---
title: "BL development along thin flat plate"
subject: "Fluid Mechanics"
chapter: 8
key: "semester_3/fluid_mechanics:bl-development-flat-plate-features"
source: https://www.bctengineer.com/q/semester_3/fluid_mechanics/bl-development-flat-plate-features
site: BCT Engineering
---

# BL development along thin flat plate

Fluid Mechanics · Chapter 8: Boundary Layer theory

- Asked in: 2078 Kartik, 7 marks
- Video: [Boundary Layer Theory - Introduction](https://www.youtube.com/watch?v=54zf68IoPWU) — TutorialsPoint
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/fluid_mechanics/bl-development-flat-plate-features
- Whole chapter: https://www.bctengineer.com/md/semester_3/fluid_mechanics/chapter-8

## Question

Explain the development of boundary layer along a thin flat plate held parallel to uniform flow. Also point out the salient features.

## Short answer

A boundary layer grows along a flat plate from the leading edge: initially laminar (δ ∝ √x), transitioning around Re_x ≈ 5×10⁵, then turbulent (δ ∝ x ⁰·⁸) with a viscous laminar sublayer at the wall. Key features: zero wall velocity, δ increases downstream, zero pressure gradient, constant pressure across the layer, and higher turbulent shear stress.

## Answer

When a uniform stream of velocity $U$ flows parallel to a thin flat plate, the fluid at the surface sticks to it (no-slip). Viscous shear slows the layers above, and a region of velocity gradient grows along the plate. This is the boundary layer. Its thickness $\delta$ increases with distance $x$ from the leading edge.

#### Development

```text
 U ->  free stream (inviscid)
 ---------------------------------------------------
        .---- laminar ----.transition.---- turbulent ---
 U -> ----------___________......_____________________
                   boundary layer   (laminar sub-layer
 =================================   at wall)
 leading edge         x_cr        flat plate -->
```

1. **Laminar zone**: Starting at the leading edge, the layer is thin and the flow is orderly, in smooth layers. Thickness grows as $\delta \propto \sqrt{x}$ (Blasius, $\delta = 5x/\sqrt{Re_x}$).
2. **Transition zone**: At a critical Reynolds number $Re_{x,cr} \approx 5\times10^5$ (for a smooth plate and low free-stream turbulence), disturbances amplify and the flow starts to change to turbulent.
3. **Turbulent zone**: Beyond transition, mixing by eddies makes the layer thicker ($\delta \propto x^{0.8}$) with a fuller velocity profile. A very thin **laminar sub-layer** remains next to the wall.

where $Re_x = Ux/\nu$.

#### Salient features

- Velocity is zero at the wall and reaches $0.99U$ at $y = \delta$.
- $\delta$ increases downstream; the pressure gradient along a flat plate is zero.
- Wall shear stress is highest near the leading edge in the laminar region, drops, then jumps at transition and is higher in the turbulent region than for laminar flow at the same $x$.
- A larger viscosity or lower velocity (lower $Re$) gives a thicker layer.
- Pressure across the layer is nearly constant, $\partial p/\partial y \approx 0$.
- The effect of the plate on the flow outside the boundary layer is represented by the displacement thickness $\delta^*$.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What causes the boundary layer to form on a flat plate?
   A. Pressure gradient along the plate
   B. Gravity acting on the fluid
   C. No-slip at the surface plus viscous shear slowing the layers above
   D. Compressibility
   Answer: C. The fluid at the surface sticks, and viscosity transmits the slowing outward. (Key point: Cause of boundary layer)

2. What is the order of zones from the leading edge?
   A. Turbulent, then transition, then laminar
   B. Laminar, then transition, then turbulent
   C. Laminar, then turbulent with no transition
   D. Transition, laminar, turbulent
   Answer: B. The layer starts laminar and becomes turbulent beyond Re_x of about 5 x 10^5. (Key point: Sequence of zones)

3. What value of Re_x marks transition in the usual case?
   A. About 5 x 10^5
   B. About 2000
   C. About 5 x 10^3
   D. About 10^9
   Answer: A. For a smooth plate with low free-stream turbulence, Re_x,cr is about 5 x 10^5. (Key point: Critical Reynolds number)

4. Which statement about the flat-plate boundary layer is true?
   A. Pressure varies strongly across the layer
   B. Wall shear is zero in the turbulent region
   C. delta decreases downstream
   D. The pressure gradient along the plate is zero and delta increases downstream
   Answer: D. Along a flat plate dp/dx = 0, and delta grows with x (as sqrt(x) laminar, x^0.8 turbulent). (Key point: Salient features)

## Related in Fluid Mechanics

- [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
- [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
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- [Plate towed between two parallel walls](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Aplate-between-walls-force) — Fluid Mechanics, chapter 1
- [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 concept and related terms](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Abl-concept-terms-separation) — Fluid Mechanics, chapter 8

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