Sizing the circulator pump

Today my plan is to size the circulator pump from the chip boiler through the manifolds of the existing oil-fired boiler.  The formula is: Q = h/(Cp*p*Delta T) Where Q is the heat transfer in Gallons per minute, Cp is the specific heat capacity, a constant based on the fluid, in this case water, p (really rho, I need help figuring out how to add greek letters and subscripts) and an assumed temperature drop or Delta T.  Since it is my intention to run the chip boiler at 180°F and set the min temp on the oil burner at 130°F this will give me a 50°F temperature before the temp of the furnace requires it to fire.  By leaving myself enough room I am hoping the Arduino controller and good temperature monitoring will preclude the oil boiler from firing.  For the formula however I am going to assume a temperature difference of 20°F.  So, again assuming a 30,ooo Btu chip boiler,  a Cp for water of 1 BTU/Lbm/1°F, p (rho) the density of water, 62.34 lb/cu ft., Delta T=20°F and to convert BTU to gal/min 7.48 Gal/cu ft  Therefore Q=30,000(7.48 gal/cu ft)/((1 Btu/lbm/1°F)(62.34 lb H2O/cu ft)(60 min/hr)(20°F)=2.9997 GPM

http://www.engineeringtoolbox.com/water-flow-rates-heating-systems-d_659.html

This formula gives the flow rate and now I need to calculate the pressure drop or head loss.   The formula for this is:

Click to access SelectingCirculators.pdf

HL = k x c x L x (f1.75)  Measuring the distance to the proposed location of the chip boiler, I get about 18′ of piping to and from the existing boiler and approx 10 of additional piping in the boiler, assuming 4 elbows.  Planning on using either 3/4″ pex tubing or 1/2″ copper.  Using Table 1 in the above link either 3/4″ pex or 1/2″ copper will be acceptable for a flow rate of 3 gpm.  I would prefer to use the 1/2′ copper since it is a relatively short run and will require less  hangers and difficulty doing a nice neat job through the utility room.    From Table 2 I see a equivalvent feet of 1.55 for each elbow so 4 x 1.55 ft= 6.2 ft  From Table 3,  k =.0159, From Table 4 Water at 180°F, c=0.933, finally the flow rate raised to the 1.75 power is 6.83.  So the total length is 18+6.2+13=37.2 ft.  I calculate a rough head loss of approx. H loss=.0159*37.2*.933*6.83=3.77 ft  Use the graph to find the correct pump having the conditions of 3 gpm  flow and 3.77 ft of head It looks like a Taco 003 or a Taco 006 pump will work just fine.   After some internet research using my normal internet heating component supplier I will probably use a Grundfos UPS 15-58FC, 3 Speed Circulator pump, 1/25 HP, 115 V

The lower manifold shown in the right hand picture is the cold return from the zones.  I am planning on adding the hot water from the chip boiler in at this point to prevent the oil-fired burner from starting.  This will also increase the heat reservoir by heating the water in the furnace as well.  Lastly I plan on adding a 4th zone onto the existing manifolds to take advantage of the existing 2nd heating coil in a solar hot water tank I have separately heated by solar evacuated tubes.  This will give additional options for the Arduino to dump heat.