---
title: "Definition: best hydraulic section"
subject: "Hydro Power"
chapter: 1
key: "semester_6/hydro_power:best-hydraulic-section-definition"
source: https://www.bctengineer.com/q/semester_6/hydro_power/best-hydraulic-section-definition
site: BCT Engineering
---

# Definition: best hydraulic section

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

- Asked in: 2072 Asoj, 3 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/hydro_power/best-hydraulic-section-definition
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-1

## Question

Define best hydraulic section.

## Short answer

A best hydraulic section is the channel cross-section that maximizes discharge for a given area, slope, and roughness by minimizing wetted perimeter and maximizing hydraulic radius. For rectangular channels, width equals twice depth (b=2y); for trapezoidal, half the top width equals the sloping side length; for triangular, side slopes are 1:1 (45°).

## Answer

A **best hydraulic section** (most efficient or most economical section) is the channel cross-section that carries the **maximum discharge** for a given area, bed slope and roughness. From $Q = AC\sqrt{RS}$, this occurs when the **wetted perimeter is minimum**, i.e. the hydraulic radius $R = A/P$ is maximum. Such a section also needs the least lining and excavation cost.

Conditions for common shapes:
| Section | Condition |
|---|---|
| Rectangular | $b = 2y$, $R = y/2$ |
| Trapezoidal | Half top width = sloping side; $R = y/2$ |
| Triangular | Side slope 1:1 (45° with vertical), $R = y/(2\sqrt{2})$ |

Example: best rectangular section with $y = 2$ m has $b = 4$ m and $R = 1$ m.

## Check yourself

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

1. A best hydraulic section carries:
   A. The minimum discharge for a given area
   B. The maximum discharge for a given area, slope and roughness
   C. The maximum area for a given discharge only
   D. Zero lining cost
   Answer: B. It is the most efficient section for given A, S and roughness. (Key point: Definition)

2. This occurs when the wetted perimeter is:
   A. Maximum
   B. Equal to top width
   C. Minimum, so R = A/P is maximum
   D. Equal to the depth
   Answer: C. With Q = AC sqrt(RS), maximum R means minimum P. (Key point: Condition)

3. For the best rectangular section with y = 2 m, the width and R are:
   A. b = 2 m, R = 2 m
   B. b = 4 m, R = 1 m
   C. b = 4 m, R = 2 m
   D. b = 8 m, R = 1 m
   Answer: B. b = 2y = 4 m and R = y/2 = 1 m. (Key point: Rectangular case)

## Related in Hydro Power

- [Best hydraulic rectangular canal design](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Abest-rectangular-canal-design) — Hydro Power, chapter 1
- [Hydraulically best trapezoidal section](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Abest-trapezoidal-section-proof) — Hydro Power, chapter 1
- [Most economical rectangular channel section](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Amost-economical-rectangular-section) — Hydro Power, chapter 1, asked 2×

## Related in other subjects

- [Best trapezoidal section and half-hexagon proof](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Atrapezoidal-proportions-half-hexagon-proof) — Hydraulics, chapter 6, asked 2×
- [Hydraulic exponent for rectangular section 10/3](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Ahydraulic-exponent-rectangular-10-3) — Hydraulics, chapter 6, asked 2×
- [Hydraulic exponent for triangular section 16/3](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Ahydraulic-exponent-triangular-16-3) — Hydraulics, chapter 6, asked 2×
- [Economical triangular section hydraulic radius](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Amost-economical-triangular-section-hydraulic-radius) — Hydraulics, chapter 6