From Appendix 2 table A-15E of the Fundamentals of Thermal Fluid Sciences book, the properties of water at 50 degrees Fahrenheit and 190 degrees Fahrenheit are documented as in Appendix A-1. From engineeringtoolbox.com a graph that compares water pressure and water discharge in gallons per minute based on different nominal hose diameters is used to find the expected water discharge from a 100-foot hose.

 

The water pressure inlet is assumed to be 40 psi based on the average inlet pressure from a hose in a house. Using the equation in Appendix A-1 and A-2 each of the flow rates from the graph are converted from gallons per minute to a velocity in feet per second. With the velocities for all three sizes of piping the Reynolds numbers is determined seen on Appendix A-3. From table 14-2 page 553 of the Fundamentals of Thermal Fluid Sciences book the roughness is given for copper and then converted from feet to inches. Next the Moody chart in Appendix 1, figure A-27 from the Fundamentals of Thermal Fluid Sciences book is used to determine the Darcy friction factor for each copper pipe size.

 

Next the maximum pipe length is determined for each of the standard pipe sizes as calculated on Appendix A-4. The energy to heat the water from 50 to 190 degrees Fahrenheit is calculated on Appendix A-5 based on the maximum flow rate in each standard size piping. With the energy determined from Appendix A-5 the ideal length of the pipe is calculated as shown on Appendix A-6 for the maximum flow rate of the water. The energy to heat the water from 50 to 190 degrees Fahrenheit for the standard size pipes at 0.5 gpm, 1.0 gpm, 1.5 gpm and 3.0 gpm seen on Appendix A-7. All of the used flow rates are within the design requirements of hot water output.

 

With the energy calculations at the specific flow rates stated the length of the pipes for each standard size were calculated for the previously specified flow rates as seen on Appendix A-8 through A-11. With these calculations, an overall length of 20 feet and 3/8 inch pipe size was selected for the design.