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A Historical Perspective of "force"

The existence of life itself has been attributed over the ages to an underlying "force." Life is manifested by change and movement--it involves actions and interactions of a variety of forces. Therefore, no measurement is more fundamental to human activity than the measurement of force in its many manifestations, including weight, pressure, acceleration, torque, work, and energy.

The purpose of this first chapter is to trace the historical evolution of the understanding of force and of the theories which evolved at various stages of human development. While the ancient civilizations of 8,000 to 6,000 B.C., in the river valleys of Southwest Asia, Mesopotamia or Egypt and others in China, India, and South America, all used lever and roller systems to amplify the muscle power of men, the first attempts to formalize a theoretical understanding of force were in ancient Greece.

From Aristotle to Hawking

The ancient Greek philosophers considered themselves qualified to make pronouncements in the field of science, but their views had little to do with the real world. Aristotle (384-322 B.C.), for example, believed that "form" caused matter to move. He defined motion as the process by which the "potentiality" of matter became the "actuality" of form. With that view of reality, it is no wonder that the Greeks of Aristotle's time created much more art than technology.

Yet, a hundred years later, the Greek physicist Archimedes (287-212 B.C.) became a pioneer of real engineering experimentation. He not only discovered the force-amplifying capability of the pulley, but also noted that the same weight of gold will displace less water than does an equal weight of silver.

Some 400 years later, the astronomer Clausius Ptolemaeus (second century A.D.) developed the first model of planetary movements. He assumed the Earth as being stationary in the center of the universe, with the Sun, Moon and stars revolving around it in circular orbits. The first revision of the Ptolemaic system came a millennium later; Nicholas Copernicus (1473-1543) replaced the Earth with the Sun as the center of the universe (a heliocentric system). Because he still did not understand the role of the force of gravity, however, he, too, assumed that the planets traveled in perfect circles.

Another century passed before Galileo Galilei (1564-1642) discovered, by dropping various items from the Leaning Tower of Pisa, that the velocity of a falling object is independent of its weight. His attitude was that of a good engineer: "I don't know why, but it works, so don't forget it!"

Johannes Kepler (1571-1630), who correctly established that the orbits of the planets about the Sun are elliptical, did not realize the cause of all this: the force of gravity. He noted that the Sun had some "mysterious power or virtue" which compelled the planets to hold to their orbits. The role of gravity escaped even Blaise Pascal (1623-1662), although he did correctly explain some related phenomena such as pressure and barometric pressure. It was also Pascal who first noted that, when pressure is applied to a confined fluid, the pressure is transmitted undiminished in all directions. It is for these discoveries that we honor him by using his name (in the SI system) as the unit of pressure.

The role of the force of gravity was first fully understood by Sir Isaac Newton (1642-1727). His law of universal gravitation explained both the fall of bodies on Earth and the motion of heavenly bodies. He proved that gravitational attraction exists between any two material objects. He also noted that this force is directly proportional to the product of the masses of the objects and inversely proportional to the square of the distance between them. On the Earth's surface, the measure of the force of gravity on a given body is its weight. The strength of the Earth's gravitational field (g) varies from 9.832 m/sec2 at sea level at the poles to 9.78 m/sec2 at sea level at the Equator.

Newton summed up his understanding of motion in three laws:

1) The law of inertia: A body displays an inherent resistance to changing its speed or direction. Both a body at rest and a body in motion tend to remain so.

2) The law of acceleration: Mass (m) is a numerical measure of inertia. The acceleration (a) resulting from a force (F) acting on a mass can be expressed in the equation a = F/m; therefore, it can be seen that the greater the mass (inertia) of a body, the less acceleration will result from the application of the same amount of force upon it.

3) For every action, there is an equal and opposite reaction.

After Newton, progress in understanding force-related phenomena slowed. James Prescott Joule (1818-1889) determined the relationship between heat and the various mechanical forms of energy. He also established that energy cannot be lost, only transformed (the principle of conservation of energy), defined potential energy (the capacity for doing work), and established that work performed (energy expended) is the product of the amount of force applied and the distance traveled. In recognition of his contributions, the unit of work and energy in the SI system is called the joule.

Albert Einstein (1879-1955) contributed another quantum jump in our understanding of force-related phenomena. He established the speed of light (c = 186,000 miles/sec) as the maximum theoretical speed that any object with mass can travel, and that mass (m) and energy (e) are equivalent and interchangeable: e = mc2.

Einstein's theory of relativity corrected the discrepancies in Newton's theory and explained them geometrically: concentrations of matter cause a curvature in the space-time continuum, resulting in "gravity waves." While making enormous contributions to the advancement of science, the goal of developing a unified field theory (a single set of laws that explain gravitation, electromagnetism, and subatomic phenomena) eluded Einstein.

Edwin Powell Hubble (1889-1953) improved our understanding of the universe, noting that it looks the same from all positions, and in all directions, and that distances between galaxies are continuously increasing. According to Hubble, this expansion of the universe started 10 to 20 billion years ago with a "big bang," and the space-time fabric which our universe occupies continues to expand.

Carlo Rubbia (1934- ) and Simon van der Meer (1925- ) further advanced our understanding of force by discovering the subatomic W and Z particles which convey the "weak force" of atomic decay. Stephen Hawking (1952- ) advanced our understanding even further with his theory of strings. Strings can be thought of as tiny vibrating loops from which both matter and energy derive. His theory holds the promise of unifying Einstein's theory of relativity, which explains gravity and the forces acting in the macro world, with quantum theory, which describes the forces acting on the atomic and subatomic levels.

Force & Its Effects

Force is a quantity capable of changing the size, shape, or motion of an object. It is a vector quantity and, as such, it has both direction and magnitude. In the SI system, the magnitude of a force is measured in units called newtons, and in pounds in the British/American system. If a body is in motion, the energy of that motion can be quantified as the momentum of the object, the product of its mass and its velocity. If a body is free to move, the action of a force will change the velocity of the body.

There are four basic forces in nature: gravitational, magnetic, strong nuclear, and weak nuclear forces. The weakest of the four is the gravitational force. It is also the easiest to observe, because it acts on all matter and it is always attractive, while having an infinite range. Its attraction decreases with distance, but is always measurable. Therefore, positional "equilibrium" of a body can only be achieved when gravitational pull is balanced by another force, such as the upward force exerted on our feet by the earth's surface.

Pressure is the ratio between a force acting on a surface and the area of that surface. Pressure is measured in units of force divided by area: pounds per square inch (psi) or, in the SI system, newtons per square meter, or pascals. When an external stress (pressure) is applied to an object with the intent to cause a reduction in its volume, this process is called compression. Most liquids and solids are practically incompressible, while gases are not.

The First Gas Law, called Boyle's law, states that the pressure and volume of a gas are inversely proportional to one another: PV = k, where P is pressure, V is volume and k is a constant of proportionality. The Second Gas Law, Charles' Law, states that the volume of an enclosed gas is directly proportional to its temperature: V = kT, where T is its absolute temperature. And, according to the Third Gas Law, the pressure of a gas is directly proportional to its absolute temperature: P = kT.

Combining these three relationships yields the ideal gas law: PV = kT. This approximate relationship holds true for many gases at relatively low pressures (not too close to the point where liquification occurs) and high temperatures (not too close to the point where condensation is imminent).

Measurement Limitations

One of the basic limitations of all measurement science, or metrology, is that all measurements are relative. Therefore, all sensors contain a reference point against which the quantity to be measured must be compared. The steelyard was one of mankind's first relative sensors, invented to measure the weight of an object (Figure 1-1). It is a beam supported from hooks (A or B), while the object to be weighed is attached to the shorter arm of the lever and a counterpoise is moved along the longer arm until balance is established. The precision of such weight scales depends on the precision of the reference weight (the counterpoise) and the accuracy with which it is positioned.

Similarly, errors in pressure measurement are as often caused by inaccurate reference pressures as they are by sensor inaccuracies. If absolute pressure is to be detected, the reference pressure (theoretically) should be zero--a complete vacuum. In reality, a reference chamber cannot be evacuated to absolute zero (Figure 1-2), but only to a few thousandths of a millimeter of mercury (torr). This means that a nonzero quantity is used as a zero reference. Therefore, the higher that reference pressure, the greater the resulting error. Another source of error in absolute pressure measurement is the loss of the vacuum reference due to the intrusion of air.

In the case of "gauge" pressure measurement, the reference is atmospheric pressure, which is itself variable (Figure 1-3). Thus, sensor output can change not because there is a change in the process pressure, but because the reference pressure is changing. The barometric pressure can change by as much as an inch of mercury (13.6 inches of water), which in some compound measurements can result in excessive and intolerable errors. By definition, a compound pressure detector measures near atmospheric pressures, both above and below atmospheric.

Consider, for example, a blanketed chemical reactor. A typical case is a reactor which (when empty) needs to be evacuated to an absolute pressure of 10 torr. After evacuation, it must be purged with an inert gas, while the pressure in the reactor is maintained at 1 in. of water above atmospheric. No pressure sensor provided with a single reference is capable of detecting both of these pressures. If a vacuum reference is used, the purge setting of 1 in. water cannot be maintained, because the instrument does not know what the barometric pressure is. On the other hand, if a barometric reference is used, the 10-torr vacuum cannot be measured because the reference can change by more than the total value of the measurement--as much as 25 torr.

Today, with microprocessors, it would be possible to provide the same pressure sensor with two references and allow the intelligence of the unit to decide which reference should be used for a particular measurement.

Another important consideration in force-related measurements is the elimination of all force components which are unrelated to the measurement. For example, if the goal is to measure the weight of the contents of a tank or reactor, it is essential to install the vessel in such a way that the tank will behave as a free body in the vertical but will be rigidly held and protected from horizontal or rotary movement. This is much more easily said than done.

Freedom for the vessel to move in the vertical direction is achieved if the tank is supported by nothing but the load cells. (The amount of vertical deflection in modern load cells is less than 0.01 in.) This means that all pipes, electrical conduits, and stay rods connected to the vessel must be designed to offer no resistance to vertical movement. In pressurized reactors, this usually requires the use of flexible piping connections installed in the horizontal plane (Figure 1-4) and ball joints in the stay rods. For best results in larger pipes, two horizontal flexible couplings are typically installed in series.

It is equally important to protect and isolate the load cells from horizontal forces. These forces can be caused by thermal expansion or by the acceleration and deceleration of vehicles on active weighing platforms. Therefore, it is essential that load cells be either free to move in the horizontal (Figure 1-5) or be provided with an adaptor that transmits virtually no side load. In addition, tanks--particularly agitated reactors--should be stayed, that is, protected from rotary motion. This is achieved by installing three stay rods, each with two ball joints (Figure 1-6).

The art of weighing requires a lot of common sense. A successful weighing system requires that tank supports be rigid and be located above the vessel's center of gravity for stability. This is particularly important outdoors, where outside forces such as the wind need to be considered. It is also important that the load be evenly distributed among the load cells. This consideration necessitates that all load buttons be positioned in the same plane. Since three points define a plane, equal load distribution is easiest to achieve by using three load cells.

Common sense also tells us that the accuracy of an installation will not match the precision of the load cells (which is usually 0.02% or better) if the full load is not being measured or if the load cells are not properly calibrated. The precision of high quality load cells does little good if they are calibrated against flowmeters with errors of 1% or more. The only way to take full advantage of the remarkable capabilities of accurate modern load cells is to zero and calibrate the system using precision dead weights. It is also important to remember that dead weights can only be attached to a reactor if hooks or platforms are provided for them.

Range considerations also are important because load cells are percent-of-full-scale devices. This means that the absolute error corresponding to, say, 0.02% is a function of the total weight being measured. If the total weight is 100,000 pounds, the absolute error is 20 pounds. But if one needs to charge a batch of 100 pounds of catalyst into that same reactor, the error will be 20%, not 0.02%.

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