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

# Define hydraulic depth

Hydraulics · Chapter 5: Basics of Open channel flow

- Asked in: 2082 Kartik, 0.5 marks; 2072 Magh, 1 marks (asked 2 times)
- Video: [[HYDRAULIC #1] Concept of Hydraulic Mean Depth and Hydraulic Radius and their Differences](https://www.youtube.com/watch?v=SON_Hh9Eibk) — Just Learn Civil
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/hydraulics/define-hydraulic-depth
- Whole chapter: https://www.bctengineer.com/md/semester_4/hydraulics/chapter-5

## Question

Define hydraulic depth.

## Short answer

Hydraulic depth Dh = A/T, ratio of flow area to top width. Used in Froude number Fr = V/sqrt(g Dh) and critical flow condition. For a rectangular channel Dh = y.

## Answer

**Hydraulic depth** ($D_h$ or $\bar{D}$) is the ratio of flow area to the top width of the water surface:
$$
D_h=\frac{A}{T}
$$
It is the depth of a rectangular channel having the same area and top width. For a rectangular channel $D_h=y$, for a triangular channel $D_h=y/2$, and for a trapezoidal channel $D_h=\dfrac{(b+zy)y}{b+2zy}$.

It is used in the Froude number, $Fr=\dfrac{V}{\sqrt{gD_h}}$, and in the critical-flow condition $\dfrac{Q^2T}{gA^3}=1$ for non-rectangular sections. Hydraulic depth should not be confused with hydraulic radius, $R=A/P$.

## Check yourself

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

1. Hydraulic depth is
   A. A/T
   B. T/A
   C. P/T
   D. A/P
   Answer: A. Area over top width. (Key point: Definition)

2. For a rectangular channel, hydraulic depth equals
   A. 2y
   B. b
   C. y/2
   D. y
   Answer: D. A/T = by/b = y. (Key point: Rectangle)

3. Hydraulic depth is used in
   A. Reynolds number
   B. Froude number Fr = V/sqrt(g D_h)
   C. Manning n
   D. Chezy C only
   Answer: B. Distinguish from hydraulic radius A/P. (Key point: Use)

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