---
title: "Definition: Froude number"
subject: "Hydro Power"
chapter: 1
key: "semester_6/hydro_power:froude-number"
source: https://www.bctengineer.com/q/semester_6/hydro_power/froude-number
site: BCT Engineering
---

# Definition: Froude number

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

- Asked in: 2072 Asoj, 3 marks
- Video: [Lecture 7 - Concept of Froude Number in Open Channel Flow](https://www.youtube.com/watch?v=Mwd3uxw9DuM) — Tech Master Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/hydro_power/froude-number
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-1

## Question

Define Froude number.

## Short answer

Froude number is the dimensionless ratio of inertia force to gravity force in open channel flow, given by Fr = V/√(gD) where V is velocity, g is gravity, and D is hydraulic depth. Flow is subcritical if Fr<1, critical if Fr=1, and supercritical if Fr>1.

## Answer

**Froude number** ($F_r$) is the dimensionless ratio of the inertia force to the gravity force in a flowing fluid. It is the most important number for open channel flow.

$$
F_r = \sqrt{\frac{\text{Inertia force}}{\text{Gravity force}}} = \frac{V}{\sqrt{gD}}
$$

where $V$ = mean velocity, $g$ = acceleration due to gravity, $D = A/T$ = hydraulic depth (equal to $y$ for a rectangular channel).

Classification of flow:
| $F_r$ | Flow type | Feature |
|---|---|---|
| < 1 | Subcritical (tranquil) | Deep, slow flow |
| = 1 | Critical | Minimum specific energy |
| > 1 | Supercritical (rapid) | Shallow, fast flow |

Uses: hydraulic jump calculations below spillways, model studies (Froude model law for spillways and dams), and design of channels. Example: $V = 2$ m/s, $y = 1$ m gives $F_r = 2/\sqrt{9.81 \times 1} = 0.64$ (subcritical).

## Check yourself

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

1. Froude number is the ratio of:
   A. Inertia force to viscous force
   B. Inertia force to gravity force
   C. Pressure force to inertia force
   D. Gravity force to surface tension
   Answer: B. Fr = sqrt(inertia/gravity) = V/sqrt(gD). (Key point: Definition)

2. In Fr = V/sqrt(gD), what is D?
   A. Hydraulic depth A/T
   B. Pipe diameter
   C. Wetted perimeter
   D. Hydraulic radius A/P
   Answer: A. D = A/T, equal to y for a rectangular channel. (Key point: Hydraulic depth)

3. A flow with Fr > 1 is:
   A. Subcritical, deep and slow
   B. Critical
   C. Supercritical, shallow and fast
   D. Always turbulent only
   Answer: C. Fr < 1 is subcritical, Fr = 1 critical, Fr > 1 supercritical. (Key point: Flow classification)

## Related in other subjects

- [Hydraulic jump definition and downstream Froude number](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Ahydraulic-jump-what-is-and-froude-after-jump) — Hydraulics, chapter 9
- [Classification of hydraulic jump by Froude number](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Ahydraulic-jump-classification-froude) — Hydraulics, chapter 9
- [Froude number ratio for alternate depths](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Aalternate-depths-froude-number-ratio) — Hydraulics, chapter 7
- [Model liquid viscosity, Froude and Reynolds](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Amodel-liquid-viscosity-froude-reynolds) — Fluid Mechanics, chapter 10