Sometimes the word, pressure, is presented as fluid pressure. Wherever there is a fluid, there is pressure and fluids, as a consequence of gravity, cause pressure. Water and air are the pervasive fluids. is The idea, pressure, began some 2000 years ago when the ancient Greeks postulated that matter was composed of infinitely vast numbers of vanishingly small particles, which they called atoms. The particles were thought to aggregate into the distinct forms they called solid and fluid. Fluid has the subclassifications liquid and gas. This particle perspective of the Greeks is proven today; it provides a clear way to explain the fluid property pressure. The understanding of pressure entails its physical description, its terminology and an introduction to measurement devices and methods.
PHYSICAL DESCRIPTION The sketch to the right depicts air at a typical location on Earth at sea level (z = 0). Two walls extend upward from Earth into the air a height of one meter. Atmospheric air bounds the walls on their sides and above and fills the space between them.
Physics has established that on average in time each cubic meter of space between the walls contains some 25 x 1021 particles. Although that is an enormous number the particles (mostly diatomic nitrogen and oxygen), they are so very small that more than 99.99% of the space of the cubic meter is void. We see through air because its particles occupy scarcely 0.01 percent of the space it occupies.
The magnifying glass shows a second, closer view of the air. One wall, seen from its end, is shown with the air particles surrounding it immensely exaggerated. A few are depicted as they move in all directions at speeds as fast as 1000 miles per hour. Some particles collide with the wall; others cross the plane 0 - 0 into the space as others at the same rate cross plane 0 - 0 leaving the space.
A common definition of pressure is fluid force that acts on an area divided by the area of that action. Consider the "area" part first. Suppose at the position in the figure notated A we selected a vertical area on the wall that is square and measures one millimeter by one millimeter. Studies of physics assure us that there will be billions of impacts of the air particles over that area of the wall. So very many impacts, that over time and at all locations of the square area the pressure (the net effect of the impacts divided by one millimeter squared) is constant and known to equal 101.3 kN/m2.
Were the area one tenth of one millimeter squared, the pressure (ratio of force to area) would be the same. Were the area one thousandth of one milimeter squared, the pressure would also equal 101.3 kN/m2. The pressure remains the same while the air behaves like a continuum. But, as we might anticipate, as the area gets smaller and smaller, as the area becomes so small that particles no longer hit the area continuously, the idea of pressure breaks down. There is no such thing as zero pressure because pressure is a continuum idea. The table below shows some approximate pressures that occur naturally.
Pressures at Natural Locations: Those interested in science have a beginning understanding of pressure as it occurs naturally in gases or liquids. Pressure is discussed generally with regard to some atmospheric or oceanic location. The next Example cites some values at asundry locations. The pressures vary slightly in time, in accord with the local weather.
Hopefully the natural pressures cited by the example above give the idea that natural pressures exists at points (more precisely, at elevations relative to Earth). It is also clear that pressure change with elevation has something to do with the density of the fluid.
If a fluid system experiences a pressure different from the ambient, environmentally local region, that system is inside some machine. Industrial machines operate to produce and control pressure of a gas or liquid within especially constructed spaces. The interior of an aircraft might be the most familiar. Airliners cruise at about 32,000 feet. The ambient, outside the aircraft pressure at that altitude is about 3.6 lbf/in². This air is too thin for breathing. Hence the shell of the aircraft is made "leak proof." The fuselages is a "confined space" for passengers; the pressure inside is maintained at about 10 lbf/in².
The local pressure in an airliner at altitude is about 10 psi. The aircraft is a "passive" machine. Exposed to low pressures, the structure (It is unnecessary to state that this is 10 psi absolute. The word "absolute" is redundant.)
Machines are used to produce great pressures in localized areas to expedite industrial processes. Other machines permit creation of low or very low localized pressures. Often some manner of gage is required to represent the pressure interior or within the space relative to the ambient or local pressure immediately outside of it.
| Manufactured HIGH Pressures | Manufactured LOW Pressures |
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Often there is confusion with regard to pressures withis confined engineered spaces. The devices or gages used to determine the pressure are, in a logical sense, pressure gages. No problem arrises with the idea of "pressure gages" as devices to determine pressure within confined spaces. Confusion arises for persons who call the reading of such a gage, "pressure" or "gage pressure." The readings of these gages are not pressures - the gage reading (G.R.) is a pressure difference. For the interior pressure to be known, the gage reading must be added (or subtracted) from the outside ambient pressure. We will see how this works later.
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At its conceptual stage, pressure was rationalized as the physical behavior of a fluid in contact with a solod, that is over a small area, greatly larger than the cross-sectional area of any of rhe fluid particles of a containing solid. Repeating somewhat, pressure is the continuum (continuous in localized space and time) result of the billions of fluid particle momentum interactions that occur over a small area of a constraining solid surface. The idea extends in a natural way to points interior to the fluid (see below). Pressure is a scalar property with the dimensions, force per area, [F/L2].
Descriptions of pressure in engineering thermodyamics texts are partially clear and elsewhere confusing. If you don't understand your text, you are normal. To set matters clear we address pressure as it occur naturally, then those pressures our machines create in special, especially constructed spaces. The following definitions are useful.
HURRICANE WILMA(October - 2005) set records. At times her winds reached 185 miles per hour and the (static) barometric pressure in the her eye was measured at 882 mbar. How possibly could one measure the pressure of winds in a hurricane?
The above terms apply principally to naturally occurring pressures. Next we address some pressures created by engineering. These pressures can be said to be created and "contained" within some engineering device.
Awkward Terminology: The above terms and ideas constitute a "toolbox" of understanding with all that is needed to solve problems correctly. However, other terms common to pressure technology are misleading and need to be used with care or avoided.
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Originally pressure was known only "as it changed." Early Greek divers experienced an increasing pressure-force on their ear drums as they dived. The Aztecs felt their ears pop as they ascended the Andes. Your own ears give you messages as the weather changes. Next we present a very common equation (to be derived later) that expresses the difference of pressure of a fluid between two elevations:
(z*) - ρfluid, avggo(z - z*) = p(z)
(1)
(2)
(3)
In the usual experience of pressure change term (1) represents the known (or experienced) pressure p(z*) at a known elevation z* in the fluid. Term (2) is calculated upon inserting a numerical value for the second elevation, z and the density of the fluid. Water, virtually incompressible, has constant density but for air an average density (or an integration) is used . The result is the unknown pressure, term (3). Term (2) might be applied more that once - as we shall see.
Some call this the "hydrostatic equation." It belongs to a group of equations that embody the "hydrostatic principle." Here elevation, the coordinat, Z, is defined "positive upward." To summarize:
Referenced to the pressure p(z*) at an elevation, z*, pressures at all contiguous locations of greater elevation (z < z*) are less than p(z*). Conversly pressures at all elevations, less than the reference (z > z*) are greater than p(z*). Engineers cannot resist stating this last fact informally as:
Pressure in a fluid decreases as one moves upward
and it increases as one moves downward.
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Torricelli's Barometer: Torricelli is credited with was the first to quantify pressure. He and fellow engineers (1645) were puzzled by the complete failure of their best water pumps (used in mining). The pumps lifted well, drawing water columns to about 34 feet, then "created vacuum" and failed. Knowing something of mercury, Torricelli rationalized that were mercury pumped (being ~14 times heavier than water), mercury would "pull vacuum" at a height of about 34/14 feet or 28.8 inches. To pump mercury was out of the question so he and Viviani improvised. They filled a long glass tube with mercury, inverted its open, covered end into a large bowl of water (with mercury at the bottom). As they tipped the tube toward vertical, it "pulled vacuum" (showed a void at the closed top) just as he had surmised. They drained the water. The remaining, sustained column of liquid mercury stood about 30 inches tall.
Torricelli declared, "There, the pressure, in that void is zero!" And with that dashing, near perfect assumption, he became the first scientist to quantify pressure. That pressure, though not zero, is indeed very small (~16Pa) and sufficiently close to zero to be a servicable "zero pressure reference" for many scientific studies. Next, Torricelli calculated some of the first values of atmospheric pressure.
STANDARD ATMOSPHERE: A properly installed barometer can be used with the hydrostatic equation to quantify the pressure of the atmosphere. With the barometer, according to Torricelli's discovery, the pressure in the void above mercury is zero (the first quantified pressure). We let the hydrostatic principle start "in the void" and be applied along a path downward through liquid mercury to the atmosphere (at zero elevation and sea level). Thus the magnitude of term (1) (previous page) is zero and the result of the calculation will be the pressure of the atmosphere.
pvacuum(z* = 0.76m) - ρmergurygo(0.0 - 0.76m) = patmosphere
To proceed, the acceleration of gravity and the density of mercury must be known and applied.
0 + 13,595(kg/m3)(9.81m/s2) (0.76m) = 101,300 N/m2 = 101.3kPa
| Standard Atmosphere |
| 25°C 101.3 kPa ρ = 1.2 kg/m3 |
| 80°F 14.7 lbf/ft2 ρ = 0.075 lbm/ft3 |
Next to the assumed "zero pressure" of the void in a barometer, the most commonly known pressure is the called Standard Atmosphere. Measurements of atmospheric pressure have been recorded at sea level all over Earth and found to vary only slightly from the average 101.3kPa (or 14.7 psi). In the absence of a specified pressure, engineers assume those values to be standard. Our next illustration begins with the assumption of standard atmospheric pressure then uses the hydrostatic principle to approximate a storm surge.