---
title: "Define section factor"
subject: "Hydraulics"
chapter: 5
key: "semester_4/hydraulics:define-section-factor"
source: https://www.bctengineer.com/q/semester_4/hydraulics/define-section-factor
site: BCT Engineering
---

# Define section factor

Hydraulics · Chapter 5: Basics of Open channel flow

- Asked in: 2081 Chaitra, 1 marks; 2069 Poush, 1 marks (asked 2 times)
- Video: [Uniform Flow Computations Manning's Formula, Conveyance Factor and Section Factor, Normal depth](https://www.youtube.com/watch?v=sMgI0A8GfR8) — Splash Environs
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/hydraulics/define-section-factor
- Whole chapter: https://www.bctengineer.com/md/semester_4/hydraulics/chapter-5

## Question

Define section factor.

## Short answer

Section factor is a geometric function of depth used to find critical or normal depth. For critical flow, Z = sqrt(A^3/T) = Q/sqrt(g); for uniform flow, AR^(2/3) = nQ/sqrt(S0). It depends only on channel shape and depth.

## Answer

**Section factor** is a geometric property of a channel section used in solving for depth. Two forms are used.

#### For critical flow
$$
Z=A\sqrt{\frac{A}{T}}=\sqrt{\frac{A^3}{T}}
$$
Critical flow occurs when $Z=\dfrac{Q}{\sqrt g}$. It depends only on the depth and shape of the section and is used to find the critical depth.

#### For uniform flow
$$
AR^{2/3}=\frac{nQ}{\sqrt{S_0}}
$$
The right side is known from the data, so the normal depth is the depth at which $AR^{2/3}$ equals this value; it is found by trial or from charts.

Both section factors are functions of depth only for a given channel shape; they are tabulated or plotted against $y/D$ or $y/b$.

## Check yourself

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

1. The section factor for critical flow is
   A. Z = A/P
   B. Z = Q/A
   C. Z = A R^(2/3)
   D. Z = sqrt(A^3/T)
   Answer: D. Critical flow when Z = Q/sqrt(g). (Key point: Critical flow factor)

2. The section factor for uniform flow is
   A. A R^(2/3)
   B. A^3/T
   C. P R
   D. A/T
   Answer: A. Equal to nQ/sqrt(S0). (Key point: Uniform flow factor)

3. Section factors are functions of
   A. Slope
   B. Roughness only
   C. Discharge
   D. Depth and shape only
   Answer: D. Used to solve for depth by trial. (Key point: Dependence)

## Related in Hydraulics

- [Series-parallel pipes with control valve](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Aseries-parallel-valve-equal-discharge) — Hydraulics, chapter 2, asked 2×
- [Momentum coefficient for compound channel](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Acompound-channel-momentum-coefficient-beta) — Hydraulics, chapter 6, asked 2×
- [Energy coefficient for compound channel](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Acompound-channel-energy-coefficient-alpha) — Hydraulics, chapter 6, asked 2×
- [GVF in 5 m channel, depth 0.25 m to 0.40 m](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Agvf-5m-channel-1-85-m3s-direct-step) — Hydraulics, chapter 8, asked 2×
- [GVF in 4 m channel, graphical integration](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Agvf-4m-channel-2-m3s-graphical-integration) — Hydraulics, chapter 8, asked 2×
- [Geometric properties of a circular channel](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Acircular-channel-geometric-properties-y1125) — Hydraulics, chapter 6

## Related in other subjects

- [Design pipes AB, BC; 160 lpcd, peak factor 3](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Apd-c71) — Water Supply Engineering, chapter 7
- [Shape factor, plastic hinge properties, T-beam](https://www.bctengineer.com/question.md?key=semester_5%2Ftheory_of_structures_ii%3Ashape-factor-t-beam-plastic-hinge) — Theory of Structures II, chapter 5
- [Plastic moment and shape factor of a beam](https://www.bctengineer.com/question.md?key=semester_5%2Fmechanics_of_solids%3Ashape-factor-plastic-moment-rectangle) — Mechanics of Solids, chapter 12
- [Section modulus of fixed beam at collapse](https://www.bctengineer.com/question.md?key=semester_5%2Ftheory_of_structures_ii%3Afixed-beam-section-modulus-collapse-60kn) — Theory of Structures II, chapter 5