HVAC Pipe Expansion Equation in Excel

HVAC stands for heating, ventilation, and air conditioning. HVAC systems use pipes to transport air, water, or refrigerant throughout buildings or vehicles. HVAC pipes are subject to thermal expansion and contraction, which means they change their length depending on the temperature. This can cause stress and deformation in the pipes, fittings, and supports, and affect the performance and safety of the system.

To prevent or reduce the effects of thermal expansion and contraction, HVAC engineers use equations to calculate the amount of change in pipe length and the required dimensions of expansion loops or joints. Expansion loops are U-shaped sections of pipe that allow for some movement and flexibility. Expansion joints are devices that connect two pipes and absorb the expansion or contraction.

Basic Theory:

When pipes in an HVAC system are subjected to temperature changes, they undergo thermal expansion or contraction. The equation for pipe expansion can be expressed as:

$\Delta L = L \cdot \alpha \cdot \Delta T$

Where:

$\Delta L$ is the change in length of the pipe.
$L$ is the original length of the pipe.
$\alpha$ is the coefficient of thermal expansion.
$\Delta T$ is the change in temperature.

Procedures:

Identify the original length of the pipe ( $L$ ).
Determine the coefficient of thermal expansion ( $\alpha$ ) for the material of the pipe.
Measure the change in temperature ( $\Delta T$ ).
Use the formula to calculate the change in length ( $\Delta L$ ).

Example Scenario:

Consider a steel HVAC pipe with an original length of 10 meters. The coefficient of thermal expansion for steel is approximately $0.000012 \, ^\circ C^{-1}$ . If the temperature increases by 20 degrees Celsius, what is the change in length?

Excel Formulas:

Input the data into an Excel table:

Parameter	Value
Original Length ( $L$ )	10
Coefficient ( $\alpha$ )	0.000012
Temperature Change ( $\Delta T$ )	20

In Excel, use the formula:

= A2 * B2 * C2

Here, A2 represents the original length, B2 is the coefficient of thermal expansion, and C2 is the temperature change.

Calculation:

$\Delta L = 10 \, \text{m} \times 0.000012 \, ^\circ C^{-1} \times 20 \, ^\circ C$

$\Delta L = 0.0024 \, \text{m}$

MATLAB Comparison:

In MATLAB, the calculation can be performed using the same formula:


L = 10;
alpha = 0.000012;
delta_T = 20;

delta_L_MATLAB = L * alpha * delta_T;
disp(delta_L_MATLAB);

The result in MATLAB will be the same as in Excel, validating the consistency of calculations between the two tools.