What's In A Unit? Flow Measurement

E-ZINE

The sun is starting to set to my left (the seats in my car are facing the rear of the train) as the suburbs of Baltimore wiz by. This has been much more enjoyable than the 6 hour drive or a flight (need I say more?). Laptops are a great convenience, and still no clickety-clacks. This issue builds on Parts 1 and 2 that are posted on the website.

Volumetric flow is expressed in units that reflect a volume per unit time. The example in Part 1 determines cubic meters and cubic feet per unit time to be volumetric flow units. Gallons and liters per unit time are also volumetric flow units.

Mass flow is expressed in units that reflect a mass per unit time. The other example in Part 1 determines kilograms and pounds per unit time to be mass flow units. (Without getting into details — a pound is assumed to be a mass unit.) Note that the units of time are independent of whether volumetric or mass flow is measured.

Let’s have a quiz.

Are the following volumetric or mass liquid flow units?

	gallons per minute
	cubic feet per second
	liters per minute
	kilograms per hour
	pounds per hour
	grams per minute

Can one have a cubic foot of feathers? YES/NO

Can one have a gallon of feathers? YES/NO

Can one have a kilogram of feathers? YES/NO

If you answered volumetric to the first three questions, mass to the next three questions, and yes to the last three questions, you are on track.

Consider purchasing fuel for your car. How does a US gallon of gasoline purchased on a hot summer day in Las Vegas, Arizona compare with a US gallon of gasoline purchased on a cold winter night in Anchorage, Alaska? It was determined that a gallon is a volumetric unit, so logic would indicate that the same volume of gasoline was purchased. Yet the temperature difference would cause their densities, and hence their masses, to be different. Using this logic, more mass would be obtained by purchasing gasoline in colder weather. Thinking locally, one might conclude that it is more economical to purchase gasoline during the wee hours of the morning when the temperature is coldest.

As you might suspect, such is not the case. Gasoline pumps compensate for d ensity variation that occurs due to temperature, and in doing so, they measure the amount (mass) of gasoline dispensed. Yet, a gallon of cold gasoline will occupy less volume than when hot. In essence, the measurement of a gallon of gasoline actually refers to its volume at a given temperature (such as 60 degF). As such, this is really a mass measurement unit because it refers to the flow of a specific substance at a given temperature.

Returning to the quiz, let’s not be so hasty with the first three questions. They could be incomplete!

ISSN 1538-5280