HVAC Air Balance Equations in Excel

HVAC air balance equations are mathematical formulas that are used to calculate the amount of air flow and pressure in a heating, ventilating, and air conditioning (HVAC) system. These equations help to ensure that the HVAC system is operating efficiently and providing adequate comfort and indoor air quality for the occupants.

Basic Theory

Air balance in HVAC refers to the process of adjusting and regulating the air distribution within a system to meet design specifications. This involves ensuring that the correct amount of air is supplied to each room or zone, and that the airflows are balanced to maintain desired conditions.

The basic equation for air balance is:

$Q = C \times \Delta P$

Where:

$Q$ is the airflow in cubic feet per minute (CFM),
$C$ is the flow coefficient,
$\Delta P$ is the pressure drop across the system.

Procedures

Determine Design Airflow: Identify the design airflow for each room or zone in the HVAC system. This information is typically provided in the project specifications.
Calculate Flow Coefficient ( $C$ ): The flow coefficient is a factor that accounts for the geometry and characteristics of the air distribution system. It is often determined through testing or obtained from HVAC literature.
Measure Pressure Drop ( $\Delta P$ ): Measure the pressure drop across the system, considering factors such as duct length, fittings, and filters.
Apply the Air Balance Equation: Use the air balance equation to calculate the required airflow for each room or zone.

Excel Formulas

Now, let’s translate the air balance equation into Excel formulas:

Assuming Design Airflow ( $Q_d$ ), Flow Coefficient ( $C$ ), and Pressure Drop ( $\Delta P$ ) are in cells B2, B3, and B4, respectively:

$Q = B2 \times B3$

This formula calculates the required airflow.

Scenario: Office HVAC System

Let’s consider an office HVAC system with the following parameters:

Design Airflow ( $Q_d$ ): 1500 CFM
Flow Coefficient ( $C$ ): 0.8
Pressure Drop ( $\Delta P$ ): 1.5 inches of water column (WC)

Excel Calculation

Parameter	Value
Design Airflow ( $Q_d$ )	1500 CFM
Flow Coefficient ( $C$ )	0.8
Pressure Drop ( $\Delta P$ )	1.5 WC

$Q = 1500 \times 0.8 = 1200 \, CFM$

Therefore, the required airflow for this office HVAC system is 1200 CFM.

MATLAB Comparison

For comparison, let’s solve the same problem using MATLAB. The MATLAB script would involve defining variables for $Q_d$ , $C$ , and $\Delta P$ and then applying the air balance equation. The result should match the Excel calculation.


% MATLAB Script
Qd = 1500; % Design Airflow in CFM
C = 0.8;   % Flow Coefficient
dP = 1.5;  % Pressure Drop in WC

Q = Qd * C; % Air Balance Equation

disp(['Required Airflow (MATLAB): ' num2str(Q) ' CFM']);