Mass flow measurement is the process of determining the amount of mass moving through a cross-section of a pipe per unit time. This measurement is crucial in industrial processes requiring precise control and monitoring of fluid flow. Unlike volumetric flow measurement, which measures the volume of fluid passing through a system, mass flow measurement accounts for the actual mass of the fluid. It’s more accurate for processes where density of the fluid can vary due to temperature, pressure or composition changes. The difference is particularly important for gases, which shrink or expand in volume with changes in pressure or temperature, but whose mass stays constant.
Some volumetric flowmeters—multivariable vortex and differential pressure flowmeters—can indirectly provide mass flow by also measuring temperature and pressure and computing the mass flow. These flowmeters determine mass flow through mounted temperature, pressure and flow sensors and the equation: mass flow = (fluid density x volumetric flow). They determine density by measuring the pressure and temperature of the flow, and velocity by a rotating turbine or vortex sensor or other means of determining volumetric flow.
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What is mass?
The concept of mass plays an important role in flow measurement. Some flowmeters, such as Coriolis and thermal are considered mass flowmeters. Others, such as positive displacement and variable area, are volumetric flowmeters. Most people in the flowmeter world understand that mass flowmeters measure mass, while volumetric flowmeters measure volume. However, understanding mass is a little more complicated.
According to the Cambridge English dictionary, the term “mass” means “the amount of matter in any solid object or in any liquid or gas.” The most important aspect of this definition is that mass is “the amount of matter.” The definition of matter in the same dictionary is “physical substance in the universe.”
Putting the above definitions together, and staying with solid objects for now, we can define mass as the amount of physical substance in a solid object, with the physical being the most important term. When Descartes defined body as “an extended thing,” he referred to the idea that a body occupies space. It is three-dimensional. Today, we say that it has length, width and height. Physical objects are all around us in the form of rocks, trees, houses, cars and even our human bodies, as Bertrand Russell says in the quote from my February column, “The world is not as it seems.”
Physical has many meanings
We established that the term physical has multiple meanings. One meaning is the physical objects around us like rocks and houses that everyone can perceive. A second meaning refers to the scientific view of these objects from the perspective of chemistry and physics, according to which these objects are composed of atoms and molecules in constant motion. They only appear solid to us because of the speed with which molecules are moving. This is what Bertrand Russell meant by saying of a physical object “to science the matter comprising it is continually changing.”
The particle hierarchy
In “the world is not as it seems” we identified a particle hierarchy. Matter, meaning the physical objects of our experience, is at the top level. Underneath in descending order as the particles get smaller are:
- molecules;
- atoms;
- nucleus with electrons;
- protons and neutrons; and
- quarks, leptons, gluons, and other subatomic particles.
Understanding this hierarchy is the key to understanding mass.
Before exploring the relationship between this hierarchy of particles and mass, however, it is important to explain mass as we experience it in matter or physical objects. There are several definitions of two types of mass: inertial mass and gravitational mass.
Inertial mass
Inertial mass can be derived by rearranging Newton’s second law of motion: F = ma to read m = F/a. This reads that mass is equal to the ratio of force over acceleration.
Gravitational mass
Gravitational mass is a measure of how much an object is affected by a gravitational field.
Inertial mass quantifies an object's inertia, or its resistance to changes in motion. If the same force is applied to two objects and one accelerates less than the other, the one with less acceleration has more mass. Higher mass means less acceleration for the same force. Lower mass means more acceleration for the same force.
This reading of Newton’s Second Law coincides with our own experience. Someone who tries to push a car becomes aware of the great amount of force required to achieve even the slightest amount of acceleration. A car has a great deal of mass. If the same person tries to push a chair, he or she will find that this is a relatively easy task, due to the reduced amount of mass that the chair has. This is how we experience mass in real life. The term ‘massive’ comes from “mass,” and can be applied to objects having a lot of mass. A car is a massive object when compared to a chair.
Constituent particles
Mass is a property of physical objects such as balls, cars, rocks, stars and trees. However, we can’t see mass; we can only observe its effects. In this respect, it is like the wind. We can’t see the wind, but we can feel and observe its effects. The mass of an object is explained in terms of the way physicists and chemists see the object: in terms of the number and types of molecules that make it. The mass of an object is determined by the type of molecules making up the object, their individual molecular weights, along with the number of molecules that make it.
Of course, the story doesn’t end there. Molecules are made of mixtures of atoms, and atoms themselves have atomic mass and weight. The mass of an atom is determined by the combined masses of its protons, neutrons and electrons, with protons and neutrons contributing the most. It’s measured using tools like mass spectrometers and expressed in atomic mass units (amu). The molecular weight of the atoms making up a molecule can be determined by consulting the Periodic Table of Elements. The values listed in the Periodic Table account for isotopic variations and provide a practical way to use atomic masses in scientific calculations. Molecular mass is calculated as the sum of atomic masses, considering isotopic composition, and is critical for understanding molecular behavior and reactions.
To understand the mass of a proton at a deeper level, it’s important to understand that a proton is made up of two up quarks and one down quark, along with what are called gluons. Gluons are massless elementary particles that facilitate the interactions between the quarks. The strong nuclear force, which is one of the four fundamental forces, governs the interactions of the quarks and the gluons. The quarks have mass, but this mass contributes only a fraction of the mass of the proton. The proton’s mass arises from the complex interaction of the quarks and the gluons, governed by the strong nuclear force. Most of the proton’s mass arises from the strong interaction that binds the quarks together. At its most basic level, mass derives from the interaction of fields of energy of subatomic particles moving at incredible speeds.
Mass and flow measurement
Understanding mass is important to understanding mass flow measurement. In some cases, such as in chemical reactions, it may be necessary to know the molecular or atomic structure of the fluid being measured. This is especially important when the ingredients of the product being manufactured are specified in mass rather volumetric terms. For thermal flowmeters it is important to know the type of gas being measured; or if it is a mixture, the components of the mixture. Knowing molar mass is important for gas flow because it helps convert between volumetric flow and mass flow. Knowing and understanding mass flow is essential to accurate flow measurement, especially for gases.
