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1 CHAPTER2 properties of FluidsIn this chapter we discuss a number of fundamental properties of fluids. Anunderstanding of these properties is essential for us to apply basic principlesof fluid mechanics to the solution of practical DISTINCTIONBETWEEN ASOLID AND AFLUIDThe molecules of a solidare usually closer together than those of a forces between the molecules of a solid are so large that a solid tendsto retain its shape. This is not the case for a fluid , where the attractive forces be-tween the molecules are smaller. An ideal elastic solid will deform under loadand, once the load is removed, will return to its original state. Some solids areplastic. These deform under the action of a sufficient load and deformation con-tinues as long as a load is applied, providing the material does not rupture.

2 De-formation ceases when the load is removed, but the plastic solid does not returnto its original intermolecular cohesive forces in a fluid are not great enough to holdthe various elements of the fluid together. Hence a fluid will flow under the ac-tion of the slightest stress and flow will continue as long as the stress is DISTINCTIONBETWEEN AGAS AND ALIQUIDA fluid may be either a gasor a molecules of a gas are much fartherapart than those of a liquid. Hence a gas is very compressible, and when all ex-ternal pressure is removed, it tends to expand indefinitely. A gas is therefore inequilibrium only when it is completely enclosed. A liquid is relatively incom-pressible, and if all pressure, except that of its own vapor pressure, is removed,the cohesion between molecules holds them together, so that the liquid does notexpand indefinitely.

3 Therefore a liquid may have a free surface, , a surfacefrom which all pressure is removed, except that of its own vaporis a gas whose temperature and pressure are such that it is verynear the liquid phase. Thus steam is considered a vapor because its state 8/10/01 5:38 PM Page 13normally not far from that of water. A gas may be defined as a highly super-heated vapor; that is, its state is far removed from the liquid phase. Thus air isconsidered a gas because its state is normally very far from that of liquid volume of a gas or vapor is greatly affected by changes in pressure ortemperature or both. It is usually necessary, therefore, to take account ofchanges in volume and temperature in dealing with gases or vapors.

4 Wheneversignificant temperature or phase changes are involved in dealing with vaporsand gases, the subject is largely dependent on heat phenomena (thermodynam-ics). Thus fluid mechanics and thermodynamics are DENSITY,SPECIFICWEIGHT,SPECIFICVOLUME,AN DSPECIFICGRAVITYThe densityr(rho),1or more strictly, mass density,of a fluid is its massper unitvolume, while the specific weightg(gamma) is its weight per unit volume. In theBritish Gravitational (BG) system (Sec. ) density rwill be in slugs per cubicfoot (kg/m3in SI units), which can also be expressed as units of lb sec2/ft4(N s2/m4in SI units) (Sec. and inside covers).Specific weight grepresents the force exerted by gravity on a unit volumeof fluid , and therefore must have the units of force per unit volume, such aspounds per cubic foot (N/m3in SI units).

5 Density and specific weight of a fluid are related as:( )Since the physical equations are dimensionally homogeneous, the dimen-sions of density areIn SI unitsNote that density ris absolute, since it depends on mass, which is indepen-dent of location. Specific weight g, on the other hand, is not absolute, since it de-pends on the value of the gravitational acceleration g, which varies with loca-tion, primarily latitude and elevation above mean sea and specific weights of fluids vary with temperature. Appendix Aprovides commonly needed temperature variations of these quantities for waterDimensions of r dimensions of gdimensions of g N/m3m/s2 N s2m4 massvolume kgm3 Dimensions of r dimensions of gdimensions of g lb/ft3ft/sec2 lb sec2ft4 massvolume slugsft3 r gg or g rg 14 CHAPTER2: properties of Fluids1 The names of Greek letters are given in the List of Symbols on page 8/10/01 5:38 PM Page 14and air.

6 It also contains densities and specific weights of common gases at stan-dard atmospheric pressure and temperature. We shall discuss the specific weightof liquids further in Sec. volumevis the volume occupied by a unit mass of com-monly apply it to gases, and usually express it in cubic feet per slug (m3/kg inSI units). Specific volume is the reciprocal of density. Thus( )Specific gravitysof a liquid is the dimensionless ratioPhysicists use 4 C ( F) as the standard, but engineers often use 60 F( C). In the metric system the density of water at 4 C is g/cm3( g/mL),3equivalent to 1000 kg/m3, and hence the specific gravity (which isdimensionless) of a liquid has the same numerical value as its density expressedin g/mL or Mg/m3.

7 Appendix A contains information on specific gravities anddensities of various liquids at standard atmospheric specific gravity of a gas is the ratio of its density to that of either hy-drogen or air at some specified temperature and pressure, but there is no gen-eral agreement on these standards, and so we must explicitly state them in anygiven the density of a fluid varies with temperature, we must determineand specify specific gravities at particular rliquidrwater at standard temperature v 1r Density, Specific Weight, Specific Volume, and Specific Gravity152 Note that in this book we use a rounded lower case v(vee), to help distinguish itfrom a capital Vand from the Greek n(nu).3 One cubic centimeter (cm3) is equivalent to one milliliter (mL).

8 Specific weight of water at ordinary pressure andtemperature is lb/ft3. The specific gravity of mercury is Compute thedensity of water and the specific weight and density of smercuryrwater ( ) slugs/ft3 gmercury smercurygwater ( ) 846 lb/ft3 rwater gwaterg ft/sec2 8/10/01 5:38 PM Page the specific weight of a liquid is 52 lb/ft3, what is its density? the specific weight of a liquid is kN/m3, what is its density? the specific volume of a gas is 375 ft3/slug, what is its specific weight in lb/ft3? the specific volume of a gas is m3/kg, what is its specific weight in N/m3? certain gas weighs N/m3at a certain temperature and pressure. What arethe values of its density, specific volume, and specific gravity relative to airweighing N/m3?

9 Specific weight of glycerin is lb/ft3. Compute its density and specificgravity. What is its specific weight in kN/m3? a certain gasoline weighs 43 lb/ft3, what are the values of its density, specificvolume, and specific gravity relative to water at 60 F? Use Appendix COMPRESSIBLE ANDINCOMPRESSIBLEFLUIDSF luid mechanics deals with both incompressible and compressible fluids, thatis, with liquids and gases of either constant or variable density. Although thereis no such thing in reality as an incompressible fluid , we use this term wherethe change in density with pressure is so small as to be negligible. This is usuallythe case with liquids. We may also consider gases to be incompressible when thepressure variation is small compared with the absolute we consider liquids to be incompressible fluids, yet soundwaves, which are really pressure waves, travel through them.

10 This is evidence ofthe elasticity of liquids. In problems involving water hammer (Sec. ) wemust consider the compressibility of the flow of air in a ventilating system is a case where we may treat a gas asincompressible, for the pressure variation is so small that the change in densityis of no importance. But for a gas or steam flowing at high velocity through along pipeline, the drop in pressure may be so great that we cannot ignore thechange in density. For an airplane flying at speeds below 250 mph (100 m/s), we16 CHAPTER2: properties of specific weight of water at ordinary pressure andtemperature is kN/m3. The specific gravity of mercury is Compute thedensity of water and the specific weight and density of smercuryrwater ( ) Mg/m3 gmercury smercurygwater ( ) kN/m3 rwater m/s2 Mg/m3 8/10/01 5:38 PM Page 16may consider the air to be of constant density.