Introduction to Fluid statics


Fluids. whether moving or stationary. exert forcel! over a given area or surface. Fluids which are stationary, and therefore have no velocity gradient, exert norma l or pressure forces whereas moving fluids exert shearing forces on the surfaces with which they are in contact. It was the Greek thinker Archimedes (c287BC-di2BC) who first published a treatise on noating bodies and provided a significant understanding of fluid statics and buoyancy. It was not for another 18 centuries that the Flemish engineer Simon Stevin ( 1548-1620) correctly .provided an explanation of the basic principles of nuid statics. Blaise Pascal ( 1623-1662), the French mathematician. physicist and theologian. performed many experiments on nuids and was able to illustrate the funda­ mental relationships involved.

In the internationally accepted SI system (Systeme International d’Unites), the preferred derived units of pressure arc Newtons per square metre (Nm-2) with base units of kgm -1s-1. These units, also known as the Pascal (Pa), arc relatively small. The term bar is therefore frequently used to represent one hundred thousand Newtons per square metre (105 Nm-2 or 0.1 MPa). Many pressure gauges encountered in the process industries are still to be found cali­  brated in traditional systems of units including the Metric System, the Absolute English System and the Engineers’ English System. This can lead to confusion in conversion although many gauges are manufactured with several scales. Further complication arises since the Pascal is a relatively small term and SJ recommends that any numerica l prefix should appear in the numerator of an expression. Although numerically the same, Nmm -2 is often wrongly used instead of MNm-2.

It is important to note that the pressure of a fluid is expressed in one of two ways. Absolute pressure refers to the pressure above total vacuum whereas gauge pressure refers to the pressure above atmospheric, which itself is a vari ­ able quantity and depends on the local meteorological conditions. The atmo­ spheric pressure used as standard corresponds to l 01.3 kNm-2 and is equivalent to approximately 14.7 pounds force per square inch, or a barometric reading of 760 mmHg. The pressure in a vacuum. known as absolute zero, therefore con·e­ sponds to a gauge pressure of -l01.3 kNm-2 assuming standard atmospheric pressure. A negative gauge pressure thus refers to a pressure below atmospheric.

The barometer is a simple instrument for accurately measuring the atmo­ spheric pressure. In its simplest form it consists of a sealed glass tube filled with a liquid (usually mercury) and inverted in a reservoir of the same liquid. The atmospheric pressure is therefore exerted downwards on the reservoir of liquid such that the liquid in the tube reaches an equilibrium elevation. Above the liquid meniscus exists a vacuum, although in actual fact it corresponds to the vapour pressure of the liquid. In the case of mercury this is a pressure of I 0 kNm-2 at 20°C.

In addition to gauges that measure absolute pressure, there are many devices and instruments that measure the difference in pressure between two parts in a system . Differential pressure is of particular use for determining indirectly the rate of flow of a process fluid in a pipe or duct, or to assess the status of a particular piece of process equipment during operation -for example, identi­ fying the accumulation of deposits restJicting flow, which is important in the case of heat exchangers and process ventilation filters.

Although there are many sophisticated pressure-measuring devices avail­ able, manometers are still commonly used for measming the pressure in vessels or in pipelines. Various forms of manometer have been designed and generally are either open (piezometer) or closed (differential). For manometer tubes with a bore of less than 12 mm, capillary action is significant and may appreciably raise or depress the meniscus, depending on the manometric tluid.

Finally, while fluids may be described as substances which offer no resis­ tance to shear and include both gases and liquids, gases differ from l iquids in that they are compressible and may be described by simple gas laws. Liquids are effectively incompressible and for most practical purposes their density remains constant and does not vary with depth (hydrostatic pressure). At ultra high pressures this is not strictly true. Water, for example, has a 3.3%

compressibility at pressures of 69 MNm-2 wich is equivalent to a depth of 7 km. It was Archimedes who first performed experiments on the density of solids by immersing objects in fluids. The famous story is told of Archimedes being asked by King Hiero to determine whether a crown was pure gold throughout or contained a cheap alloy, without damag-ing the crown. Suppos­edly, while in a public bath, Archimedes is said to have had a sudden thought of immersing the crown in water and checking its density. He was so excited that he ran home through the streets naked shouting ‘Eureka! Eureka! -I have found it! I have found it!’.

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