“Clickety-clack clickety-clack, the wheels go rolling down the track. This childhood song (?) comes to mind as I ride the train from suburban New York City to Washington, DC to attend flow measurement standards committee meetings. Yet, something has changed — the clickety-clack seems to be missing (perhaps due to improved rail design and installation). This contrasts the fundamentally unchanging nature of flow.
So you want to measure flow? The answer would seem to be to purchase a flowmeter. With fluid flow defined as the amount of fluid that travels past a given location, this would seem to be straightforward — any flowmeter would suffice. However, consider the following equation describing the flow of a fluid in a pipe.
Q is flow rate, A is the cross-sectional area of the pipe, and v is the average fluid velocity in the pipe. Putting this equation into action, the flow of a fluid traveling at an average velocity of a 1 meter per second through a pipe with a 1 square meter cross-sectional area is 1 cubic meter per second. Note that Q is a volume per unit time, so Q is commonly denoted as the “volumetric” flow rate.
where W is flow rate (again – read on), and rho is the fluid density. Putting this equation into action, the flow rate will be 1 kilogram per second when 1 cubic meter per second of a fluid with a density of 1 kilogram per cubic meter is flowing. (The same can be done for the commonly-used “pounds”. Without getting into details — a pound is assumed to be a mass unit.) Note that W is a mass per unit time, so W is commonly denoted as the “mass” flow rate.
Now — which flow do you want to measure? Not sure? In some applications, measuring the volumetric flow is the thing to do. Consider filling a tank. Volumetric flow may be of interest to avoid overflowing a tank where liquids of differing densities can be added. (Then again, a level transmitter and high level switch/shutoff may obviate the need for a flowmeter.) Consider controlling fluid flow into a process that can only accept a limited volume per unit time. Volumetric flow measurement would seem applicable.
In other processes, mass flow is important. Consider chemical reactions where it is desireable to react substances A, B and C. Of interest is the number of molecules present (its mass), not its volume. Similarly, when buying and selling products (custody transfer) the mass is important, not its volume.
The train just pulled out of Philadelphia and I heard a brief “clickety-clack”. Your assignment (should you decide to accept it) is to memorize the above equations. The plot will thicken in the next issue.