (52.5 sq m). Full exposure to the South. I would have preferred 70 sq m to match the surface area of the pool, and by the end of summer in 2014 I decided to extend the number of coils to a total of 26, or 97.5 sq m. While a pool cover is said to almost double the usefulness of any pool heating system, I hope to avoid that. Pool covers tend to be both quite ugly and a discouragement to spontaneous use of the pool.

Our pool has 2" piping for the filtration. 26 tubes each with an OD of 15mm all taking water in parallel will have a cross-sectional area larger than the cross-sectional area of a 2" pipe. Initially I expected that we could route the entire flow of the water ex-filter through the collector coils. Unfortunately I had forgotten about pressure drops through such long, 15mm tubing (1/2" ID). I am assuming a 12.5mm ID. This calculator is a handy method for calculating pressure drops for given flow rates:

http://irrigation.wsu.edu/Content/Calculators/General/Pipeline-Pressure-Loss.php

The pool holds some 97,000 litres that is circulated by a pump rated at 26,000 l/hr, or a throughput of 7.2 litres/second. The pump turns over the pool every 3.7 hours, obviously way over-sized by the usual criterion of once every 6 hours. We can use the above calculator to see how much water we can send through each 250m coil and still keep the pressure drop to under 5psi. This turns out to be quite low; only 0.042 lps per coil. I.e. 15% of the filtered water may be sent via the 26 coils but no more, for a 5 psi pressure drop. We do have the fallback of tapping into each 250m coil several times, say, 4x each, so that each section within the large coil becomes only 63m long. Only nuisance is as we add connections, we are also exposing ourselves to more risk of leaks. So it's a compromise between more connections leading to smaller pressure drops, or lower flow per coil leading to a higher temperature for the return water and more exposure to leaks because of a higher operating pressure. Ideally, for trouble-free longevity one wants a minimal pressure drop with a minimal temperature rise, with the fewest possible connections. Straight runs of the agri tubing, each 25m or so in length, massively parallel, would offer the lowest pressure drops, but with hundreds of leak-prone connections :-(

How much electricity will I save? I managed to find a Solar Irradiance Calculator for nearby Dubai here:
http://solarelectricityhandbook.com/solar-irradiance.html

Measured in kWh/m2/day onto a horizontal surface:

Jan-----Feb-----Mar----Apr----May----Jun----Jul----Aug----Sep----Oct-----Nov-----Dec
3.95---4.91---5.33---6.39---7.29---7.40---6.61---6.39---6.09---5.55---4.48---3.68

People who have bothered to measure the efficiency of this type of agri-tubing coil collectors report efficiencies of around 70%, similar to commercial uninsulated (no glass cover) versions. Consequently our final 97.5 sq m installation should be able to capture a remarkable 8000 kWh per month during the coldest months of December and January; some 240 Rials Omani's (US$ 600) worth of electricity via a resistive heater per winter month. The hardware and labour for the 26 coils cost about R.O.1500; say, roughly R.O.15 per sq m. Looks good so far. Here are the monthly weather data for Oman (from http://en.wikipedia.org/wiki/Oman ):

Deg C: Jan-----Feb-----Mar----Apr----May----Jun----Jul----Aug----Sep----Oct-----Nov-----Dec
Avg Hi: 27-----26-----29-----34------39------40-----38-----36-----36-----35-----30-----27
Avg Lo: 17-----17-----21-----24------29------31-----30-----28-----27-----24-----21-----18

So how much heating can we expect?

Specific Heat Capacity of water is 4185.5 Joules/kg-degK
or approximately (4.19/3600) kWh/liter-degC = 0.001163kWh/liter-degC

Delta T in deg C = 860*kWh / (water volume in liters)
260 kWh per day in December and January should heat up the water by about 2.3 deg C

Unfortunately the continuous evaporation of water from the pool implies a continuous chilling and the 2.3deg C does not get carried over fully into the following day. Let us make a rough estimate of how much heat is lost purely because of evaporation:

Following some casual checks, I determined that our pool loses about a cm depth of water daily, reducing to perhaps 0.5cm during cooler winter days. That is at least 350 liters or 350 kg of water per winter day! The Latent Heat of water vaporization is 2.26*10^6 Joules/kg (or 0.628 kWh/kg). Consequently the pool loses some 200 kWh daily just because of water evaporation during a winter 24 hour period. That's why you have to pay attention to the area of the pool, and also why a pool cover makes such a huge difference if you are heating a pool.

Still, even though the ambient temperature at night on average drops to 17 deg C, and despite the continuous evaporation of water, the solar heating does manage to nudge the pool temperature to the daily high (mid 20s) on most December and January afternoons. To be absolutely certain that I did end up with an effective heating system, I measured the temperature in our pool on an average mid-December late afternoon and compared it immediately thereafter with a nearby neighbor's unheated pool. His pool was at 22 deg C, ours was at 26 deg C. Ambient temperature at that time was 25 deg C. So, it does work! Anyway, if a swimmer feels a bit cold, he can always sit or stand in front of one of the return jets in the pool and feel a bit of warmish water caress him...