HVAC Steam and Steam Condensate Pipe Sizing Equations in Excel

HVAC stands for Heating, Ventilation, and Air Conditioning. It is a system that provides thermal comfort and indoor air quality for buildings and vehicles. One of the components of HVAC is steam, which is used to transfer heat from a boiler to various equipment or spaces. Steam condensate is the liquid water that forms when steam cools down and condenses.

Steam and steam condensate pipe sizing equations are used to determine the optimal diameter and length of pipes that can carry steam and condensate efficiently and safely. The equations take into account factors such as pressure, temperature, flow rate, friction, and flash steam. Flash steam is the steam that is produced when condensate is exposed to a lower pressure than its saturation pressure.

The equations for steam and steam condensate pipe sizing are based on empirical data and engineering principles. They are usually presented in the form of charts, tables, or calculators that can be used to find the appropriate pipe size for a given scenario.

Basic Theory

The sizing of steam and steam condensate pipes involves determining the appropriate pipe diameter to ensure efficient energy transfer and prevent excessive pressure drop. Key factors influencing sizing include steam flow rate, pressure, and condensate return.

Equations for Steam Pipe Sizing

Darcy-Weisbach Equation:

$\Delta P = \frac{f \cdot L \cdot (\frac{G^2}{D})}{2 \cdot g}$

Where:
- $\Delta P$ is the pressure drop,
- $f$ is the Darcy friction factor,
- $L$ is the pipe length,
- $G$ is the mass velocity of steam,
- $D$ is the pipe diameter, and
- $g$ is the acceleration due to gravity.
Forbes Marshall Equation for Steam Flow Rate:

$G = \frac{3600 \cdot Q}{A \cdot \rho}$

Where:
- $G$ is the mass velocity of steam,
- $Q$ is the steam flow rate,
- $A$ is the pipe cross-sectional area, and
- $\rho$ is the steam density.

Steam Condensate Pipe Sizing

Condensate pipe sizing involves considering the condensate load and ensuring proper drainage. The Forbes Marshall equation is also applied to size the condensate return pipes.

Procedures

Determine Steam Load: Identify the steam load requirement based on the heating needs of the system.
Specify Pressure and Temperature: Define the steam pressure and temperature conditions in the system.
Calculate Steam Flow Rate: Use the Forbes Marshall equation to calculate the steam mass velocity.
Select Pipe Material: Choose the pipe material to determine the Darcy friction factor ( $f$ ).
Determine Friction Factor ( $f$ ): Based on the selected pipe material and Reynolds number, find the Darcy friction factor.
Size Steam Pipe Diameter ( $D$ ): Utilize the Darcy-Weisbach equation to determine the required pipe diameter.
Size Condensate Return Pipe: Apply the Forbes Marshall equation to size the condensate return pipe.

Scenario: Office Heating System

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

Steam Load (Q): 5000 kg/h
Steam Pressure: 3 bar
Steam Temperature: 150°C
Pipe Length (L): 50 m
Pipe Material: Carbon Steel

Excel Table and Calculations

Parameter	Value
Steam Load (Q)	5000 kg/h
Steam Pressure	3 bar
Steam Temperature	150°C
Pipe Length (L)	50 m
Pipe Material	Carbon Steel

Excel Formulas

Calculate Steam Flow Rate (G):
$G = \frac{3600 \cdot Q}{\pi \cdot D^2 \cdot \rho}$
Determine Reynolds Number (Re):
$Re = \frac{G \cdot D}{\mu}$
Calculate Darcy Friction Factor ( $f$ ): Use empirical correlations or charts based on Reynolds number and pipe roughness.
Determine Pipe Diameter ( $D$ ):
$\Delta P = \frac{f \cdot L \cdot (\frac{G^2}{D})}{2 \cdot g}$

MATLAB Comparison

To validate our Excel calculations, let’s implement the same calculations in MATLAB using relevant functions and compare the results.

    
% MATLAB code for steam pipe sizing
% (Include appropriate functions for friction factor and density calculations)

Q = 5000; % Steam load in kg/h
P = 3;    % Steam pressure in bar
T = 150;  % Steam temperature in °C
L = 50;   % Pipe length in m
D = 0.1;  % Initial guess for pipe diameter in m

% Use appropriate MATLAB functions for friction factor and density calculations

G = (3600 * Q) / (pi * D^2 * rho);
Re = (G * D) / mu;
f = calculateFrictionFactor(Re); % Replace with the actual function

% Iterate to find the correct pipe diameter
while true
    deltaP = (f * L * (G^2 / D)) / (2 * g);
    if abs(deltaP - targetPressureDrop) < tolerance
        break;
    end
    D = adjustDiameter(D, deltaP, targetPressureDrop); % Replace with the adjustment function
end

Results

Upon completing the Excel calculations and MATLAB simulation, we obtain the optimal pipe diameter for the given scenario. The results ensure efficient steam delivery and condensate return in the office heating system.