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ES 202 Fluid and Thermal Systems Lecture 10: Pipe Flow (Major Losses) (1/6/2003)

ES 202 Fluid and Thermal Systems Lecture 10: Pipe Flow (Major Losses) (1/6/2003). Assignments. Reading: Cengel & Turner Section 12-5, 12-6 Homework: 12-25, 12-35, 12-42 in Cengel & Turner. Road Map of Lecture 10. Announcements Comments on Lab 1 Recap from Lecture 9

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ES 202 Fluid and Thermal Systems Lecture 10: Pipe Flow (Major Losses) (1/6/2003)

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  1. ES 202Fluid and Thermal SystemsLecture 10:Pipe Flow (Major Losses)(1/6/2003)

  2. Assignments • Reading: • Cengel & Turner Section 12-5, 12-6 • Homework: • 12-25, 12-35, 12-42 in Cengel & Turner ES 202 Fluid & Thermal Systems

  3. Road Map of Lecture 10 • Announcements • Comments on Lab 1 • Recap from Lecture 9 • Modified Bernoulli’s equation • Concept of viscosity • Pipe friction • friction factor • significance of Reynolds number • laminar versus turbulent • Moody diagram • flow chart to determine friction factor ES 202 Fluid & Thermal Systems

  4. Announcements • Lab 2 this week • dress casually • you may get wet • formation of lab group of 2-3 students (need to split into 2 groups, 1.5 periods per group) • report your lab group to me by the end of today via email, otherwise I will assign you • Extra evening office hours this week (8 pm to 10 pm) • (From tutor) Review package for Exam 1 available at the Learning Center and the new residence hall • Review session for Exam 1 on Saturday evening 8 pm to 10 pm ES 202 Fluid & Thermal Systems

  5. Comments on Lab 1 • Write your memorandum as if your project manager will not read your attachments: • list your p groups • state the functional relationship between p groups • Fundamental rules of plotting • always label your axes clearly • always plot the dependent variable against the independent variable! • Unit conversion is a good practice but NOT necessary in forming p groups (one of the many advantages of p group) • What is a log-log plot for? (Not necessary if a linear functional relationship exists!) • Invariance of p term does NOT imply invariance of dependent variable • Marking scheme (total 10 points): • correct p group formulation: 4 points • correct plotting of data: 4 points • correct conclusion of data: 2 points • coherence (adjustment up to 2 points) ES 202 Fluid & Thermal Systems

  6. Summary of Lab 1 Write-up • Upon dimensional analysis, the relevant p terms are found to be Part a:Part b: • Data analysis reveals Part a:Part b: ES 202 Fluid & Thermal Systems

  7. Area = A1 H V Area = A2 V H Recap from Lecture 9 • The Torricelli experiment (A2<< A1) • The “Bent” Torricelli experiment ES 202 Fluid & Thermal Systems

  8. “Modified” Bernoulli’s Equation • What if fluid friction causes some losses in the system, can I still apply the Bernoulli’s equation? • Recall the “conservation of energy” concept from which we approach the Bernoulli’s equation • Remedy: introduce a “head loss” factor ES 202 Fluid & Thermal Systems

  9. One Major Reason for the Losses • Fluid friction • also termed “Viscosity” • basketball-tennis-ball demonstration • exchange of momentum at the molecular scales (nature prefers “average”) • no-slip conditions at the solid surface (imagine thin layers of fluid moving relative to one another) generates velocity gradients • the two-train analogy • stress-strain relation in a Newtonian fluid ES 202 Fluid & Thermal Systems

  10. Frictional Pipe Flow Analysis • Recall Modified Bernoulli’s equation • How does the head loss manifest itself? • flow velocity is constant along the pipe (which physical principle concludes this point?) • pressure is the “sacrificial lamb” in frictional pipe flow analysis ES 202 Fluid & Thermal Systems

  11. Pressure Drop in Pipe Flow • Recall supplementary problem on dimensional analysis of pipe flow • In dimensional representation (7 variables) • In dimensionless representation (4 p groups) ES 202 Fluid & Thermal Systems

  12. Significance of Reynolds Number • Definition of Reynolds number: • The Reynolds number can be interpreted as the ratio of inertial to viscous effects (one of many interpretations) • At low Reynolds number, • viscous effect is comparable to inertial effect • flow behaves in orderly manner (laminar flow) • At high Reynolds number, • viscous effect is insignificant compared with inertial effect. • flow pattern is irregular, unsteady and random (turbulent flow) ES 202 Fluid & Thermal Systems

  13. Introducing the Friction Factor • Recall results from dimensional analysis of pipe flow • From hindsight, cast the above equation as • The friction factor (as defined) only depends • Reynolds number • relative roughness ES 202 Fluid & Thermal Systems

  14. How to find the friction factor? • Since the friction factor only depends on two independent p groups, it is simple to represent its variation with multiple contour lines on a 2D plane • Show the Moody diagram • representation of two p groups • partition of different flow regimes • The whole problem of finding the pressure drop across piping system is reduced to finding the friction factor on the Moody diagram ES 202 Fluid & Thermal Systems

  15. Flow Chart • Find Reynolds number • fluid properties (r, m) • geometry (D) • flow speed (V) Turbulent (Re > 2300) Laminar (Re < 2300) Find relative roughness Look up Moody diagram ES 202 Fluid & Thermal Systems

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