# Calling All M.E.'s! Q=VA, sometimes?

This question comes out of duct sizing methodologies. Sizing ducts by velocities, I have always used (a) the Trane ductulator and (b) ASHRAE’s friction chart. They agree. But, others insist on using © Q=VA. Fixing “A” and knowing “Q”, they find determine "V"and then take that “V” to the friction chart. But, when doing so, results come up short, regardign the “A” to pass the required “Q” at that “V”. The difference is significant, as high as a 25% difference in some calcs.

Is there a margin of error built into methods (a) and (b) as opposed to ©? If so, what is that margin? …And, is it written anywhere? - Jinx

IIRC, the Q=V*A works okay for the cocktail napkin variety calculation and is closer to reality for laminar flow conditions. For more stringent applications, duct geometry, roughness, friction, Reynold’s numbers, etc. come into play. I haven’t ever used Trane’s Ductulator, but I would bet that it uses the same calculations that were used to derive ASHRAE’s tables, which take all of the messy factors into consideration. And even after all of that, it’s still an approximation so you have to include balance dampers and pay a test and balance firm to set all the flows per design and calculate a k factor for all the VAV boxes. But at least when you use the tables or calculator, you can be (fairly) sure that you have enough air for the system, but not so much that you’re wasting energy on oversized fans and ducts.

Is this true? I know very little about duct sizing, but from a fundamental fluid dynamics standpoint, I’d expect the back-of-the-envelope calcs to work better for turbulent flow situations. Boundary layers are going to be much thicker in a laminar flow than a turbulent flow. V*A calculations assume a plug flow with no boundary layer unless you apply some fudge factor to your area calculation.

However, it’s unlikely you could actually maintain a laminar flow in a real duct for more than a few feet unless the installers took great care with the interior surface and joints.

Q=VA is a good back-of-the-envelope assumption, but it does ignore boundary layers and other losses. I don’t know what the ductulator or the friction chart are, but they sound like tables derived from empirical data rather than theoretical data. If that’s the case, then I would use the empirical data.

One of the things that irritated me about college mechanical engineering classes was the complete cognitive vacuum in which we did our problems. I recognize that the point was to calculate it from first principles, but I spent four years calculating theoretical values from first principles, and then was told that in almost every non-academic environment, numerical methods and empirical data are used because they’re faster and more accurate.

I would stick with the pre-fab tables, or go with whichever answer has fewer consequences if you’re wrong. For instance, it might be better to slightly oversize the blowers, on the assumption that eventually dust will accrue, or the motors will lose a little power.