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

ES 202 Fluid & Thermal Systems Assignments Reading: Cengel & Turner Section 12-5, 12-6 Homework: 12-25, 12-35, 12-42 in Cengel & Turner Lecture 10 ES 202 Fluid & Thermal Systems

ES 202 Fluid & Thermal Systems 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 Lecture 10 ES 202 Fluid & Thermal Systems

ES 202 Fluid & Thermal Systems 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 Lecture 10 ES 202 Fluid & Thermal Systems

ES 202 Fluid & Thermal Systems 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) Lecture 10 ES 202 Fluid & Thermal Systems

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: Lecture 10 ES 202 Fluid & Thermal Systems

ES 202 Fluid & Thermal Systems Recap from Lecture 9 The Torricelli experiment (A2<< A1) The “Bent” Torricelli experiment V H Area = A1 Area = A2 V H Lecture 10 ES 202 Fluid & Thermal Systems

“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 Lecture 10 ES 202 Fluid & Thermal Systems

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 Lecture 10 ES 202 Fluid & Thermal Systems

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 Lecture 10 ES 202 Fluid & Thermal Systems

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) Lecture 10 ES 202 Fluid & Thermal Systems

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) Lecture 10 ES 202 Fluid & Thermal Systems

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 Lecture 10 ES 202 Fluid & Thermal Systems

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 Lecture 10 ES 202 Fluid & Thermal Systems

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 Lecture 10 ES 202 Fluid & Thermal Systems