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

# Define gradually varied flow

Hydraulics · Chapter 5: Basics of Open channel flow

- Asked in: 2072 Magh, 1 marks; 2072 Asoj, 1 marks (asked 2 times)
- Video: [Introduction to GVF | Gradually Varied Flow | Hydraulics and Fluid Mechanics](https://www.youtube.com/watch?v=iFifn3zhVFI) — The Content Paradox
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/hydraulics/define-gradually-varied-flow
- Whole chapter: https://www.bctengineer.com/md/semester_4/hydraulics/chapter-5

## Question

Define gradually varied flow.

## Short answer

Gradually varied flow is steady non-uniform flow with slowly changing depth, nearly parallel streamlines and hydrostatic pressure. Discharge is constant. Profile given by dy/dx = (S0 - Sf)/(1 - Fr^2). Examples: backwater behind a dam, drawdown to an overfall.

## Answer

**Gradually varied flow (GVF)** is steady non-uniform flow in which the depth changes gradually along the channel length, so that streamlines are almost parallel and the pressure distribution is hydrostatic. The discharge is constant.

Examples: the backwater curve upstream of a weir or dam, drawdown curve approaching a free overfall, and flow in a canal where the slope changes from mild to steep.

```text
        ______ GVF (backwater) 
   ~~~~~~          ~~~~~~|
   _____________________| dam
```
Its profile is governed by the dynamic equation
$$
\frac{dy}{dx}=\frac{S_0-S_f}{1-Fr^2}
$$
It is different from rapidly varied flow, in which the depth changes abruptly over a short length (for example, a hydraulic jump).

## Check yourself

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

1. Gradually varied flow has
   A. Unsteady flow
   B. Steady flow with slowly changing depth, near-parallel streamlines, hydrostatic pressure
   C. Abrupt depth change
   D. Varying discharge
   Answer: B. Discharge is constant. (Key point: Definition)

2. An example of GVF is
   A. Flow below a sluice gate
   B. Hydraulic jump
   C. Side weir flow
   D. Backwater curve upstream of a dam
   Answer: D. Jump and sluice flow are RVF. (Key point: Example)

3. The GVF equation is
   A. dy/dx = 0
   B. dy/dx = (S0 - Sf)/(1 - Fr^2)
   C. dy/dx = S0 + Sf
   D. dy/dx = Fr^2
   Answer: B. It governs profile shapes. (Key point: Dynamic equation)

## Related in Hydraulics

- [Define GVF, RVF and spatially varied flow](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Agvf-rvf-svf-define-with-examples) — Hydraulics, chapter 5, asked 5×
- [Explain GVF and spatially varied flow](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Agvf-and-svf-explain-example) — Hydraulics, chapter 5
- [Define spatially varied flow](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Adefine-spatially-varied-flow) — Hydraulics, chapter 5, asked 5×
- [Steady uniform, non-uniform and spatially varied flow](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Aflow-types-uniform-nonuniform-svf-examples) — Hydraulics, chapter 5, asked 4×
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