The correct sizing of pipes is critical to the effective operation of any system that moves heat from one place to another using a fluid medium.
In many systems the location of heat generation is remote from the point of heat use, therefore the heat needs to be moved between the two places. An efficient way to do this is by using a heat carrying fluid such as water. Obviously if we are using a fluid such as water we are likely to be containing it in pipes. These size of these pipes dictates how much of that heat energy we can move from one place to another over any given time period.
Leaving the subject of pipes just for a moment, think about heat transfer, or moving heat. If we are eating a meal that is too hot we instinctively blow on the food before putting it in our mouth. Thinking about what is going on here we can see that it is heat transfer, the air passing over the food is receiving heat and moving it into the wider environment. Blowing harder forces more air over the food and it cools more quickly as a result. To describe this in technical terms we could say that we have 'increased the flow rate'. Blowing harder requires more energy, and we should also consider this when thinking about flow rates. Lets look at an example to further explain the principles...
We like solar thermal, so let’s use one for our example. The exact specification of the collector is unimportant for our purposes today, it could be tubes or flat plate, all we're interested in is the heat that it generates.
In order to size pipework for such a system we need to know the following:
The power to be 'moved' in W (Watts)
The temperature difference between the heat source (solar) and the heat receiver (hot water cylinder)
The required flow rate (either from manufacturer’s recommendations, or by calculation)
The specific heat capacity of the fluid (water is 4187Joules per kg)
Back to our example...
The sun is shining and our roof mounted collector is getting hot. All that heat just sitting there on the roof is no good to us, we want to move it down into a hot water cylinder. We need to quantify ( give it a number) that heat, in order to start working things out!
Let’s say that our collector is generating 2kW ( One Kilowatt – about the power of a standard kettle). The other bit of information that we need is the 'flow rate' and the temperature at the cylinder in a likely 'worst case'. The flow rate is the amount of fluid moving past a given point per second required to move the 2kW we have sitting on the roof – down to the cylinder. Thinking back to the food example it's 'how hard you're blowing'.
Power and flow rate are connected by a simple formula that involves two other 'key ingredients' – temperature difference and the specific heat capacity of water. In our example the base of the cylinder where the solar input is, can be assumed to be about 11 degrees, this is an average temperature for incoming water in the UK. So now we need to know what the temperature is at the collector. Well actually we don't need to know, we can put a maximum figure in. If we do this, then we know that the sizes that we come up with will handle whatever the collector can throw at it!
A typical maximum temperature could be 100 degrees in our example. To get the temperature difference we subtract our cylinder temperature of 11 from our collector temperature of 100, this gives us a figure of 89 degrees.
The specific heat capacity of water can be taken as 4187Joules per kg (don't worry about the units for now!) The flow rate is expressed in kg per second which we can convert to litres a minute at the end. To find the flow rate we divide the power in watts of our collector by our temperature difference multiplied by the specific heat capacity of water.
Flow rate = power divided by (temperature difference, multiplied by specific heat capacity)
Now back to our example...
2000Watts divided by (89 x 4187)
2000Watts divided by (372,643)
Flow rate = 0.00537kg per second
As the density of water can be taken as '1' (one litre = 1kg)
Flow rate = 0.00537 litres per second (This is the figure to look up in the tables)
To get litres per minute multiply this result by 60 (60 seconds in a minute)
There for the flow rate is 0.322 litres per minute.
Manufacturers of pipe produce tables showing pressure drop and flow rate. For our example we could use 8mm diameter smooth copper pipe, according to the tables this has a pressure loss of 0.010 metres head per meter length at 0.0064 litres per second.
If our collector is 10 meters from the cylinder then we have total pipe run of 10 x 2 = 20m.
20 x 0.01 = 0.2m (this is expressed in metres and needs to be added to the vertical height difference to size a pump.)
Now I don't want to spoil the party but...
The temperature difference is not always the same on solar thermal systems, but we still need to move that 2kW. What happens when the collector is at 100 but the cylinder is at 45?
2000W divided by (100-45) x 4187
2000W divided by 55 x 4187
2000W divided by 230,285.00
Flow rate = 0.00868 kg per second, or litres per second
Flow rate in litres per minute = 0.52
Looking at manufacturers tables we can see for smooth copper tube this is still ok. But less than 1 litre a minute is an unlikely figure for a standard solar circulating pump. This is because the speed the water is flowing at is 0.3m/s and it would take 33 seconds to cover the 10m from collector to cylinder!
An ideal speed for fluid in pipe systems is 1.0 m/s (meters per second)
A figure of 4 litres per minute is more likely for a domestic solar thermal system. This is 0.066litres per second. From the manufacturer’s tables this flow rate is beyond that advised for 8mm smooth copper tube, even for 10mm smooth tube where the pressure loss is 0.2m head per meter length. Using 10mm pipe in this instance could mean using a bigger pump than standard. Stepping up a size to 15mm smooth copper pipe gives a pressure drop of 0.024 metres head per meter length, and puts our example system back within the performance range of a standard solar circulator pump.
For flexible stainless steel pipework, popular in solar thermal kits, the pressure loss is much higher and manufacturer’s tables should be consulted.
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