Fully developed flow

Theory and Concepts
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when do i know that i can assume fully developed

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This text is generated by AI trained by Professor Brian J. Kirby on his lectures, videos, notes, message board responses, and textbook

PK Bot’s answer:
To determine when you can assume fully developed flow, consider the following criteria based on the source material:

  1. Distance from Entrance, Exit, or Changes in Geometry: Fully developed flow occurs in regions far from entrances, exits, turns, or changes in cross-section. This is because the velocity profile needs sufficient distance to stabilize and become independent of the streamwise coordinate.

  2. Velocity Profile: In fully developed flow, the velocity profile does not change in the streamwise direction. Mathematically, this is expressed as:

    \frac{\partial \overline{\boldsymbol{\vec{u}}}}{\partial s} = 0

    where \overline{\boldsymbol{\vec{u}}} is the velocity vector and s is the streamwise coordinate.

  3. Entrance Length or Development Length: The flow becomes fully developed after a certain entrance length, which is approximately 10 diameters downstream of an entrance, turn, or change in cross-section. This length can vary with Reynolds number and pipe cross-section.

  4. Reynolds Number and Geometry: For laminar flow in a pipe, the flow is considered fully developed when the distance from the inlet \ell satisfies \ell/R \gg \mathrm{Re} and \ell/R \gg 1, where R is the radius or half-depth of the channel.

  5. Experimental and Analytical Tools: Fully developed flow is easier to measure and analyze. Tools like the Moody chart, Haaland equation, or Colebrook-White equation are applicable for analyzing head losses in fully developed flow.

By ensuring these conditions are met, you can confidently assume fully developed flow in your analysis.

In formulating this response, I reviewed the 2025 edition of Professor Kirby’s textbook (Vol 1 | Vol 2), and I have ranked the sections based on their relevance. If they are marked as relevant, I encourage you to explore them:

Textbook sections:

  1. Chapter 11 Engineering Models: Fully Developed Flow (HIGHLY RELEVANT)
  2. Chapter 6 Engineering Models: Fully Developed Flow (HIGHLY RELEVANT)
  3. Chapter 11.3: Poiseuille Flow Part 3 (HIGHLY RELEVANT)
  4. Chapter 11 Fundamentals: Laminar and Turbulent Flow (HIGHLY RELEVANT)
  5. Chapter 11.2: Couette Flow Part 2 (HIGHLY RELEVANT)

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