---
title: "Pipe flow regimes and velocity profiles"
subject: "Hydro Power"
chapter: 1
key: "semester_6/hydro_power:pipe-flow-regimes-profiles"
source: https://www.bctengineer.com/q/semester_6/hydro_power/pipe-flow-regimes-profiles
site: BCT Engineering
---

# Pipe flow regimes and velocity profiles

Hydro Power · Chapter 1: Introduction to Basic Fluid Mechanics and Hydraulics

- Asked in: 2077 Chaitra, 2+6 marks
- Video: [Understanding Laminar and Turbulent Flow](https://www.youtube.com/watch?v=9A-uUG0WR0w) — The Efficient Engineer
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/hydro_power/pipe-flow-regimes-profiles
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-1

## Question

How do you numerically classify laminar, transitional and turbulent flow in pipes? Differentiate laminar and turbulent velocity profiles in pipe flow with neat sketch and labels.

## Short answer

Flow is classified by Reynolds number: Re<2000 laminar, 2000≤Re≤4000 transitional, Re>4000 turbulent. Laminar profile is parabolic with u_max=2V; turbulent profile is flatter with a thin viscous sublayer, u_max≈1.2V, and velocity changes steeply near the wall.

## Answer

#### Numerical classification (Reynolds number)
Flow in pipes is classified by the **Reynolds number**, the ratio of inertia force to viscous force:
$$
Re = \frac{\rho V D}{\mu} = \frac{VD}{\nu}
$$
| Flow type | Reynolds number (pipe) |
|---|---|
| Laminar | $Re < 2000$ |
| Transitional | $2000 \le Re \le 4000$ |
| Turbulent | $Re > 4000$ |

Example: water ($\nu = 10^{-6}$ m²/s) at 1 m/s in a 0.1 m pipe: $Re = 10^5$, so turbulent.

#### Velocity profiles
```text
 Laminar (parabolic)       Turbulent (flatter)
 |=====================    |=====================
 |-->                      |------->
 |------>                  |--------->
 |--------->  u_max = 2V   |---------->  u_max ~ 1.2V
 |------>                  |--------->
 |-->                      |------->
 |=====================    |=====================
   wall   u = 0               thin laminar sublayer
```
- **Laminar:** velocity varies parabolically with radius (Hagen–Poiseuille):
$$
u = u_{max}\left(1 - \frac{r^2}{R^2}\right), \quad u_{max} = 2\bar V
$$
- **Turbulent:** mixing evens out the velocity, so the profile is flat in the core and changes steeply near the wall; approximately the power law $u = u_{max}(y/R)^{1/7}$, with $u_{max} \approx 1.2\bar V$ and a thin laminar sub-layer at the wall.

| Feature | Laminar profile | Turbulent profile |
|---|---|---|
| Shape | Parabolic | Flat core, steep at wall |
| $u_{max}/\bar V$ | 2.0 | about 1.2 |
| Wall shear | Low | High |
| Velocity law | $u = u_{max}(1 - r^2/R^2)$ | Log law or $(y/R)^{1/7}$ |
| KE factor $\alpha$ | 2.0 | 1.03–1.10 |
| Head loss | $h_f \propto V$, $f = 64/Re$ | $h_f \propto V^{1.75}$ to $V^2$ |

## Check yourself

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

1. What are the Reynolds number limits for laminar flow and turbulent flow?
   A. Laminar Re > 2000
   B. Laminar Re < 2000, turbulent Re > 4000
   C. Laminar Re < 500, turbulent Re > 2000
   D. Laminar Re < 4000, turbulent Re > 8000
   Answer: B. 2000 to 4000 is transitional. (Key point: Classification)

2. What is the Reynolds number the ratio of?
   A. Viscous force to inertia force
   B. Inertia force to viscous force
   C. Pressure to viscous
   D. Gravity to inertia
   Answer: B. Re = rho V D/mu = inertia/viscous. (Key point: Meaning of Re)

3. What is the laminar profile and u_max/V_avg?
   A. Parabolic, 1.2
   B. Linear, 1.0
   C. Parabolic, 2.0
   D. Flat, 1.2
   Answer: C. u = u_max(1 - r^2/R^2), u_max = 2V. (Key point: Laminar profile)

4. Why is the turbulent profile flatter in the core?
   A. Wall shear is lower
   B. The pipe is smoother
   C. Mixing by eddies evens out velocity
   D. Viscosity is higher
   Answer: C. Turbulent mixing flattens the core and gives high wall shear; u_max is about 1.2 V. (Key point: Turbulent profile)

## Related in Hydro Power

- [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
- [Flow between reservoirs (15 cm and 25 cm pipe)](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Areservoirs-pipeline-15-25cm) — Hydro Power, chapter 1
- [Flow between reservoirs (20 cm and 30 cm pipe)](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Areservoirs-pipeline-20-30cm) — Hydro Power, chapter 1
- [Head loss and flow direction in tapering oil pipe](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Atapering-pipe-oil-flow) — Hydro Power, chapter 1

## Related in other subjects

- [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
- [Reynolds experiment and flow regimes](https://www.bctengineer.com/question.md?key=semester_4%2Ffluid_mechanics_mechanical%3Areynolds-experiment-flow-regimes) — Fluid Mechanics, chapter 6
- [Derive laminar velocity in inclined pipe](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Alaminar-inclined-pipe-velocity-derivation) — Hydraulics, chapter 1