Fluid Flow LAMINAR AND TURBULENT FLOWAverage(Bulk)VelocityIn many fluid flow problems, instead of determining exact velocities at different locations in thesame flow cross-section, it is sufficient to allow a single average velocity to represent thevelocity of all fluid at that point in the pipe. This is fairly simple for turbulent flow since thevelocity profile is flat over the majority of the pipe cross-section. It is reasonable to assume thatthe average velocity is the same as the velocity at the center of the pipe.If the flow regime is laminar (the velocity profile is parabolic), the problem still exists of tryingto represent the "average" velocity at any given cross-section since an average value is used inthe fluid flow equations. Technically, this is done by means of integral calculus. Practically, thestudent should use an average value that is half of the center line value.ViscosityViscosity is a fluid property that measures the resistance of the fluid to deforming due to a shearforce. Viscosity is the internal friction of a fluid which makes it resist flowing past a solidsurface or other layers of the fluid. Viscosity can also be considered to be a measure of theresistance of a fluid to flowing. A thick oil has a high viscosity; water has a low viscosity. Theunit of measurement for absolute viscosity is:µ = absolute viscosity of fluid (lbf-sec/ft^{2}).The viscosity of a fluid is usually significantly dependent on the temperature of the fluid andrelatively independent of the pressure. For most fluids, as the temperature of the fluid increases,the viscosity of the fluid decreases. An example of this can be seen in the lubricating oil ofengines. When the engine and its lubricating oil are cold, the oil is very viscous, or thick. Afterthe engine is started and the lubricating oil increases in temperature, the viscosity of the oildecreases significantly and the oil seems much thinner.IdealFluidAn ideal fluid is one that is incompressible and has no viscosity. Ideal fluids do not actuallyexist, but sometimes it is useful to consider what would happen to an ideal fluid in a particularfluid flow problem in order to simplify the problem.ReynoldsNumberThe flow regime (either laminar or turbulent) is determined by evaluating the Reynolds numberof the flow (refer to figure 5). The Reynolds number, based on studies of Osborn Reynolds, isa dimensionless number comprised of the physical characteristics of the flow. Equation 3-7 isused to calculate the Reynolds number (N_{R}) for fluid flow.N_{R} = r v D / µ g_{c}(3-7)Rev. 0 Page 19 HT-03

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