CONTINUITY EQUATION Fluid FlowEven though a detailed analysis of fluid flow can be extremely difficult, the basic conceptsinvolved in fluid flow problems are fairly straightforward. These basic concepts can be appliedin solving fluid flow problems through the use of simplifying assumptions and average values,where appropriate. Even though this type of analysis would not be sufficient in the engineeringdesign of systems, it is very useful in understanding the operation of systems and predicting theapproximate response of fluid systems to changes in operating parameters.The basic principles of fluid flow include three concepts or principles; the first two of which thestudent has been exposed to in previous manuals. The first is the principle of momentum(leading to equations of fluid forces) which was covered in the manual on Classical Physics. Thesecond is the conservation of energy (leading to the First Law of Thermodynamics) which wasstudied in thermodynamics. The third is the conservation of mass (leading to the continuityequation) which will be explained in this module.PropertiesofFluidsA fluid is any substance which flows because its particles are not rigidly attached to one another.This includes liquids, gases and even some materials which are normally considered solids, suchas glass. Essentially, fluids are materials which have no repeating crystalline structure.Several properties of fluids were discussed in the Thermodynamics section of this text. Theseincluded temperature, pressure, mass, specific volume and density. Temperature was defined asthe relative measure of how hot or cold a material is. It can be used to predict the direction thatheat will be transferred. Pressure was defined as the force per unit area. Common units forpressure are pounds force per square inch (psi). Mass was defined as the quantity of mattercontained in a body and is to be distinguished from weight, which is measured by the pull ofgravity on a body. The specific volume of a substance is the volume per unit mass of thesubstance. Typical units are ft3/lbm. Density, on the other hand, is the mass of a substance perunit volume. Typical units are lbm/ft3. Density and specific volume are the inverse of oneanother. Both density and specific volume are dependant on the temperature and somewhat onthe pressure of the fluid. As the temperature of the fluid increases, the density decreases and thespecific volume increases. Since liquids are considered incompressible, an increase in pressurewill result in no change in density or specific volume of the liquid. In actuality, liquids can beslightly compressed at high pressures, resulting in a slight increase in density and a slightdecrease in specific volume of the liquid.BuoyancyBuoyancy is defined as the tendency of a body to float or rise when submerged in a fluid. Weall have had numerous opportunities of observing the buoyant effects of a liquid. When we goswimming, our bodies are held up almost entirely by the water. Wood, ice, and cork float onwater. When we lift a rock from a stream bed, it suddenly seems heavier on emerging from thewater. Boats rely on this buoyant force to stay afloat. The amount of this buoyant effect wasfirst computed and stated by the Greek philosopher Archimedes. When a body is placed in afluid, it is buoyed up by a force equal to the weight of the water that it displaces.HT-03 Page 2 Rev. 0
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