Triangular Duct Sizing and Calculations

• A triangular duct has one side measuring 14 inches.

• The airflow through the duct is 2,000 cubic feet per minute (cfm).

• The friction loss (head loss) is 0.1 inches per 100 feet of duct.

• The problem requires determining the appropriate size of the triangular duct.

Duct Sizing and Calculations

• Duct sizing involves determining the optimal dimensions of a duct to deliver the required airflow with acceptable pressure loss and noise levels.

• Several methods exist for duct sizing, including equal friction, velocity reduction, and static regain methods.

• The equal friction method aims to maintain a constant friction loss per unit length of duct.

• The velocity reduction method gradually reduces the air velocity in the duct system to minimize noise and pressure loss.

• The static regain method designs the duct system to recover static pressure, improving energy efficiency.

Triangular Duct Considerations

• Triangular ducts are less common than rectangular or circular ducts due to manufacturing and installation complexities.

• Triangular ducts may be used in specific situations where space is limited or unique airflow patterns are desired.

• The hydraulic diameter is an important parameter for calculating friction loss in non-circular ducts.

• The hydraulic diameter (Dh) is defined as four times the cross-sectional area (A) divided by the wetted perimeter (P): Dh = 4A/P.

• For a triangular duct, the area and perimeter depend on the triangle's geometry (equilateral, isosceles, or scalene).

Calculating Duct Size

• Since only one side of the triangular duct is given (14 inches), we need to assume the type of triangle to proceed with calculations.

• Assuming an equilateral triangle:

  • All sides are equal (14 inches).
  • The area (A) can be calculated as (sqrt(3)/4) * side^2.
  • The perimeter (P) is 3 * side.

• Calculate the area: A = (sqrt(3)/4) * 14^2 ≈ 60.62 square inches.

• Calculate the perimeter: P = 3 * 14 = 42 inches.

• Convert the area to square feet: A ≈ 60.62 / 144 ≈ 0.421 square feet.

Velocity Calculation

• Airflow (Q) is given as 2,000 cfm. Convert to cubic feet per second (cfs): Q = 2000 / 60 ≈ 33.33 cfs.

• Calculate the air velocity (V) in the duct: V = Q / A = 33.33 / 0.421 ≈ 79.17 feet per second.

Friction Loss Evaluation

• The given friction loss is 0.1 inches per 100 feet. This value needs to be compared with calculated or recommended values.

• The Darcy-Weisbach equation or similar friction loss equations can be used to estimate the actual friction loss in the duct. These equations require knowing the friction factor, which depends on the Reynolds number and the duct's roughness. Since these parameters were not provided, friction loss cannot currently be validated.

Considerations and Next Steps

• To accurately determine if the 14-inch equilateral triangular duct is suitable, you would need to:

  • Determine the acceptable velocity range for the application (e.g., for noise and energy considerations).
  • Calculate the Reynolds number to estimate the friction factor.
  • Use the Darcy-Weisbach equation (or a similar formula) to calculate the actual friction loss.
  • Compare the calculated friction loss to the target friction loss (0.1 inches per 100 ft).

• If the calculated friction loss is significantly higher than the target, a larger duct would be needed. If it is significantly lower, a smaller duct could be considered.