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ES 202 Fluid and Thermal Systems Lecture 11: Pipe Flow (Major and Minor Losses) (1/7/2003)

ES 202 Fluid and Thermal Systems Lecture 11: Pipe Flow (Major and Minor Losses) (1/7/2003). Assignments. Reading: Cengel & Turner Section 12-6 Homework: 12-72, 12-79 in Cengel & Turner. Road Map of Lecture 11. Announcements Recap from Lecture 10 “modified” Bernoulli’s equation

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ES 202 Fluid and Thermal Systems Lecture 11: Pipe Flow (Major and Minor Losses) (1/7/2003)

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  1. ES 202Fluid and Thermal SystemsLecture 11:Pipe Flow (Major and Minor Losses)(1/7/2003)

  2. Assignments • Reading: • Cengel & Turner Section 12-6 • Homework: • 12-72, 12-79 in Cengel & Turner ES 202 Fluid & Thermal Systems

  3. Road Map of Lecture 11 • Announcements • Recap from Lecture 10 • “modified” Bernoulli’s equation • concept of viscosity • Major losses • friction factor • Moody diagram • flow chart to determine friction factor • non-circular ducts • Minor losses ES 202 Fluid & Thermal Systems

  4. Announcements • Lab 2 this week in Olin 110 from 7thto 9thperiod • Section 5 meets tomorrow • Section 6 meets on Friday • Post lab group schedule • 2 lab sessions over the 3 hour period • 1st session starts at 1:35 pm • 2nd session starts at 2:55 pm • Homework assigned on Monday and Tuesday will be due on Friday by 5 pm • Solutions to all homework sets are available at reserve library under Mayhew ES 202 Fluid & Thermal Systems

  5. 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

  6. 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 • Display and describe the Moody diagram • representation of two p groups • partition of different flow regimes • independent of surface roughness in laminar regime • insensitivity at high Reynolds number in turbulent regime • 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

  7. 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

  8. Example on Moody Diagram • 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? • What if the pipe/duct is not circular? • needs a representative length measure of the duct cross-section • notion of hydraulic diameter • example with a rectangular duct • extra factor of 4 recovers the diameter for a circular pipe ES 202 Fluid & Thermal Systems

  9. Alternative Method • The Moody Diagram is a handy way to represent data on friction factor. • If reading off the diagram does not seem appealing, the same amount of data can be curve-fitted to give an explicit functional relationship between friction factor, Reynolds number and relative roughness. • The Haaland formula offers another alternative ES 202 Fluid & Thermal Systems

  10. 1 2 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? ES 202 Fluid & Thermal Systems

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