This section covers the sizing of the collector circulation pump and
the pipe diameters for a solar space or water heating system. The example worked out below is for a drainback system, but the comments at the end explain what adjustments to make for a closed loop system with antifreeze.

The basic underlying requirement is that you want a pump and plumbing system that will push enough heat transfer fluid (typically water) through your solar collectors to efficiently remove the heat that the sun is depositing in them. Too little flow, and the collectors will run hotter and less efficiently, too much flow and you are wasting money on bigger pipes and pumps than the system needs, and using more pump power than you need to.
The steps involved in the pump and plumbing sizing:
I will use my Solar Shed project as an example. Its shown in detail here....
In a nutshell, it has 6 collectors of 40 sqft each. The collectors have half inch vertical risers tubes (about 9 per collector), and 1 inch top and bottom manifolds. The collectors are placed side by side with the manifolds connected together. From a flow point of view, this puts all the collectors in parallel. All the details are shown here....
Water is pumped from a storage tank just behind and below the collectors to the lower manifold on the right most collector.
Water returns from the bank of collectors to the tank via the upper manifold on the left most collector.
On the Solar Shed, all the plumbing runs are very short, so I'll make the example a little more realistic by saying that the tank is another 20 ft away from the collector  this will lengthen the supply are return pipes and number of fittings to more realistic values.
The example covers sizing the pump (3), and the supply and return lines to the
collector (1).
This is a drainback system, meaning that the when the pump is not operating, all of the fluid in the collector and plumbing system drains back into the storage tank by gravity. This provides the freeze protection for the system, and means that plain water without antifreeze can be used. At the end of the example, I'll briefly cover what the changes would be to do the pump and pipe sizing for a closed loop system with antifreeze.
The collectors need to have sufficient flow to remove the heat from the collector under sunny conditions. This flow rate can be calculated knowing the solar heat input to the collector and collector efficiency, but its easier to just use the manufacturers recommendation. Since my collectors are homemade, I will use the recommendations for a similar commercial flat plate collector. Heliodyne makes a series of similar flat plate collectors, and recommends that the flow rate be between 0.025 and 0.075 gpm per sqft of collector. You can probably guess from this wide range that its not critical to hit some particular flow rate  anywhere in this wide range is OK.
If you want to see the actual loss in efficiency and heat output from the collector as you reduce flow rate, look here...
So, lets try for the middle of the range at 0.04 gpm per sqft of collector. The target flow rate the is:
Target Flow Rate = (240 sqft)(0.04 gpm/sqft) = 9.6 gpm
So, about 10 gpm flow to the whole collector array. Note that the flow could be anywhere from 6 gpm up to 18 gpm and still be in the recommended range.
Just as a side note, 6 collectors is about the maximum number of collectors that you want to connect in parallel this way. If too many collectors are connected in parallel, the flow to all of the collectors will not be even. For larger numbers of collectors, the collectors can be divided into banks of parallel connected collectors.
For a drainback system, when the sun comes on the collectors, the controller will turn the pump on, and the pump must be able to pump water all the way up to the top of the collector to start the flow. In order to make sure the pump can do this, you must carefully measure the VERTICAL distance between the water level in the tank, and the top of the collector. If the top of the collector is 30 ft over and 11 ft up from the tank water level, the number you want is the 11 ft  this is the vertical distance from water level to top of collector. Measure this carefully  don't eyeball it. Note that you measure from the water surface level in the tank, not from the pump level.
This requirement at startup to pump water from the tank all the way to the top of the collector is a tough requirement for pumps, and it will likely be the main consideration in picking the pump to use.
For the my Solar Shed system, the vertical distance from the water level in the tank to the top of the collector is 11 feet 3 inches.
So, the pump must be capable of pushing water up at least this vertical distance. Some margin should be allowed about the vertical distance. In other words, don't choose a pump that just barely has enough static head to make the top of the collectors. People vary on how much margin should be added, but Alan R.ushforth, who has done a number of drainback systems and has had experience with pumps that don't quite get the flow started recommends that the pump have a static head capability that is 20 to 30% greater than the vertical distance from tank water level to the top of collector. I would use that recommendation.
So, for the Solar Shed, the minimum pump static head would (11.25ft)(1.25) = 14 ft of static (startup) head.
Once flow is well established, and the return line is running full, the only pressure that the pump has to overcome is the friction losses in the pipe  that's what the next step is about.
In this step, we will guess pipe sizes, and
then calculate the total pressure drop through the system for: 1) the
collectors, 2) the supply and return pipes and the fittings in these
pipes, and 3) any valves or other pressure drop causing components. With the trial pipe sizes, we look up the flow velocity and pressure drop. If the velocity is too high, or pressure drops larger than a reasonable pump handle, then we up the pipe diameter and try again. 
Pressure Units You will find several units used to express pressure drop in pipes and in pump specs. Here is how to convert between them:

We will need the lengths of the supply and return pipes, and the number and type of each fitting and valve. For the Solar Shed, the supply and return lines are very short, because the tank is right below the collectors. This is nice, but probably not typical, so I've added another 20 ft to each and a few extra fittings.
Lets try adding up the system pipe pressure drop with 10 gpm flow and 3/4 inch supply and return pipes. The system uses type M copper pipe (this is the thinner wall pipe commonly sold at hardware stores).
Adding up the pipe lengths and fittings for the system:
Item Supply
Return
Qty Equivalent Length (ft) Pressure drop
(psi)Qty Equivalent Length (ft) Pressure Drop
(psi)Manifold (1 inch) 12 12 0.3 12 12 0.3 Pipe (3/4 inch) 28 28 2.5 52 52 4.6 Elbows (3/4) 4 8 0.7 6 12 1.1 Couplings (3/4) 2 0 0 2 0 0 Valves (3/4) 0 0 0 1 0 0 Total 3.5 6.0
Build a little table like the one above to record and sum up the pressure drop numbers.
Pipe Pressure Losses
Using the numbers from the table above, we will sum up the pressure drops for the supply and return piping and all of the fittings and valves.
To get the pressure drop for the 28 ft of 3/4 inch
supply plumbing at the 10 gpm flow rate, look up the loss per foot at 10
gpm for 3/4 inch type M pipe. From the table at the right, this is
0.089 psi per foot of pipe. So, 28 ft would be (28 ft)(0.089
psi/ft) = 2.5 psi. Note also the flow velocity of 6.2 ft/sec. Velocities between 5 and 8 ft/sec are considered marginally high. Velocities over 8 ft/sec should not be allowed  if you get a velocity over 8 ft/sec the tube diameter is too small. Do the same lookup for the 1 inch diameter collector manifolds using the 1 inch diameter pipe chart at the link just below. You should get 0.025 psi per ft at 10 gpm flow rate  this gives 0.3 psi for the manifold drop. Here are some pressure loss tables for the various types of pipe: Pressure drop for copper pipes...
PEX pipe pressure drops... CPVC Household Plumbing Pipe dimensions and pressure drops .. And, CPVC Household Plumbing Pipe dimensions and pressure drops... (look for the "CTS" tables), or just the CPVC table here... Industrial CPVC/PVC pipe pressure drops... Black polyethylene pipe pressure drops... Note that all of these
different pipe materials have different inside diameters for the same
nominal size pipe. For example, on 3/4 inch pipe, M copper is
0.811 inch ID, household CPVC is about 0.715 inch ID, Industrial CPVC is
0.824 inch ID , PEX is 0.677 inch ID, HPPE (common black poly) is 0.824
inch ID. (1) The CPVC commonly available in hardware stores is "copper tube sized", meaning the OD matches copper tubing for the same nominal size  since the wall thickness is greater than copper pipe, this makes the ID (and pressure drops) larger. 

Fitting Pressure Drops
Use the fitting equivalent length table to
the right to convert the fittings (elbows etc.) into equivalent lengths
of straight pipe. So, for the 4 elbows in the supply line, the equivalent length of pipe is 2 ft per elbow, or 8 ft total. Then calculate the pressure drop for this 8 ft the same you did for the straight pipe sections  (8 ft)(0.089 psi/ft) = 1.1 psi.
Do the same thing for the couplings and the gate valve  which turn out to have 0 equivalent lengths for 3/4 inch pipe. The fittings equivalent length table is from www.Copper.org


Evaluating the Results
Filling in all the pressure drops in the table, we get a total of 3.5 psi loss on the supply lines and 6.0 psi loss on the return line. This gives a total pressure drop of 9.5 psi, or 22 ft of pressure head. We also have a velocity in the 3/4 inch lines of 6.2 ft/second, which is marginally high.
As we will discover in the pump sizing step (next) this is quite a bit of pressure loss, and that coupled with relatively high velocity probably means we should take a look at going up to 1 inch diameter supply and return lines  so, lets do that.
If you go up to 1 inch and work the pressure drops in exactly the same way, but using the 1 inch pipe diameter table, you get this result:
Item Supply
Return
Qty Equivalent Length (ft) Pressure drop
(psi)Qty Equivalent Length (ft) Pressure Drop
(psi)Manifold (1 inch) 12 12 0.3 12 12 0.3 Pipe (1 inch) 28 28 0.7 52 52 1.3 Elbows (1 inch) 4 10 0.3 6 15 0.4 Couplings (1 inch) 2 0 0 2 0 0 Valves (1 inch) 0 0 0 1 0 0 Total 1.3 2.0
The 1 inch pipe lowers the total pressure drop from 9.5 psi down to 3.3 psi ( 7.6 ft head), and it gets our 6.2 ft/sec marginally high velocity down to 3.7 ft/sec. A little bit of extra diameter makes a big difference.
So, this is likely to be the way to go, but we will see
after the pump sizing. Another option if you did not want to go up to the 1 inch pipe would be to lower the flow rate down toward the lower end of the allowed flow rates. Dropping the flow rate down to the low end of the allowed flow rate would cut the pressure drop in the 3/4 inch pipe down by about half.

Side Notes Why are we
ignoring the pressure drop in the collector riser tubes? On the other hand, If you have a serpentine collector in which a single length of pipe is wound back and forth through through the full collector, the pressure drop will be larger and should be included. Just as an example, if a 25 sqft serpentine collector uses a single 50 ft length of half inch copper pipe to collect heat, the the flow will be about (0.04 gpm/sqft)(25 sqft) = 1.0 gpm. The pressure drop for 50 feet of half inch copper pipe (from the table below) is about (0.007 psi/ft)(50 ft) = 0.35 psi, or about 10 inches of water head. Effective Manifold Length In the above estimates, I've included only half of the collector manifold length. The idea is that the flow is steadily decreasing in the manifolds as each collector takes some of the flow out of the manifold  so, including half the length is a rough way of accounting for this. If you have a lot of loss in the manifolds, then you might want to do this more accurately by dividing the manifold up into segments, each with a different flow rate. Minimum Pipe Diameter In drainback systems its not considered a good idea to go to less than 3/4 inch supply and return pipes no mater what the pressure loss in that smaller diameter pipes may not allow a full drainback. Supply and return pipes must also be sloped downward toward the tank, and the runs should be kept as direct as possible 
We need to pick a pump that provides:
You use pump curves to determine which pumps might meet those criteria. We will use the pump curve family for the Taco HVAC circulator pumps to pick a candidate. This series of pumps has been used for lots of solar applications, but there are many other options pump options out there that you could look at...
These are the pump curves for the entire Taco "00" series circulators. For each pump, the curves show the combination of flow rates and pressure heads that the pump can produce.
We need a pump that can produce a startup or static head of at least 14 ft. To find the startup head for a pump, trace its curve over to where it meets the left vertical access  this is the startup or static head for the pump. For example, the 006 pump produces about 8 ft of static head  not enough for our 14 ft requirement.
We need a pump that produces about 10 gpm with 22 ft of head (for 3/4 inch pipe), or 8 ft of head (for 1 inch pipe). To see how each pump does in meeting this requirement, go vertically up the 10 gpm line, and read to the left the pressure head that each pump can produce at the 10 gpm flow rate. For example, a 008 pump can produce almost 8 ft of head at 10 gpm flow rate.
So, for the 3/4 inch pipes, the pumps that might make it are: (we need 14 ft startup head, and 22 ft pressure head at 10 gpm)
011  30 ft of startup head, 23 ft of pressure head at 10 gpm
013  34 ft of startup head, 27 ft of pressure head at 10 gpm
014  22 ft of startup head, 17 ft of pressure head at 10 gpm
The 014 is a bit short on pressure head at 10 gpm, so the flow would fall at bit below the 10 gpm, but still well within the OK range.
But, these are pretty honking big pumps with high power consumption  lets see how things turn out for the 1 inch pipe.
For the 1 inch diameter, the pumps that might make it are: (we need 14 ft of startup head, and 7.6 ft of pressure head at 10 gpm)
007  11 ft of startup head, 7.5 ft of pressure head at 10 gpm
008  15 ft of starup head, 7.8 ft of pressure head at 10 gpm
Some of the larger pumps would also easily meet the flow and pressure requirements, but would be serious overkill.
The 007 is a bit tempting, but does not quite even make the 11.25 ft of actual startup head let alone the 14 ft that includes the recommended 25% margin.
Overall, I like the 008 as a good match on both flow and startup head at a reasonable power consumption  so that's why I picked it for the system:) It has been doing great for 5 years.
If I were to look further into this example with an eye toward lowering the system cost a bit and the pumping power a bit, I'd have a look at keeping the 3/4 inch pipe, and lowering the flow rate closer to the lower edge of the acceptable range. This would save a little money on piping and also might allow changing to a pump that uses less power. The flip side of lowering flow rate is the the collector will run a little bit hotter, and will not be quite as efficient. But, it does not look like any of the Taco pumps would work for this, but a look at Grundfos or other pumps might find a good one.
There are many other pumps out there, and you want to consider things like price, power consumption, reliability, ...  not just the that the pump meets the flow and pressure requirements.
Closed loop system that use antifreeze for freeze protection are always completely full of fluid, so there is no startup head requirement as there is for drainback systems.
But, the antifreeze increases viscosity and pipe friction losses, and the antifreeze has a lower heat capacity, so more antifreeze mix must be circulated to transfer the same amount of heat out of the collector.
The following rough procedure to cover closed loop systems assumes a 5050 water glycol antifreeze mix.
To do a closed loop system, use the same procedure as for the drainback system with these changes.
Note that these correction factors (1.15 and 1.3) actually change with temperature  the ones I've used are for 140F with a 50/50 mix of glycol antifreeze and water.
There could be a whole section on using antifreeze, but a couple highlights: 1) use polypropylene glycol, which is nontoxic, 2) use an antifreeze formulated for solar systems  it will have additives to keep it from turning into ugly stuff that can ruin your system, 3) check the pH of the antifreeze every year, and replace it if the pH is to low (acid) or its otherwise not looking good.
Gary June 25, 2010
Updated Aug 18, to include 25% margin on startup head.