---
title: "Reynolds number and flow regime in pipes"
subject: "Applied Computational Fluid Dynamics"
chapter: 1
key: "semester_7/applied_computational_fluid_dynamics:reynolds-number-flow-regime"
source: https://www.bctengineer.com/q/semester_7/applied_computational_fluid_dynamics/reynolds-number-flow-regime
site: BCT Engineering
---

# Reynolds number and flow regime in pipes

Applied Computational Fluid Dynamics · Chapter 1: Introduction to CFD and Fluid Mechanics Review

- Asked in: year not given, 6 marks
- Video: [Laminar flow, turbulence, and Reynolds number](https://www.youtube.com/watch?v=BBWrf3ONRRE) — Osmosis from Elsevier
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/applied_computational_fluid_dynamics/reynolds-number-flow-regime
- Whole chapter: https://www.bctengineer.com/md/semester_7/applied_computational_fluid_dynamics/chapter-1

## Question

Define Reynolds number and explain its physical meaning. (a) Water at 20 °C ($\rho = 998$ kg/m³, $\mu = 1.002\times10^{-3}$ Pa·s) flows at 0.9 m/s in a 40 mm diameter pipe. Find the Reynolds number and state the flow regime. (b) Find the velocity at which the same pipe flow would reach $Re = 2300$. (c) Why is the Reynolds number important in CFD?

## Short answer

Reynolds number is inertia force divided by viscous force. For water, Re=rho V D/mu = 3.59x10^4, turbulent. The velocity for Re=2300 is 0.0577 m/s. In CFD, Re selects laminar or turbulent models and sets mesh resolution through boundary-layer requirements.

## Answer

#### Definition and meaning
The **Reynolds number** is the ratio of inertia force to viscous force:
$$
Re=\frac{\rho V L}{\mu}=\frac{VL}{\nu}
$$
For pipe flow $L=D$. A small $Re$ means viscous forces dominate and disturbances are damped (laminar flow); a large $Re$ means inertia dominates, disturbances grow and the flow becomes turbulent.

Typical limits for pipes: laminar for $Re<2300$, transitional for about 2300 to 4000, turbulent for $Re>4000$.

#### (a) Reynolds number
$$
Re=\frac{998\times0.9\times0.04}{1.002\times10^{-3}}=3.59\times10^{4}
$$
Since $Re\gg4000$, the flow is **turbulent**.

#### (b) Velocity for $Re=2300$
$$
V=\frac{Re\,\mu}{\rho D}=\frac{2300\times1.002\times10^{-3}}{998\times0.04}=0.0577\ \text{m/s}
$$
So only a very slow flow (5.8 cm/s) is laminar in this pipe.

#### (c) Importance in CFD
- It decides whether a laminar solver or a turbulence model is required.
- It sets the mesh needs: higher $Re$ gives thinner boundary layers, so finer wall meshes (small $y^+$) are needed.
- It is the similarity parameter: a CFD model at small scale with the same $Re$ represents the full-size case.
- Drag coefficient, friction factor and transition behaviour are all functions of $Re$.

**Answer:** $Re=3.59\times10^4$ (turbulent); $V_{Re=2300}=0.0577$ m/s.

## Check yourself

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

1. The Reynolds number is the ratio of:
   A. Viscous force to inertia force
   B. Inertia force to viscous force
   C. Gravity force to inertia force
   D. Pressure force to viscous force
   Answer: B. Re = rho V L / mu is inertia over viscous force; high Re means inertia dominates and flow becomes turbulent. (Key point: Meaning of Re)

2. Water at 0.9 m/s in a 40 mm pipe gives Re = 3.59 x 10^4. The regime is:
   A. Laminar
   B. Transitional
   C. Turbulent
   D. Creeping
   Answer: C. Re is far above 4000, so the flow is turbulent. (Key point: Regime of the pipe flow)

3. What velocity gives Re = 2300 in the same pipe?
   A. 0.9 m/s
   B. 5.77 m/s
   C. 0.577 m/s
   D. 0.0577 m/s
   Answer: D. V = Re mu /(rho D) = 2300 x 1.002e-3 /(998 x 0.04) = 0.0577 m/s. (Key point: Velocity for Re = 2300)

4. Why is Re important when setting up a CFD model?
   A. It decides if a turbulence model is needed and how fine the wall mesh must be
   B. It sets the colour scale of plots
   C. It determines the CAD geometry
   D. It fixes the number of processors
   Answer: A. Re decides laminar vs turbulent modelling, and higher Re gives thinner boundary layers requiring finer wall meshes. (Key point: Re in CFD)

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