---
title: "Define GVF, RVF and spatially varied flow"
subject: "Hydraulics"
chapter: 5
key: "semester_4/hydraulics:gvf-rvf-svf-define-with-examples"
source: https://www.bctengineer.com/q/semester_4/hydraulics/gvf-rvf-svf-define-with-examples
site: BCT Engineering
---

# Define GVF, RVF and spatially varied flow

Hydraulics · Chapter 5: Basics of Open channel flow

- Asked in: 2077 Chaitra, 4 marks; 2074 Bhadra, 2×3 marks; 2070 Magh, 4 marks; 2070 Bhadra, 4 marks (asked 4 times)
- Video: [Gradually varied flow & Rapidly varied flow | Types of Non Uniform Flow | GVF | RVF l Open Channel](https://www.youtube.com/watch?v=YaNsgt9r60E) — Professor Nidhi Trivedi
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/hydraulics/gvf-rvf-svf-define-with-examples
- Whole chapter: https://www.bctengineer.com/md/semester_4/hydraulics/chapter-5

## Question

Define gradually varied, rapidly varied and spatially varied flow with examples (sketches).

## Short answer

Gradually varied flow: depth changes slowly over long distance, pressure hydrostatic; e.g., backwater behind dam, drawdown to fall. Rapidly varied flow: depth changes abruptly over short distance, pressure non-hydrostatic; e.g., hydraulic jump, flow over weir. Spatially varied flow: discharge varies along channel due to lateral inflow/outflow; e.g., side weir, roadside gutter.

## Answer

#### Gradually varied flow (GVF)
Steady non-uniform flow in which the depth changes slowly over a long distance, so the streamlines are nearly parallel and the pressure is hydrostatic. Examples: the backwater curve upstream of a dam or weir, and the drawdown curve towards a free fall.

#### Rapidly varied flow (RVF)
Steady non-uniform flow in which the depth changes abruptly over a short distance; the streamlines are strongly curved and the pressure is not hydrostatic. The energy loss is local and may be large (as in a hydraulic jump). Examples: a hydraulic jump, flow over a weir or spillway crest, and flow below a sluice gate.

#### Spatially varied flow (SVF)
Flow in which the discharge changes along the channel due to lateral inflow or outflow. Examples: a side channel spillway, side weir, roadside gutter, or a drain with lateral inflow.

```text
 GVF (backwater)      RVF (jump)          SVF (side weir)
   ____                 ___                 ~~~~~~~\ 
 ~~~     ~~~~            \_/\___            ~~~~~~~~~~>
 ~~~~~~~~~~~~~~        ~~~~~\_ ____        ____/weir____
  dam |                    jump
```
| Flow | Depth change | Length | Discharge |
|---|---|---|---|
| GVF | gradual | long | constant |
| RVF | abrupt | short | constant |
| SVF | gradual or abrupt | any | varies along the length |

## Check yourself

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

1. Gradually varied flow has
   A. No depth change
   B. Slow depth change over a long distance with hydrostatic pressure
   C. Abrupt depth change
   D. Varying discharge
   Answer: B. Streamlines are nearly parallel. (Key point: GVF)

2. Which is rapidly varied flow?
   A. Backwater curve
   B. Uniform canal flow
   C. Side channel spillway
   D. Hydraulic jump
   Answer: D. The depth changes abruptly over a short length. (Key point: RVF example)

3. What distinguishes spatially varied flow?
   A. Supercritical flow only
   B. Constant depth
   C. Discharge varies along the length
   D. Very short length
   Answer: C. GVF and RVF have constant discharge. (Key point: SVF)

## Close variants set in other exams

- [Differentiate GVF, RVF and SVF with sketches](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Adifferentiate-gvf-rvf-svf-sketch) — Hydraulics, chapter 5, asked 5×

## Related in Hydraulics

- [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 gradually varied flow](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Adefine-gradually-varied-flow) — Hydraulics, chapter 5, asked 2×
- [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×
- [Dynamic equation of GVF, wide rectangular form](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Agvf-dynamic-equation-wide-rectangular) — Hydraulics, chapter 8, 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×