Pressure

Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure is the pressure relative to the ambient pressure. Various units are used to express pressure; some of these derive from a unit of force divided by a unit of area. Pressure may be expressed in terms of standard atmospheric pressure. Manometric units such as the centimetre of water, millimetre of mercury, inch of mercury are used to express pressures in terms of the height of column of a particular fluid in a manometer. Pressure is the amount of force applied at right angles to the surface of an object per unit area; the symbol for it is p or P. The IUPAC recommendation for pressure is a lower-case p. However, upper-case P is used; the usage of P vs p depends upon the field in which one is working, on the nearby presence of other symbols for quantities such as power and momentum, on writing style. Mathematically: p = F A, where: p is the pressure, F is the magnitude of the normal force, A is the area of the surface on contact.

Pressure is a scalar quantity. It relates the vector surface element with the normal force acting on it; the pressure is the scalar proportionality constant that relates the two normal vectors: d F n = − p d A = − p n d A. The minus sign comes from the fact that the force is considered towards the surface element, while the normal vector points outward; the equation has meaning in that, for any surface S in contact with the fluid, the total force exerted by the fluid on that surface is the surface integral over S of the right-hand side of the above equation. It is incorrect to say "the pressure is directed in such or such direction"; the pressure, as a scalar, has no direction. The force given by the previous relationship to the quantity has a direction, but the pressure does not. If we change the orientation of the surface element, the direction of the normal force changes accordingly, but the pressure remains the same. Pressure is distributed to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point.

It is a fundamental parameter in thermodynamics, it is conjugate to volume. The SI unit for pressure is the pascal, equal to one newton per square metre; this name for the unit was added in 1971. Other units of pressure, such as pounds per square inch and bar, are in common use; the CGS unit of pressure is 0.1 Pa.. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre and the like without properly identifying the force units, but using the names kilogram, kilogram-force, or gram-force as units of force is expressly forbidden in SI. The technical atmosphere is 1 kgf/cm2. Since a system under pressure has the potential to perform work on its surroundings, pressure is a measure of potential energy stored per unit volume, it is therefore related to energy density and may be expressed in units such as joules per cubic metre. Mathematically: p =; some meteorologists prefer the hectopascal for atmospheric air pressure, equivalent to the older unit millibar. Similar pressures are given in kilopascals in most other fields, where the hecto- prefix is used.

The inch of mercury is still used in the United States. Oceanographers measure underwater pressure in decibars because pressure in the ocean increases by one decibar per metre depth; the standard atmosphere is an established constant. It is equal to typical air pressure at Earth mean sea level and is defined as 101325 Pa; because pressure is measured by its ability to displace a column of liquid in a manometer, pressures are expressed as a depth of a particular fluid. The most common choices are water; the pressure exerted by a column of liquid of height h and density ρ is given by the hydrostatic pressure equation p = ρgh, where g is the gravitational acceleration. Fluid density and local gravity can vary from one reading to another depending on local factors, so the height of a fluid column

Vortex

In fluid dynamics, a vortex is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, may be observed in smoke rings, whirlpools in the wake of a boat, the winds surrounding a tropical cyclone, tornado or dust devil. Vortices are a major component of turbulent flow; the distribution of velocity, vorticity, as well as the concept of circulation are used to characterize vortices. In most vortices, the fluid flow velocity is greatest next to its axis and decreases in inverse proportion to the distance from the axis. In the absence of external forces, viscous friction within the fluid tends to organize the flow into a collection of irrotational vortices superimposed to larger-scale flows, including larger-scale vortices. Once formed, vortices can move, stretch and interact in complex ways. A moving vortex carries with it some angular and linear momentum and mass. A key concept in the dynamics of vortices is the vorticity, a vector that describes the local rotary motion at a point in the fluid, as would be perceived by an observer that moves along with it.

Conceptually, the vorticity could be observed by placing a tiny rough ball at the point in question, free to move with the fluid, observing how it rotates about its center. The direction of the vorticity vector is defined to be the direction of the axis of rotation of this imaginary ball while its length is twice the ball's angular velocity. Mathematically, the vorticity is defined as the curl of the velocity field of the fluid denoted by ω → and expressed by the vector analysis formula ∇ × u →, where ∇ is the nabla operator and u → is the local flow velocity; the local rotation measured by the vorticity ω → must not be confused with the angular velocity vector of that portion of the fluid with respect to the external environment or to any fixed axis. In a vortex, in particular, ω → may be opposite to the mean angular velocity vector of the fluid relative to the vortex's axis. In theory, the speed u of the particles in a vortex may vary with the distance r from the axis in many ways. There are two important special cases, however: If the fluid rotates like a rigid body – that is, if the angular rotational velocity Ω is uniform, so that u increases proportionally to the distance r from the axis – a tiny ball carried by the flow would rotate about its center as if it were part of that rigid body.

In such a flow, the vorticity is the same everywhere: its direction is parallel to the rotation axis, its magnitude is equal to twice the uniform angular velocity Ω of the fluid around the center of rotation. Ω → =, r → =, u → = Ω → × r → =, ω → = ∇ × u → = = 2 Ω →. If the particle speed u is inversely proportional to the distance r from the axis the imaginary test ball would not rotate over itself. In this case the vorticity ω → is zero at any point not on that axis, the flow is said to be irrotational. Ω → =, r → =, u → = Ω → × r → =, ω → = ∇ × u → = 0. In the absence of external forces, a vortex evolves quickly toward the irrotational flow pattern, where the flow velocity u is inversely proportional to the distance r. Irrotational vortices are called free vortices. For an irrotational vortex, the circulation is zero along any closed contour that does not encl

Viscosity

The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity can be conceptualized as quantifying the frictional force that arises between adjacent layers of fluid that are in relative motion. For instance, when a fluid is forced through a tube, it flows more near the tube's axis than near its walls. In such a case, experiments show; this is because a force is required to overcome the friction between the layers of the fluid which are in relative motion: the strength of this force is proportional to the viscosity. A fluid that has no resistance to shear stress is known as an inviscid fluid. Zero viscosity is observed only at low temperatures in superfluids. Otherwise, the second law of thermodynamics requires all fluids to have positive viscosity. A fluid with a high viscosity, such as pitch, may appear to be a solid; the word "viscosity" is derived from the Latin "viscum", meaning mistletoe and a viscous glue made from mistletoe berries.

In materials science and engineering, one is interested in understanding the forces, or stresses, involved in the deformation of a material. For instance, if the material were a simple spring, the answer would be given by Hooke's law, which says that the force experienced by a spring is proportional to the distance displaced from equilibrium. Stresses which can be attributed to the deformation of a material from some rest state are called elastic stresses. In other materials, stresses are present which can be attributed to the rate of change of the deformation over time; these are called. For instance, in a fluid such as water the stresses which arise from shearing the fluid do not depend on the distance the fluid has been sheared. Viscosity is the material property which relates the viscous stresses in a material to the rate of change of a deformation. Although it applies to general flows, it is easy to visualize and define in a simple shearing flow, such as a planar Couette flow. In the Couette flow, a fluid is trapped between two infinitely large plates, one fixed and one in parallel motion at constant speed u.

If the speed of the top plate is low enough in steady state the fluid particles move parallel to it, their speed varies from 0 at the bottom to u at the top. Each layer of fluid moves faster than the one just below it, friction between them gives rise to a force resisting their relative motion. In particular, the fluid applies on the top plate a force in the direction opposite to its motion, an equal but opposite force on the bottom plate. An external force is therefore required in order to keep the top plate moving at constant speed. In many fluids, the flow velocity is observed to vary linearly from zero at the bottom to u at the top. Moreover, the magnitude F of the force acting on the top plate is found to be proportional to the speed u and the area A of each plate, inversely proportional to their separation y: F = μ A u y; the proportionality factor μ is the viscosity of the fluid, with units of Pa ⋅ s. The ratio u / y is called the rate of shear deformation or shear velocity, is the derivative of the fluid speed in the direction perpendicular to the plates.

If the velocity does not vary linearly with y the appropriate generalization is τ = μ ∂ u ∂ y, where τ = F / A, ∂ u / ∂ y is the local shear velocity. This expression is referred to as Newton's law of viscosity. In shearing flows with planar symmetry, it is what defines μ, it is a special case of the general definition of viscosity, which can be expressed in coordinate-free form. Use of the Greek letter mu for the viscosity is common among mechanical and chemical engineers, as well as physicists. However, the Greek letter eta is used by chemists and the IUPAC; the viscosity μ is sometimes referred to as the shear viscosity. However, at least one author discourages the use of this terminology, noting that μ can appear in nonshearing flows in addition to shearing flows. In general terms, the viscous stresses in a fluid are defined as those resulting from the relative velocity of different fluid particles; as such, the viscous stresses. If the velocity gradients are small to a first approximation the v

Carl Wilhelm Oseen

Carl Wilhelm Oseen was a theoretical physicist in Uppsala and Director of the Nobel Institute for Theoretical Physics in Stockholm. Oseen was born in Lund, took a Fil. Kund. degree at Lund University in 1897. Oseen formulated the fundamentals of the elasticity theory of liquid crystals, as well as the Oseen equations for viscous fluid flow at small Reynolds numbers, he gave his name to the Oseen tensor and, with Horace Lamb, to the Lamb–Oseen vortex. The Basset–Boussinesq–Oseen equation describes the motion of – and forces on – a particle moving in an unsteady flow at low Reynolds numbers, he was a Plenary Speaker of the ICM in 1936 in Oslo. Oseen was a member of the Royal Swedish Academy of Sciences from 1921, a member of the Academy's Nobel Prize committee for physics from 1922; as a full professor of a Swedish university, Oseen had the right to nominate Nobel Prize winners. It was Oseen who nominated Albert Einstein for the Nobel Prize in 1921, for Einstein's work on the photoelectric effect.

Einstein was awarded the prize for 1921 when Oseen repeated the nomination in 1922. Oseen, C. W.. Neuere Methoden und Ergebnisse in der Hydrodynamik. Berlin: Akademie Verlag. Oseen, C. W.. "The theory of liquid crystals". Transactions of the Faraday Society. 29: 883–885. Doi:10.1039/tf9332900883. Oseen equations Oseen's approximation Lamb–Oseen vortex Basset–Boussinesq–Oseen equation Broberg, Gunnar. "Before 1932: Scientists writing their own history". History of Science in Sweden: the Growth of a Discipline, 1932-1982. Uppsala: Uppsala Studies in the History of Science. Pp 9–24