Ventilation duct sizing tools - tradition and modernity

One of the most important problems in the hydraulic design of various building services systems is the calculation of the friction factor involved in Darcy-Weisbach equation. Ventilation duct sizing is a good case study, showing how classic, old-school design tools collide with modern instruments of the digital era. The friction factor is a function of Reynolds number, relative roughness and flow regime. Apart from the graphical representation in Moody’s chart, those variables are packed in the famous Colebrook-White equation, widely accepted by engineers and scientists. Unfortunately, this equation is an implicit one and must be solved using numerical methods. This is a major disadvantage for the average engineer, who often wants a quick result, if possible using a simple, explicit equation. Therefore, the traditional hydraulic design tool offered to engineers in handbooks was a chart (nomograph), giving directly the pressure drop per unit length (Pa/m), thus hiding the complexity of finding the friction factor. Later, when personal computers became available, the tactics have changed: Colebrook-White equation needed to be replaced by a simpler one. So, during the last two decades, many authors proposed their own explicit equations, more or less complicated, making the choice of young engineers even more difficult than before. The present paper tries to make an overview of the most used alternatives to Colebrook-White equation, analyzing their complexity and mathematical accuracy for different Reynolds numbers and relative roughnesses. Also, some modern software instruments for ventilation duct sizing were investigated.