# Determining Proper Duct Size Using ASHRAE Duct Friction Chart ## Objective Find the proper round duct size for an airflow of **200 CFM** with a **friction loss of .08 to .09 inches of water** using the ASHRAE duct friction chart. --- ## Step-by-Step Solution ### Step 1: Understand the Data - **Airflow (CFM):** 200 CFM - **Friction Loss:** .08 to .09 inches of water - **Duct Size Options:** 13, 14, 15, 16 inches ### Step 2: Use ASHRAE Duct Friction Chart The chart relates **friction loss per 100 feet** of duct to **duct diameter** and **airflow**. Since we are given a friction loss range, we aim to find a duct size where the **friction loss per 100 ft** falls within .08 to .09 inches. ### Step 3: Find the Required Duct Diameter for 200 CFM The relationship between airflow, duct diameter, and friction loss is approximately: \[ Q = \text{Area} \times V \] where: - \( Q \) = CFM (convert to CFM) - \( \text{Area} \) = cross-sectional area of the duct - \( V \) = velocity in ft/min But more directly, the ASHRAE chart gives typical velocities and corresponding friction losses for standard duct sizes at certain flows. ### Step 4: Approximate Velocity for Given Friction Loss The typical velocity ranges for round ducts at typical friction losses are: | Friction Loss (inches/100 ft) | Approximate Velocity (ft/min) | |------------------------------|------------------------------| | .08 to .09 | 800 - 100 | For our case, the velocity should be around **800 - 100 ft/min**. ### Step 5: Calculate Duct Diameter Use the formula: \[ Q = \frac{\pi}{4} \times D^2 \times V \] Rearranged for \( D \): \[ D = \sqrt{\frac{4Q}{\pi V}} \] Where: - \( Q = 200\, \text{CFM} \) - \( V \) = velocity in ft/min Convert CFM to CFM, noting that: \[ D \text{ in ft} = \sqrt{\frac{4 \times 200}{\pi \times V}} \] --- ## Calculation for Different Velocities ### For \( V = 800\, \text{ft/min} \): \[ D = \sqrt{\frac{4 \times 200}{\pi \times 800}} \approx \sqrt{\frac{800}{2513}} \approx \sqrt{3.183} \approx 1.78\, \text{ft} \] Convert to inches: \[ 1.78\, \text{ft} \times 12 = 21.36\, \text{inches} \] This is too large compared to options, so check the larger diameters. --- ### For \( V = 100\, \text{ft/min} \): \[ D = \sqrt{\frac{4 \times 200}{\pi \times 100}} \approx \sqrt{\frac{800}{3141}} \approx \sqrt{2.55} \approx 1.60\, \text{ft} \] Convert to inches: \[ 1.60\, \text{ft} \times 12 = 19.2\, \text{inches} \] Again, larger than our options, so we need smaller diameters. --- ## Step 6: Use Approximate Duct Sizes from Chart Based on typical data: - **13-inch duct**: Usually handles around **150-200 CFM** at low friction loss. - **14-inch duct**: Slightly larger, more capacity. - **15-inch duct**: Better at 200 CFM with acceptable friction. - **16-inch duct**: Usually oversized. From the ASHRAE chart, for **200 CFM** and a friction loss of **.08 to .09 inches**, the appropriate duct size is approximately **15 inches**. --- ## **Final Answer** ### **Option c) 15 inches** This size provides the proper balance for **200 CFM** airflow at the specified friction loss range. --- ## Summary - Use the ASHRAE duct friction chart to approximate velocities. - Calculate the duct diameter based on airflow and velocity. - For 200 CFM and .08-.09 inches of friction loss, **15 inches** is the appropriate duct size. **Correct choice: c) 15 inch**