• HVAC,
• fire safety,
• smoke control

# Ventilation opening areas explained - Part 2

Part 2/3: K-factor vs coefficient of discharge Cd

The (required) ventilation subject is a broad one and involves numerous definitions that are not fully transparent to the users. This series of blog posts aims to clarify the definitions and demonstrate the calculations on worked examples.

The previous part (Part 1) focuses on the definitions. This part aims to explain what k-factor is and its relation to coefficient of discharge by deriving with equations.

The K-factor, minor loss coefficient, is a dimensionless value that expresses the aerodynamic resistance of the grille/duct or other impediments to the airflow. It can be derived from the coefficient of discharge.

To understand the fundamentals of the k-factor further, we dive deeper and express the phenomena in physical expressions. A pressure difference of ΔP between two ends of an opening can ideally generate a maximum velocity, vdyn.

When an element (filter, louvre etc.) is added to the opening a certain pressure, Ploss, is lost due to resistance of the element while the fluid velocity is at vf. The amount of the pressure loss is expressed as:

The actual velocity in the opening can also be expressed as:

This expression which involves the pressure loss (k-factor) can also be incorporated into the discharge coefficient . The discharge coefficient is the ratio of actual flow rate (vf) to the theoretical flow rate (vdyn). Therefore Cd is:

Application in CFD

In CFD applications it is often impractical to model grilles in full detail with all geometrical details. Instead, the k-factor is used as a volumetric loss coefficient in a volume representing the grille. The streamwise loss is given by the K-factor divided by the width of the volume representing the grille. Inlet and outlet losses are not incorporated into the applied k-factor since they are already present in the CFD simulation due to the air flow near the object.

In the last part of this blog a few worked examples about defining the equivalent area and choosing the right grille size with the right Cd value are demonstrated.