# ME201: Fluid Mechanics

Unit 6: Analysis of Simple Flow Geometries (Pipe Flow and Boundary Layers)   In this unit, you will learn about the details of two simple flow geometries which form the basis of much engineering analysis of practical flow situations.  These geometries are flow in a circular conduit or pipe and flow near a submerged surface.  Pipes or similar geometries occur widely in both nature and engineering; consider blood flow, oil pipelines, steam pipelines, and the internal plumbing of a building or automobile, for example.  Analysis of flow near submerged surfaces is important in airfoil design, coating processes, and entrance flows, amongst other.  An important aspect of both of these flow situations is whether the flow is laminar or turbulent.

This unit will take you approximately 27 hours to complete.

☐    Subunit 6.1: 4 hours

☐    Subunit 6.2: 6 hours

☐    Subunit 6.3: 6 hours

☐    Subunit 6.4: 6 hours

☐    Subunit 6.5: 5 hours

Unit6 Learning Outcomes
Upon successful completion of this unit, the student will be able to: - Derive the Hagen–Poiseuille solution for pipe flows. - Use Moody chart to calculate friction factor for turbulent flows. - Distinguish laminar versus turbulent pipe flows. - Calculate pressure loss due to friction. - Derive basic equations for boundary layers. - Calculate drag and lift for simple geometries.

6.1 Laminar Pipe Flow and the Hagen—Poiseuille Equation   - Reading: University of Kentucky: Professor J. M. McDonough’s Lectures Notes on Introduction to Fluid Mechanics: “Lectures on Elementary Fluid Dynamics” Link: University of Kentucky: Professor J. M. McDonough’s Lectures Notes on Introduction to Fluid Mechanics: “Lectures on Elementary Fluid Dynamics” (PDF)

Instructions: Please download the PDF file for Lecture Notes of ME330: Elementary Fluid Dynamics and read pages 126-133.  You will be introduced to pipe flow and the Hagen-Poiseuille solution for pipe flows.  Note that this reading will cover the material you need to know for subunits 6.1 and 6.2.

6.2 Laminar and Turbulent Pipe Flows   - Reading: University of Kentucky: Professor J. M. McDonough’s Lectures Notes on Introduction to Fluid Mechanics: “Lectures on Elementary Fluid Dynamics” Link: University of Kentucky: Professor J. M. McDonough’s Lectures Notes on Introduction to Fluid Mechanics: “Lectures on Elementary Fluid Dynamics” (PDF)

Instructions: Please download the PDF file for Lecture Notes of ME330: Elementary Fluid Dynamics and read pages 133-141.  In this reading, you will learn how to calculate velocity profiles for laminar and turbulent pipe flows.  You will also learn how to use Moody chart to calculate friction factor as function of Reynold number and surface roughness.

• Web Media: MIT: Professor Ascher Shapiro’s National Committee for Fluid Mechanics Films: “Turbulence” Link:  MIT: Professor Ascher Shapiro’s National Committee for Fluid Mechanics Films: “Turbulence” (RealPlayer)

• Assessment: University of Delaware: Dr. Shreeram Inamdar’s “Applied Fluid Mechanics: Pipe Flow” Link: University of Delaware: Dr. Shreeram Inamdar’s “Applied Fluid Mechanics: Pipe Flow” (PDF)

Instructions: Please click on the hyperlink titled “Pipeflow.pdf” to download the PDF.  Solve Problem 6.9 on page 19 of the document.  Read the problem statement carefully and try to solve it yourself before looking up the solution.  The solution to the problem is given on pages 20-23.

6.3 Head Losses   - Reading: University of Kentucky: Professor J. M. McDonough’s Lectures Notes on Introduction to Fluid Mechanics: “Lectures on Elementary Fluid Dynamics” Link: University of Kentucky: Professor J. M. McDonough’s Lectures Notes on Introduction to Fluid Mechanics: “Lectures on Elementary Fluid Dynamics” (PDF)

Instructions: Please download the PDF file for Lecture Notes of ME330: Elementary Fluid Dynamics and read pages 141-157.  As fluids flow through pipes, they experience a number of losses that reduce their velocities.  Losses can occur due to viscous effects (think, for example, of friction along the walls of the pipe) or flow through bends or valves.  In this reading, you will learn how to calculate these losses.

• Assessment: University of Delaware: Dr. Shreeram Inamdar’s “Applied Fluid Mechanics: Minor Loss” Link: University of Delaware: Dr. Shreeram Inamdar’s “Applied Fluid Mechanics: Minor Loss” (PDF)

Instructions: Please click on the hyperlink titled “Minor_loss.pdf” to download the PDF.  Solve Problem 10.1 on page 6 of the document.  Read the problem statement carefully and try to solve it yourself before looking up the solution.  The solution to the problem is given on page 7.

6.4 Boundary Layers   - Reading: University of Iowa: Professor Fred Stern’s Lectures Notes on Fluid Mechanics: “Chapter 9: Flow Over Immersed Bodies” Link: University of Iowa: Professor Fred Stern’s Lectures Notes on Fluid Mechanics: “Chapter 9: Flow Over Immersed Bodies” (PDF)

Instructions: Please download the PDF file for Chapter 9 and read the entire document.  When fluids flow past an object, they experience viscous effects near the surface in an area known as the “boundary layer.”  Flow outside of the boundary layer is considered to be inviscid, or unaffected by resistance along the object.  We need to understand boundary layers in order to analyze lift (reactant forces acting perpendicular to the applied force, typically pushing an object up) and drag (forces that oppose the applied force—think of air resistance). Note that this reading will cover the material you need to know for subunits 6.4.1-6.4.7.

• Web Media: MIT: Professor Ascher Shapiro’s National Committee for Fluid Mechanics Films: “Fundamentals of Boundary Layers” Link:  MIT: Professor Ascher Shapiro’s National Committee for Fluid Mechanics Films: “Fundamentals of Boundary Layers” (RealPlayer)