Size section (5) in the drawing above using the branch length method.

Steps to Solve

1. Identify the flow rates for the sections Determine the total flow rate in section (5) by adding the flow rates of all outlets connected to this section:

• Outlet D (Hydronic Boiler): 120,000 Btu/h
• Outlet C (Water Heater): 50,000 Btu/h
• Outlet E (Gas Fireplace): 40,000 Btu/h
• Outlet B (Range/Oven): 75,000 Btu/h
• Outlet A (Clothes Dryer): 35,000 Btu/h

Total flow rate: $$ Q_{\text{total}} = 120,000 + 50,000 + 40,000 + 75,000 + 35,000 $$

2. Calculate the total flow rate Now calculate the total: $$ Q_{\text{total}} = 120,000 + 50,000 + 40,000 + 75,000 + 35,000 = 320,000 \text{ Btu/h} $$

3. Calculate the equivalent length using the branch length method Using the branch length method, consider the lengths of the pipe sections and their fittings.

Assume the lengths:

• Section (5): 20 ft
• Outlet pressures and friction loss for pipe materials will also account for the fittings: Assuming 1 fitting contributes 5 ft equivalent length.

4. Combine lengths for total equivalent length The total equivalent length (EHD) can be calculated as: $$ L_{\text{total}} = L_{\text{section (5)}} + n \times L_{\text{fitting}} $$ Assuming there are 4 fittings contributing 5 ft each, the total equivalent length: $$ L_{\text{total}} = 20 + 4 \times 5 = 40 \text{ ft} $$

5. Approximate the size using the flow rate and equivalent length Use tables or charts to determine the size of section (5) based on the calculated flow rate (320,000 Btu/h) and equivalent length (40 ft).

At this point, through reference to typical gas piping charts, we find that for approximately 320,000 Btu/h:

• Size (5) can be estimated as 30 EHD.