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<br />E2 = the total energy at pOint 2 <br /> <br />6E = the energy lost between pOints 1 and 2 <br />and WORK. any external energy added between points 1 and 2 <br />In fluid dynamics problems. as in the more familiar case of solid <br />bodies in motion. the units for terms in equation 2-1 are foot-pounds <br />(ft-lbs) in the British system and meter-kilogram force (m-kgf) in the <br />gravitational metric system. When applied to fluid problems, the above <br />relationship results in the Bernoulli equation for a fluid filament <br /> <br />of infinitesimal cross section; and when integrated over the entire <br /> <br />cross section of flow. the One-Dimensional Energy Equation is developed. <br />The second principle introduced above. conservation of mass, is <br />also an important consideration in both solid and fluid dynamics. but <br />in the case of solid bodies which display a strong resistance to defor- <br /> <br />mation. conservation of mass is readily satisfied. Fluid mechanics, on <br /> <br />the other hand, requires a mathematical expression to account for a <br /> <br /> <br />continuously deforming body of moving fluid. The basic assumption is <br /> <br /> <br />that a continuum of fluid exists throughout the body in both time and <br /> <br />space. This principle is generally referred to as "continuity." <br />It is useful to illustrate these principles with a problem involv- <br />i'ng flow of a fluid between two points in space. To illustrate the <br /> <br />Bernoulli equation, assume a continuous filament of flow exists in a <br /> <br />streamtube of infinitesimal cross section and for the period of time <br />required for a particle of fluid to pass between the two points. <br /> <br />Furthermore, no flow crosses the boundary of this streamtube except at <br />its end points. Oy definition, kinetic energy is 1/2 MV2 where M is <br />the total mass that flows and V is the flow velocity. Also, by defini- <br /> <br />2.02 <br />