---
title: "Reynolds experiment and flow regimes"
subject: "Fluid Mechanics"
chapter: 6
key: "semester_4/fluid_mechanics_mechanical:reynolds-experiment-flow-regimes"
source: https://www.bctengineer.com/q/semester_4/fluid_mechanics_mechanical/reynolds-experiment-flow-regimes
site: BCT Engineering
---

# Reynolds experiment and flow regimes

Fluid Mechanics · Chapter 6: Viscous Effects

- Asked in: year not given, 6 marks
- Video: [Reynold's Experiment to identify the type of flow](https://www.youtube.com/watch?v=KDCtmq3q6_c) — Uff (Unleash fluid flow)
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/fluid_mechanics_mechanical/reynolds-experiment-flow-regimes
- Whole chapter: https://www.bctengineer.com/md/semester_4/fluid_mechanics_mechanical/chapter-6

## Question

Describe Reynolds' experiment with a neat sketch. Define Reynolds number and state its critical values for pipe flow. Differentiate between laminar and turbulent flow, and sketch their velocity profiles.

## Short answer

Reynolds injected a dye filament into pipe flow; at low velocity it remained a straight line (laminar), at high velocity it diffused (turbulent). Reynolds number Re = ρVD/μ = VD/ν. Critical values: Re < 2000 laminar, 2000–4000 transition, >4000 turbulent. Laminar flow is orderly with parabolic velocity profile; turbulent flow is chaotic with flatter profile and higher mixing.

## Answer

#### Reynolds' experiment
Osborne Reynolds (1883) studied the nature of flow in a glass tube by injecting a thin filament of dye into flowing water.

```text
  water tank
 +-----------+      dye
 |           |       |
 |           |   ____v___
 |           |==|  tube  |=====> to valve
 +-----------+  |_________|
```

**Observations**
1. At low velocity, the dye moves as a straight, thin line parallel to the tube axis: **laminar flow** (layers slide over each other).
2. When the velocity is increased, the dye line begins to wave: **transition**.
3. At high velocity, the dye mixes completely with the water, showing eddies and random motion: **turbulent flow**.

Reynolds found that the change depends on the dimensionless group:

$$
Re = \frac{\rho V D}{\mu} = \frac{V D}{\nu} = \frac{\text{inertia force}}{\text{viscous force}}
$$

#### Critical values (pipe flow)
- $Re < 2000$: laminar
- $2000 < Re < 4000$: transition (unstable)
- $Re > 4000$: turbulent

The exact values depend on the disturbances present; the lower critical value of about 2000 is the commonly used limit.

#### Laminar vs turbulent flow
| Basis | Laminar | Turbulent |
|---|---|---|
| Motion | Orderly layers, no mixing | Random, eddying, mixing |
| Reynolds number | $Re < 2000$ | $Re > 4000$ |
| Shear stress | Due to viscosity: $\tau = \mu\,du/dy$ | Viscous plus turbulent (Reynolds) stress |
| Velocity profile | Parabolic, $V_{avg} = 0.5\,u_{max}$ | Flatter, $V_{avg} \approx 0.8\,u_{max}$ |
| Head loss | $h_f \propto V$ | $h_f \propto V^{1.75\text{ to }2}$ |
| Friction factor | $f = 64/Re$ | Depends on $Re$ and roughness |

```text
  Laminar          Turbulent
  |   .--          |  .----
  |  /             | |
  | |              | |
  |  \             | |
  |   '--          |  '----
```

## Check yourself

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

1. In Reynolds' experiment, what does the dye filament do at high velocity?
   A. It stays a straight thin line
   B. It mixes completely with the water with eddies, showing turbulent flow
   C. It moves backwards
   D. It disappears at the wall only
   Answer: B. At high velocity the dye mixes fully due to random eddy motion, indicating turbulent flow. (Key point: Reynolds experiment observation)

2. Which are the pipe-flow limits used?
   A. Laminar below 4000, turbulent above 2000
   B. Laminar below 500, turbulent above 2000
   C. Laminar below 2000, transition 2000-4000, turbulent above 4000
   D. Laminar above 2000, turbulent below 4000
   Answer: C. Re < 2000 laminar, 2000-4000 transition, Re > 4000 turbulent. (Key point: Critical Reynolds numbers)

3. Which statement about laminar flow is correct?
   A. Velocity profile is flat with V_avg about 0.8 u_max
   B. Friction factor f = 64/Re and head loss proportional to V
   C. Head loss is proportional to V^1.75 to 2
   D. Shear stress includes Reynolds (turbulent) stress
   Answer: B. Laminar flow has a parabolic profile (V_avg = 0.5 u_max), f = 64/Re and h_f proportional to V. (Key point: Laminar vs turbulent)

## Related in Fluid Mechanics

- [Laminar oil flow in a pipe](https://www.bctengineer.com/question.md?key=semester_4%2Ffluid_mechanics_mechanical%3Alaminar-oil-pipe-pressure-drop) — Fluid Mechanics, chapter 6
- [Laminar flow between fixed parallel plates](https://www.bctengineer.com/question.md?key=semester_4%2Ffluid_mechanics_mechanical%3Alaminar-flow-between-fixed-parallel-plates) — Fluid Mechanics, chapter 6
- [Hagen-Poiseuille flow in a circular tube](https://www.bctengineer.com/question.md?key=semester_4%2Ffluid_mechanics_mechanical%3Ahagen-poiseuille-derivation-circular-tube) — Fluid Mechanics, chapter 6

## Related in other subjects

- [Pipe flow regimes and velocity profiles](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Apipe-flow-regimes-profiles) — Hydro Power, chapter 1
- [Velocity for fully turbulent flow in rough pipe](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Afully-turbulent-velocity-1200mm-pipe) — Hydraulics, chapter 1
- [Parabolic velocity profile in laminar pipe flow](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Alaminar-parabolic-velocity-profile) — Hydraulics, chapter 1
- [Laminar/turbulent flow and friction factor](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Alaminar-turbulent-friction-factor) — Hydro Power, chapter 1