HVAC Flat Oval Ductwork Calculations Using Excel Formulas

Flat oval ductwork is a type of ductwork that has an oval shape with two flat sides. It is often used in HVAC systems where space is limited or aesthetics are important. Flat oval ductwork has some advantages over round or rectangular ductwork, such as lower air resistance, less noise, and better appearance.

To calculate the area and perimeter of flat oval ductwork, we need to know the major axis (A) and the minor axis (a) of the oval. The major axis is the longest diameter of the oval, and the minor axis is the shortest diameter. The area of flat oval ductwork is the sum of the area of a circle with radius a and the area of a rectangle with length A and width a. The perimeter of flat oval ductwork is the sum of the circumference of a circle with radius a and the length of two straight lines with length A-a.

To convert flat oval ductwork to round ductwork, we need to find the equivalent diameter of the oval. The equivalent diameter is the diameter of a circle that has the same cross-sectional area and perimeter as the oval. There is a formula that relates the equivalent diameter to the area and perimeter of the oval1. The equivalent diameter is useful for comparing the performance of different duct shapes and sizes.

Basic Theory

Flat oval ducts are commonly used in HVAC systems due to their space-saving characteristics. The basic theory involves calculating the equivalent diameter ( $D_{eq}$ ) of the flat oval duct, which is then used in standard round duct equations. The aspect ratio ( $AR$ ), defined as the ratio of the major axis to the minor axis, is a key parameter.

The equivalent diameter is calculated using the following formula:

$D_{eq} = \sqrt{4 \times \frac{A}{\pi}}$

where $A$ is the cross-sectional area of the flat oval duct.

Procedures

Calculate Cross-Sectional Area ( $A$ ): Measure the major axis ( $a$ ) and minor axis ( $b$ ) of the flat oval duct and use the formula $A = \frac{\pi \times a \times b}{4}$ .
Determine Aspect Ratio ( $AR$ ): Calculate $AR = \frac{a}{b}$ .
Calculate Equivalent Diameter ( $D_{eq}$ ): Use the formula mentioned earlier.
Apply Standard Round Duct Formulas: Once $D_{eq}$ is determined, standard round duct equations can be applied for further calculations.

Scenario

Consider a flat oval duct with a major axis ( $a$ ) of 24 inches and a minor axis ( $b$ ) of 12 inches. The air temperature is 70°F, and the air velocity is 800 feet per minute.

Excel Implementation

Let’s set up an Excel table to perform the calculations.

	Input Parameters	Values
Major Axis ( $a$ )		24 inches
Minor Axis ( $b$ )		12 inches
Air Temperature		70°F
Air Velocity		800 ft/min

Now, we’ll use Excel formulas to calculate:

Cross-Sectional Area ( $A$ ): =PI() * A2 * B2 / 4
Aspect Ratio ( $AR$ ): =A2 / B2
Equivalent Diameter ( $D_{eq}$ ): =SQRT(4 * C2 / PI())

Results

1. Cross-Sectional Area ( $A$ ): $A = \frac{\pi \times 24 \times 12}{4} \approx 226.195 \, \text{in}^2$

2. Aspect Ratio ( $AR$ ): $AR = \frac{24}{12} = 2$

3. Equivalent Diameter ( $D_{eq}$ ): $D_{eq} = \sqrt{4 \times \frac{226.195}{\pi}} \approx 15.12 \, \text{in}$

Now, with $D_{eq}$ , further HVAC calculations can be performed using standard round duct equations.

MATLAB Comparison

In MATLAB, the same calculations can be implemented using the following script:

% MATLAB Script
a = 24; % major axis
b = 12; % minor axis

A = (pi * a * b) / 4; % Cross-sectional Area
AR = a / b; % Aspect Ratio
Deq = sqrt(4 * A / pi); % Equivalent Diameter

Both Excel and MATLAB should yield similar results, providing confidence in the accuracy of the calculations.