Pascal, defined

P) force per unit area. The SI unit of pressure is the pascal, defined as one newton per square meter. Other common pressure units are the atmosphere, the bar, and the Torr. 

The dynamic viscosity, or coefficient of viscosity, 77 of a Newtonian fluid is defined as the force per unit area necessary to maintain a unit velocity gradient at right angles to the direction of flow between two parallel planes a unit distance apart. The SI unit is pascal-second or newton-second per meter squared [N s m ]. The c.g.s. unit of viscosity is the poise [P] 1 cP = 1 mN s m . The dynamic viscosity decreases with the temperature approximately according to the equation log rj = A + BIT. Values of A and B for a large number of liquids are given by Barrer, Trans. Faraday Soc. 39 48 (1943). 

Pressure is defined as force per unit of area. The International System of Units (SI) pressure unit is the pascal (Pa), defined as 1.0 N /m. Conversion factors from non-SI units to pascal are given in Table 1 (see also Units and conversion factors front matter). An asterisk after the sixth decimal place indicates that the conversion factor is exact and all subsequent digits are 2ero. Relationships that are not followed by an asterisk are either the results of physical measurements or are only approximate. The factors are written as numbers greater than 1 and less than 10, with 6 or fewer decimal places (1). 

The pascal is defined as the pressure exerted by a force of one newton acting on an area of one square meter (recall that pressure = force/area). 

When we consider the mechanical properties of polymeric materials, and in particular when we design methods of testing them, the parameters most generally considered are stress, strain, and Young s modulus. Stress is defined as the force applied per unit cross sectional area, and has the basic dimensions of N m in SI units. These units are alternatively combined into the derived unit of Pascals (abbreviated Pa). In practice they are extremely small, so that real materials need to be tested with a very large number of Pa... 

The accepted SI unit for pressure is the pascal (Pa). Pressure is defined as force per unit area, P/, so the pascai can be expressed by combining the SI units for these two variabies. The SI unit of force is the newton (N), and area is measured in square meters (m ). Thus, the pascai is 1 N/m. Expressed in pascais, the numericai vaiue of atmospheric pressure is quite iarge. By intemationai agreement, 1 atm is defined exactiy in terms of pascais ... 

Column inlet pressures in hplc can be as much as 200 times atmospheric pressure, and hplc columns are packed using much larger pressures (up to 700 times atmospheric). The SI unit of pressure is the Pascal (1 Pa = 1 Nm-2) normal atmospheric pressure is about 105 Pa. Because it is convenient to express pressure using reasonably small numbers, experimental workers and instrument manufacturers report pressures in bar, or pounds per square inch (psi), or sometimes in kg cm-2. The bar is defined by 1 bar = 105 Pa, so that 1 bar corresponds roughly to normal atmospheric pressure. You will need to be able to convert between these units. 

The tensile test is performed by placing a specially shaped specimen in the heads of the testing machine. The specimen is pulled apart through a hydraulic or mechanical loading system (Figure 15.33). Most ordinary tensile tests are conducted at room temperature and the tensile load is applied slowly. The unit measure of tensile strength is the pascal (Pa), or newtons per square meter (N-nf2), and is defined by the following equation ... 

The stress is simply defined as the force divided by the area over which it is applied. Pressure is a compressive bulk stress. When we hang a weight on a wire, we are applying an extensional stress and when we slide a piece of paper over a gummed surface to reach the correct position, we are applying a shear stress. We will focus more strongly on this latter stress because most of our instruments are designed around this format. The units of stress are Pascals. 

A mathematical theorem defining the form of the polynomial corresponding to (a + b)", where n is a positive integer. The coefficients for each term of such a polynomial are given by Pascal s triangle. See Pascal s Triangle... 

Table 1-2 lists some quantities that are defined in terms of the fundamental quantities. For example, force is measured in newtons (N), pressure is measured in pascals (Pa), and energy is measured in joules (J), each of which can be expressed in terms of the more fundamental units of length, time, and mass. 

PRESSURE. If a body of fluid is at rest, the forces are in equilibrium or the fluid is in static equilibrium. The types of force that may aci on a body are shear or tangential force, tensile force, and compressive force. Fluids move continuously under the action of shear or tangential forces. Thus, a fluid at rest is free in each part from shear forces one fluid layer does not slide relative to an adjacent layer. Fluids can be subjected to a compressive stress, which is commonly called pressure. The term may be defined as force per unit area. The pressure units may be dynes per square centimeter, pounds per square foot, torr. mega-Pascals, etc. Atmospheric pressure is the force acting upon a unit area due to the weight of the atmosphere. Gage pressure is the difference between the pressure of the fluid measured (at some point) and atmospheric pressure. Absolute pressure, which can be measured by a mercury barometer, is the sum of gage pressure plus atmospheric pressure. 

The word viscosity comes from the Latin word for mistletoe, viscum. Anyone familiar with this plant is aware that it exudes a viscous sticky sap when harvested. Viscosity is defined after Isaac Newton in his Principia as the ratio of stress to shear rate and is given the symbol T. Stress (a) in a fluid is simply force/area, like pressure, and has the units of pascals (Pa S.I. units) or dynes/cm2 (c.g.s.). Shear rate or strain rate (y or dyldt) is the differential of strain (y) with respect to time. Strain is simply the change in shape of a volume of fluid as a result of an applied stress and has no units. The shear rate is in fact a velocity gradient, not a flow rate. It has the bizarre units of 1/time (sec-1) and is the velocity at a given point in the fluid divided by the distance of that point from the stationary plane. 

This unit describes a method for measuring the viscosity (r ) of Newtonian fluids. For a Newtonian fluid, viscosity is a constant at a given temperature and pressure, as defined in unit hi. i common liquids under ordinary circumstances behave in this way. Examples include pure fluids and solutions. Liquids which have suspended matter of sufficient size and concentration may deviate from Newtonian behavior. Examples of liquids exhibiting non-Newtonian behavior (unit hi. i) include polymer suspensions, emulsions, and fruit juices. Glass capillary viscometers are useful for the measurement of fluids, with the appropriate choice of capillary dimensions, for Newtonian fluids of viscosity up to 10 Pascals (Newtons m/sec 2) or 100 Poise (dynes cm/sec 2). Traditionally, these viscometers have been used in the oil industry. However, they have been adapted for use in the food industry and are commonly used for molecular weight prediction of food polymers in very dilute solutions (Daubert and Foegeding, 1998). There are three common types of capillary viscometers including Ubelohde, Ostwald, and Cannon-Fenske. These viscometers are often referred to as U-tube viscometers because they resemble the letter U (see Fig. HI.3.1). 

A gas is a collection of atoms or molecules moving independently through a volume that is largely empty space. Collisions of the randomly moving particles with the walls of their container exert a force per unit area that we perceive as pressure. The SI unit for pressure is the pascal, but the atmosphere and the millimeter of mercury are more commonly used. The physical condition of any gas is defined by four variables pressure (P), temperature (T), volume (V), and molar amount (n). The specific relationships among these variable are called the gas laws ... 

Global basis functions. Common global basis functions, where the interpolation functions for multi-dimensional domains can be obtained, come from expansions of Pascal s triangle. In 2D, Pascal s triangle is defined by,... 

The pascal represents a very small pressure, and therefore the most common applications, such as tire pressure, will use kilopascals (kPa) instead of Pa. Other units of pressure include the torr (or millimeter of mercury, mmHg), inches of mercury, the atmosphere (atm), and the bar. A torr is an amount of pressure necessary to support a column of mercury 1 mm in height. One atmosphere of pressure is loosely defined by the atmospheric pressure at sea level, but is more precisely defined as the pressure necessary to support a column of mercury 760 mm in height. One bar of pressure is equal to 100 kPa. The relationships between the various units of pressure are given below ... 

Pressure is defined as force per unit area. In the International System of Units (SI, or mks), unit pressure corresponds to one newton per square meter, which is denoted as one pascal or Pa (named after Blaise Pascal, the seventeenth-century French scientist). There are several other, more commonly used pressure units, however. One is the atmosphere or atm it is... 

One pascal corresponds to a very small pressure as compared with one atm, that is, 1 Pa = 9.86923 X 10 6 atm. The bar is another commonly used pressure unit. One bar is defined as 105 Pa and is equal to 750 torr. 

If pressure is given in atmospheres and volume is given in liters, a value for R of 0.08206 L-atm/(mol-K) is used. If pressure is given in Pascal (newtons/m2) and volume in cubic meters, then the SI value for R of 8.314 J/(mol-K) may be used because a joule is defined as a Newton-meter. A value for R of 8.314 m3-Pa/(mol-K) is identical to the ideal gas constant using joules. 

The pressure P of a fluid on a surface is defined as the normal force exerted by the fluid per unit area of the surface. If force is measured in N and area in m2, the unit is the newton per square meter or N nTJ, called the pascal, symbol Pa, the basic SI unit of pressure. In the English engineering system the most common unit is the pound force per square inch (psi). 

As you learned in previous studies, pressure is defined in physical terms as the force exerted on an object per unit of surface area (P = FI A). One commonly used SI unit of pressure is the pascal (Pa), equal to 1 N/m2. More often, pressure is reported in kilopascals (kPa), equal to 1000 Pa. (You will learn about other units of pressure later in this section.)... 

For many years, atmospheric pressure was measured in millimetres of mercury (mm Hg). In the British Commonwealth and the United States, inches of mercury were used. Standard atmospheric pressure, the pressure of the atmosphere at sea level and 0°C, is 760 mm Hg. More recently, in honour of the work of Torricelli, standard atmospheric pressure has been defined as 760 torr. 1 torr represents a column of mercury 1 mm in height at 0°C. Another common unit for measuring pressure is atmospheres (atm), where 1 atm is equivalent to 760 torr. While mm Hg, torr, and atm are still used to measure pressure, especially in technological and medical applications, the SI units are pascals (Pa) or kilopascals (kPa). 

U and V respectively. Systeme International (SI) units, described in Appendix B, are used extensively but not slavishly. Chemically convenient quantities such as the gram (g), cubic centimeter (cm ), and hter (L = dm =10 cm ) are still used where useful—densities in g cm , concentrations in mol L , molar masses in g. Conversions of such quantities into their SI equivalents is trivially easy. The situation with pressure is not so simple, since the SI pascal is a very awkward unit. Throughout the text, both bar and atmosphere are used. Generally bar = 10 Pa) is used when a precisely measured pressure is involved, and atmosphere = 760 Torr = 1.01325 X 10 Pa) is used to describe casually the ambient air pressure, which is usually closer to 1 atm than to 1 bar. Standard states for all chemical substances are officially defined at a pressure of 1 bar normal boiling points for liquids are still understood to refer to 1-atm values. The conversion factors given inside the front cover will help in coping with non-SI pressures. 

Rahier and his co-workers also characterized the activities of a sterol C-4 methyl oxidase (SMO), a 4-carboxysterol-3-hydroxysteroid dehydrogenase/ C-4 decarboxylase (3-HSD/D) and an NADPH-dependent 3-oxosteroid reductase in order to define the steps involved in C-4 demethylation in plants (Pascal et al, 1993 Rondet et al, 1999). Only recently, they have isolated two cDNAs from Arabidopsis thaliana encoding bifunctional 3-HSD/D. Transformation of a yeast ergosterol auxotroph mutant, which lacks 3-HSD/D activity, with either of these cDNAs restored ergosterol biosynthesis in the yeast mutant (Rahier et al, 2006). 

Shepherd satellite—planetary satellite whose gravitational perturbations on a particle tend to keep it in a stable orbit around the planet. The Pascal (Pa) is the metric unit of pressure (force per unit area). One Pascal is defined as a pressure of one Newton per square meter. The standard sea level atmospheric pressure on Earth is 101,200 Pascals. 

Pressure is expressed in various units. The SI unit for pressnre is the pascal (Pa), which is 1 kg m s. One standard atmosphere (1 atm) is defined as exactly 1.01325 X 10 Pa. The standard atmosphere is a nsefnl nnit becanse the pascal is inconveniently small and because atmospheric pressure is important as a standard of reference. We must express pressures in pascals when we perform calculations entirely in SI units. 

Pressure is defined as force/area measured in atm, bar, pascal, and torn The empirical gas laws of Boyle, Charles, and Avogadro combine to give the ideal gas law PV = nRT. 

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