--- title: "BL growth in closed conduit" subject: "Fluid Mechanics" chapter: 8 key: "semester_3/fluid_mechanics:bl-growth-closed-conduit-examples" source: https://www.bctengineer.com/q/semester_3/fluid_mechanics/bl-growth-closed-conduit-examples site: BCT Engineering --- # BL growth in closed conduit Fluid Mechanics · Chapter 8: Boundary Layer theory - Asked in: 2073 Shrawan, 1+3+1 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/fluid_mechanics/bl-growth-closed-conduit-examples - Whole chapter: https://www.bctengineer.com/md/semester_3/fluid_mechanics/chapter-8 ## Question Define the concept of boundary layer. Explain the growth of boundary layer in a close conduit (pipe flow). Give three examples of use of boundary layer concept. ## Short answer Boundary layer is the thin viscous region next to a solid surface where velocity rises from zero to free-stream value. In a closed conduit, layers grow from the wall inward and meet at the entrance length, after which the profile becomes fully developed. Uses include calculating skin-friction drag, explaining separation and stall, and designing wind tunnels and ducts. ## Answer #### Concept of boundary layer The boundary layer is the thin layer next to a solid surface in which the fluid velocity changes from zero (at the wall, no-slip) to nearly the free-stream value. Viscous effects are confined to this layer; outside it the flow is inviscid. #### Growth in a closed conduit (pipe flow) ```text inlet entrance length Le fully developed --------------------------------------------------------- U0 -> boundary layers grow core meets parabolic / uniform from wall inward -> at centre turbulent profile --------------------------------------------------------- ``` 1. At the pipe entrance the velocity is nearly uniform, $U_0$. A boundary layer begins to grow from the wall at the entrance. 2. The layer thickens along the pipe, slowing the fluid near the wall. By continuity the core fluid, outside the layer, accelerates, and the pressure drops faster than in fully developed flow. 3. At a distance called the **entrance (inlet) length** $L_e$, the layers from the opposite walls meet at the centre. After this the velocity profile no longer changes with $x$, and the flow is fully developed. 4. Entrance length: laminar flow $L_e \approx 0.05\,Re\,D$; turbulent flow $L_e \approx 4.4\,Re^{1/6}D$ (about 25 to 40 diameters). #### Three examples of use of the boundary layer concept 1. Calculation of **skin friction drag** on ships, aircraft wings and plates. 2. Explaining **separation and stall** on aerofoils, and the design of streamlined bodies to reduce form drag. 3. Design of **wind tunnels, diffusers and ducts** (allowing for displacement thickness), and prediction of the heat transfer from surfaces. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How does the boundary layer begin in a pipe? A. Fully developed from the inlet B. Starts at the pipe centre C. Starts only after the entrance length D. Velocity is nearly uniform at the entrance and layers grow from the wall inward Answer: D. A boundary layer begins at the wall at the entrance and thickens along the pipe. (Key point: Start of growth) 2. What happens to the core fluid as the layers grow? A. It decelerates B. It stays unchanged C. It accelerates by continuity and pressure drops faster D. It becomes turbulent immediately Answer: C. Slower wall fluid means the core must speed up to carry the same Q. (Key point: Effect on core) 3. What defines the entrance length Le? A. Distance where the pipe diameter doubles B. Distance at which layers from opposite walls meet at the centre, after which the profile is fully developed C. Distance where Re = 2000 D. Distance where pressure is zero Answer: B. After Le the velocity profile no longer changes with x. (Key point: Entrance length) 4. For laminar flow Le is approximately A. 0.05 Re D B. 4.4 Re^(1/6) D C. 25 D regardless of Re D. 0.37 Re D Answer: A. Turbulent entrance length is 4.4 Re^(1/6) D, much shorter. (Key point: Entrance length formula) ## Related in Fluid Mechanics - [Boundary layer concept and related terms](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Abl-concept-terms-separation) — Fluid Mechanics, chapter 8 - [BL growth along thin plate, examples](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Abl-growth-thin-plate-examples) — Fluid Mechanics, chapter 8 - [Laminar sub-layer; laminar vs turbulent BL](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Alaminar-sublayer-laminar-vs-turbulent-bl) — Fluid Mechanics, chapter 8 - [Boundary layer separation and stagnation point](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Abl-separation-stagnation-point) — Fluid Mechanics, chapter 8 - [BL, displacement and momentum thickness](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Abl-thickness-displacement-momentum-applications) — Fluid Mechanics, chapter 8 - [BL development along thin flat plate](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Abl-development-flat-plate-features) — Fluid Mechanics, chapter 8 ## Related in other subjects - [Pipe insulation: extra layer to cut heat 40%](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Apipe-insulation-additional-layer-40-percent) — Fundamental of Thermodynamics & Heat Transfer, chapter 7 - [Three reservoirs with pressurised closed tank](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Athree-reservoir-closed-tank-pressure) — Hydraulics, chapter 3 - [Boundary shear stress and compound channel flow](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Ashear-stress-boundary-compound-channel-flow) — Hydraulics, chapter 6 - [Three reservoirs with pump in pipe 2](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Apump-three-reservoir-flow-and-head-j) — Hydraulics, chapter 3