Determine the size of the pipe in section (3) using the longest length method.

Steps to Solve

1. Identify Total Flow Rate for Section (3)

First, determine the total flow rate that will be used in section (3). The outlets connected to this section are:

• Outlet D (Furnace): 115,000 Btu/h
• Outlet C (Water Heater): 55,000 Btu/h

Total flow rate $Q_{total}$ can be calculated as: $$ Q_{total} = 115,000 + 55,000 = 170,000 , \text{Btu/h} $$

2. Calculate Equivalent Length for Section (3)

Next, calculate the equivalent length of section (3). The actual length from the point of delivery (10 ft) and velocity changes (optional fittings) can be considered. If we assume we have no extra fittings here:

The total equivalent length $L$ would simply be: $$ L = 20 , \text{ft} , (\text{length of section (3)}) $$

3. Convert Flow Rate to Cubic Feet per Hour

To find the appropriate pipe size, we need to convert the flow rate from Btu/h to Cubic Feet per Hour (CFH). The conversion factor for natural gas is approximately: $$ 1 \text{ Btu/h} \approx 0.001 \text{ CFM} $$

Thus, $$ Q_{CFH} = Q_{total} \times 0.001 = 170,000 \times 0.001 = 170 , \text{CFM} $$

4. Determine Pipe Diameter Using the Longest Length Method

Using a gas piping chart or formula for the chosen pressure drop of 0.5 in. wc., we can find the diameter of pipe needed for $170 , \text{CFM}$ with a length of 20 ft. From tables or calculations, we can determine pipe sizes.

5. Consulting Table for Pipe Size

Using the appropriate table for pipe sizes and the determined flow rate and length, let's say it indicates that for 170 CFM:

• An approximate pipe size of 1 ¼ inch diameter might be necessary based on common fittings and pressure drop.