The three characteristics of fluid pressure described above have a number of implications and applications, among them, what is known as Pascal's principle. Like the SI unit of pressure, Pascal's principle is named after Blaise Pascal (1623-1662), a French mathematician and physicist who formulated the second of the three statements: that the external pressure applied on a fluid is transmitted uniformly throughout the entire body of that fluid. Pascal's principle became the basis for one of the important machines ever developed, the hydraulic press.
A simple hydraulic press of the variety used to raise a car in an auto shop typically consists of two large cylinders side by side. Each cylinder contains a piston, and the cylinders are connected at the bottom by a channel containing fluid. Valves control flow between the two cylinders. When one applies force by pressing down the piston in one cylinder (the input cylinder), this yields a uniform pressure that causes output in the second cylinder, pushing up a piston that raises the car.
In accordance with Pascal's principle, the pressure throughout the hydraulic press is the same, and will always be equal to the ratio between force and pressure. As long as that ratio is the same, the values of F and A may vary. In the case of an auto-shop car jack, the input cylinder has a relatively small surface area, and thus, the amount of force that must be applied is relatively small as well. The output cylinder has a relatively large surface area, and therefore, exerts a relatively large force to lift the car. This, combined with the height differential between the two cylinders (discussed in the context of mechanical advantage elsewhere in this book), makes it possible to lift a heavy automobile with a relatively small amount of effort.
The car jack is a simple model of the hydraulic press in operation, but in fact, Pascal's principle has many more applications. Among these is the hydraulic ram, used in machines ranging from bulldozers to the hydraulic lifts used by firefighters and utility workers to reach heights. In a hydraulic ram, however, the characteristics of the input and output cylinders are reversed from those of a car jack.
The input cylinder, called the master cylinder, has a large surface area, whereas the output cylinder (called the slave cylinder) has a small surface area. In addition—though again, this is a factor related to mechanical advantage rather than pressure, per se—the master cylinder is short, whereas the slave cylinder is tall. Owing to the larger surface area of the master cylinder compared to that of the slave cylinder, the hydraulic ram is not considered efficient in terms of mechanical advantage: in other words, the force input is much greater than the force output.
Nonetheless, the hydraulic ram is as well-suited to its purpose as a car jack. Whereas the jack is made for lifting a heavy automobile through a short vertical distance, the hydraulic ram carries a much lighter cargo (usually just one person) through a much greater vertical range—to the top of a tree or building, for instance.
A pump utilizes Pascal's principle, but instead of holding fluid in a single container, a pump allows the fluid to escape. Specifically, the pump utilizes a pressure difference, causing the fluid to move from an area of higher pressure to one of lower pressure. A very simple example of this is a siphon hose, used to draw petroleum from a car's gas tank. Sucking on one end of the hose creates an area of low pressure compared to the relatively high-pressure area of the gas tank. Eventually, the gasoline will come out of the low-pressure end of the hose. (And with luck, the person siphoning will be able to anticipate this, so that he does not get a mouthful of gasoline!)
The piston pump, more complex, but still fairly basic, consists of a vertical cylinder along which a piston rises and falls. Near the bottom of the cylinder are two valves, an inlet valve through which fluid flows into the cylinder, and an outlet valve through which fluid flows out of it. On the suction stroke, as the piston moves upward, the inlet valve opens and allows fluid to enter the cylinder. On the downstroke, the inlet valve closes while the outlet valve opens, and the pressure provided by the piston on the fluid forces it through the outlet valve.
One of the most obvious applications of the piston pump is in the engine of an automobile. In this case, of course, the fluid being pumped is gasoline, which pushes the pistons by providing a series of controlled explosions created by the spark plug's ignition of the gas. In another variety of piston pump—the kind used to inflate a basketball or a bicycle tire—air is the fluid being pumped. Then there is a pump for water, which pumps drinking water from the ground It may also be used to remove desirable water from an area where it is a hindrance, for instance, in the bottom of a boat.
Though Pascal provided valuable understanding with regard to the use of pressure for performing work, the thinker who first formulated general principles regarding the relationship between fluids and pressure was the Swiss mathematician and physicist Daniel Bernoulli (1700-1782). Bernoulli is considered the father of fluid mechanics, the study of the behavior of gases and liquids at rest and in motion.
While conducting experiments with liquids, Bernoulli observed that when the diameter of a pipe is reduced, the water flows faster. This suggested to him that some force must be acting upon the water, a force that he reasoned must arise from differences in pressure. Specifically, the slower-moving fluid in the wider area of pipe had a greater pressure than the portion of the fluid moving through the narrower part of the pipe. As a result, he concluded that pressure and velocity are inversely related—in other words, as one increases, the other decreases.
Hence, he formulated Bernoulli's principle, which states that for all changes in movement, the sum of static and dynamic pressure in a fluid remain the same. A fluid at rest exerts static pressure, which is commonly meant by "pressure," as in "water pressure." As the fluid begins to move, however, a portion of the static pressure—proportional to the speed of the fluid—is converted to what is known as dynamic pressure, or the pressure of movement. In a cylindrical pipe, static pressure is exerted perpendicular to the surface of the container, whereas dynamic pressure is parallel to it.
According to Bernoulli's principle, the greater the velocity of flow in a fluid, the greater the dynamic pressure and the less the static pressure: in other words, slower-moving fluid exerts greater pressure than faster-moving fluid. The discovery of this principle ultimately made possible the development of the airplane.
As fluid moves from a wider pipe to a narrower one, the volume of that fluid that moves a given distance in a given time period does not change. But since the width of the narrower pipe is smaller, the fluid must move faster (that is, with greater dynamic pressure) in order to move the same amount of fluid the same distance in the same amount of time. One way to illustrate this is to observe the behavior of a river: in a wide, unconstricted region, it flows slowly, but if its flow is narrowed by canyon walls, then it speeds up dramatically.
Bernoulli's principle ultimately became the basis for the airfoil, the design of an airplane's wing when seen from the end. An airfoil is shaped like an asymmetrical teardrop laid on its side, with the "fat" end toward the airflow. As air hits the front of the airfoil, the airstream divides, part of it passing over the wing and part passing under. The upper surface of the airfoil is curved, however, whereas the lower surface is much straighter.
As a result, the air flowing over the top has a greater distance to cover than the air flowing under the wing. Since fluids have a tendency to compensate for all objects with which they come into contact, the air at the top will flow faster to meet with air at the bottom at the rear end of the wing. Faster airflow, as demonstrated by Bernoulli, indicates lower pressure, meaning that the pressure on the bottom of the wing keeps the airplane aloft.
One hundred and twenty years before the first successful airplane flight by the Wright brothers in 1903, another pair of brothers—the Mont-golfiers of France—developed another means of flight. This was the balloon, which relied on an entirely different principle to get off the ground: buoyancy, or the tendency of an object immersed in a fluid to float. As with Bernoulli's principle, however, the concept of buoyancy is related to pressure.
In the third century B.C. , the Greek mathematician, physicist, and inventor Archimedes (c. 287-212 B.C. ) discovered what came to be known as Archimedes's principle, which holds that the buoyant force of an object immersed in fluid is equal to the weight of the fluid displaced by the object. This is the reason why ships float: because the buoyant, or lifting, force of them is less than equal to the weight of the water they displace.
The hull of a ship is designed to displace or move a quantity of water whose weight is greater than that of the vessel itself. The weight of the displaced water—that is, its mass multiplied by the downward acceleration caused by gravity—is equal to the buoyant force that the ocean exerts on the ship. If the ship weighs less than the water it displaces, it will float; but if it weighs more, it will sink.
The factors involved in Archimedes's principle depend on density, gravity, and depth rather than pressure. However, the greater the depth within a fluid, the greater the pressure that pushes against an object immersed in the fluid. Moreover, the overall pressure at a given depth in a fluid is related in part to both density and gravity, components of buoyant force.
The pressure that a fluid exerts on the bottom of its container is equal to dgh, where d is density, g the acceleration due to gravity, and h the depth of the container. For any portion of the fluid, h is equal to its depth within the container, meaning that
In this context, the ocean may be viewed as a type of "container." At its surface, the air exerts downward pressure equal to 1 atm. The density of the water itself is uniform, as is the downward acceleration due to gravity; the only variable, then, is h, or the distance below the surface. At the deepest reaches of the ocean, the pressure is incredibly great—far more than any human being could endure. This vast amount of pressure pushes upward, resisting the downward pressure of objects on its surface. At the same time, if a boat's weight is dispersed properly along its hull, the ship maximizes area and minimizes force, thus exerting a downward pressure on the surface of the water that is less than the upward pressure of the water itself. Hence, it floats.
The Montgolfiers used the principle of buoyancy not to float on the water, but to float in the sky with a craft lighter than air. The particulars of this achievement are discussed elsewhere, in the context of buoyancy; but the topic of lighter-than-air flight suggests another concept that has been alluded to several times throughout this essay: air pressure.
Just as water pressure is greatest at the bottom of the ocean, air pressure is greatest at the surface of the Earth—which, in fact, is at the bottom of an "ocean" of air. Both air and water pressure are examples of hydrostatic pressure—the pressure that exists at any place in a body of fluid due to the weight of the fluid above. In the case of air pressure, air is pulled downward by the force of Earth's gravitation, and air along the surface has greater pressure due to the weight (a function of gravity) of the air above it. At great heights above Earth's surface, however, the gravitational force is diminished, and, thus, the air pressure is much smaller.
In ordinary experience, a person's body is subjected to an impressive amount of pressure. Given the value of atmospheric pressure discussed earlier, if one holds out one's hand—assuming that the surface is about 20 in 2 (0.129 m 2 )—the force of the air resting on it is nearly 300 lb (136 kg)! How is it, then, that one's hand is not crushed by all this weight? The reason is that the human body itself is under pressure, and that the interior of the body exerts a pressure equal to that of the air.
The human body is, in fact, suited to the normal air pressure of 1 atm, and if that external pressure is altered, the body undergoes changes that may be harmful or even fatal. A minor example of this is the "popping" in the ears that occurs when one drives through the mountains or rides in an airplane. With changes in altitude come changes in pressure, and thus, the pressure in the ears changes as well.
As noted earlier, at higher altitudes, the air pressure is diminished, which makes it harder to breathe. Because air is a gas, its molecules have a tendency to be non-attractive: in other words, when the pressure is low, they tend to move away from one another, and the result is that a person at a high altitude has difficulty getting enough air into his or her lungs. Runners competing in the 1968 Olympics at Mexico City, a town in the mountains, had to train in high-altitude environments so that they would be able to breathe during competition. For baseball teams competing in Denver, Colorado (known as "the Mile-High City"), this disadvantage in breathing is compensated by the fact that lowered pressure and resistance allows a baseball to move more easily through the air.
If a person is raised in such a high-altitude environment, of course, he or she becomes used to breathing under low air pressure conditions. In the Peruvian Andes, for instance, people spend their whole lives at a height more than twice as great as that of Denver, but a person from a low-altitude area should visit such a locale only after taking precautions. At extremely great heights, of course, no human can breathe: hence airplane cabins are pressurized. Most planes are equipped with oxygen masks, which fall from the ceiling if the interior of the cabin experiences a pressure drop. Without these masks, everyone in the cabin would die.
Another aspect of pressure and the human body is blood pressure. Just as 20/20 vision is ideal, doctors recommend a target blood pressure of "120 over 80"—but what does that mean? When a person's blood pressure is measured, an inflatable cuff is wrapped around the upper arm at the same level as the heart. At the same time, a stethoscope is placed along an artery in the lower arm to monitor the sound of the blood flow. The cuff is inflated to stop the blood flow, then the pressure is released until the blood just begins flowing again, producing a gurgling sound in the stethoscope.
The pressure required to stop the blood flow is known as the systolic pressure, which is equal to the maximum pressure produced by the heart. After the pressure on the cuff is reduced until the blood begins flowing normally—which is reflected by the cessation of the gurgling sound in the stethoscope—the pressure of the artery is measured again. This is the diastolic pressure, or the pressure that exists within the artery between strokes of the heart. For a healthy person, systolic pressure should be 120 torr, and diastolic pressure 80 torr.
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