1. ES 202 Fluid and Thermal Systems Lecture 12: Pipe Flow Overview (1/9/2003)

2. Lecture 12ES 202 Fluid & Thermal Systems2 Assignments Homework: –11-105 in Cengel & Turner Study for Exam 1

3. Lecture 12ES 202 Fluid & Thermal Systems3 Announcements Lab 2 this week in Olin 110 from 7 th to 9 th period –Section 6 meets on tomorrow –post lab group assignment for Section 6 Comments on Lab 2 write-up Homework assigned on Monday and Tuesday will be due on tomorrow by 5 pm Review session on Saturday from 4 pm to 6 pm in GM Room What can you bring to the exam? What is covered on the exam?

4. Lecture 12ES 202 Fluid & Thermal Systems4 Road Map of Lecture 12 Recap from Lecture 11 –major losses friction factor (functional dependency, Moody diagram, Haaland formula) –notion of kinematic viscosity Major losses –relationship between friction factor, viscous stress and head loss –categorization of design problems Minor losses –flow visualization –empirical expressions Total loss –schematic summary Pipe system –in series –in parallel

5. Lecture 12ES 202 Fluid & Thermal Systems5 Revisit an Example Example: Water flows in a commercial steel pipe pipe diameter = 10 cm mean speed = 10 m/s pipe length = 3 m  Find the pressure drop between the entrance and exit of the pipe.  What will be the difference if water is replaced by oil?  density  decreases  dynamics viscosity  increases  Reynolds number decreases significantly! Notion of kinematic viscosity

6. Lecture 12ES 202 Fluid & Thermal Systems6 Friction Factor, Viscous Stress and Head Loss Central question: is there a relationship between –friction factor, –viscous stress, –head loss? Consider the following pipe flow problem: –Perform a mechanical energy balance for the above system –Perform a momentum balance for the above system –What can you conclude from the above analyses? –If the pipe is tilted at an angle of 30 deg with the horizontal, what will be the difference in your analysis? 12

7. Lecture 12ES 202 Fluid & Thermal Systems7 Head Loss, Pressure Loss, Mechanical Energy Loss Relationship between various losses –just representation of the same measure in different dimensions Pressure loss Mechanical energy loss Head loss is likely to be the easiest one to visualize or

8. Lecture 12ES 202 Fluid & Thermal Systems8 Categorization of Design Problems 1)Given the flow rate at design condition, what is the required pump power to drive the flow? 2)Given a design pressure difference between inlet and outlet of a pipe, what is the flow rate? - requires iteration ?

9. Lecture 12ES 202 Fluid & Thermal Systems9 Introducing Minor Losses Clarification: “minor” does NOT imply “small” Flow is NOT always “well-behaved” and attached especially at –entrance –exit –connection –turn (elbow) Visualizations from Multi-Media Fluid Mechanics –flow separation over a step –flow separation in a diffuser Results in losses due to viscous effects (minor losses)

10. Lecture 12ES 202 Fluid & Thermal Systems10 Quantification of Minor Losses Similar to the concept of friction factor in major losses, a dimensionless parameter, K L, is introduced to quantify minor losses so that: Show empirical expressions for various configurations Relatively “localized” event, NO L/D dependence as in major losses –notion of equivalent length used in text –interpreted as a hypothetical addition of pipe length

11. Lecture 12ES 202 Fluid & Thermal Systems11 Total Loss in a Pipe System Total loss includes both –major losses –minor losses Adopt a “divide and conquer” approach –identify the individual sources of loss (major and/or minor) –formulate pressure drop across individual sources –integrate results to give total loss Pressure losses are additive in a series configuration, i.e.

12. Lecture 12ES 202 Fluid & Thermal Systems12 Schematic Summary Total Loss Major LossesMinor Losses Subscript i stands for individual source of loss

13. Lecture 12ES 202 Fluid & Thermal Systems13 Pipe Systems Integration of knowledge you have learned so far Two typical configurations: –in series mass (volumetric) flow rate remains constant –what does it mean by velocity? –in parallel pressure drop across each section is the same Analogy to electrical circuit system