---
title: "Differentiate GVF, RVF and SVF with sketches"
subject: "Hydraulics"
chapter: 5
key: "semester_4/hydraulics:differentiate-gvf-rvf-svf-sketch"
source: https://www.bctengineer.com/q/semester_4/hydraulics/differentiate-gvf-rvf-svf-sketch
site: BCT Engineering
---

# Differentiate GVF, RVF and SVF with sketches

Hydraulics · Chapter 5: Basics of Open channel flow

- Asked in: 2068 Bhadra, 3 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/hydraulics/differentiate-gvf-rvf-svf-sketch
- Whole chapter: https://www.bctengineer.com/md/semester_4/hydraulics/chapter-5

## Question

Differentiate gradually, rapidly and spatially varied flow with neat sketches and examples.

## Short answer

Gradually varied flow (GVF) features slow depth change, constant discharge, hydrostatic pressure; e.g., backwater behind a dam. Rapidly varied flow (RVF) has abrupt depth change, constant discharge, non-hydrostatic pressure; e.g., hydraulic jump. Spatially varied flow (SVF) involves varying discharge due to lateral addition or removal; e.g., side channel spillway.

## Answer

| Basis | Gradually varied flow (GVF) | Rapidly varied flow (RVF) | Spatially varied flow (SVF) |
|---|---|---|---|
| Depth change | Slow, over a long reach | Abrupt, over a short reach | Gradual or abrupt, along the reach |
| Discharge | Constant | Constant | Varies along the length |
| Streamlines | Nearly parallel | Strongly curved | Depends |
| Pressure | Hydrostatic | Non-hydrostatic | Hydrostatic (usually) |
| Energy loss | Mainly friction (distributed) | Local, may be large (eddies) | Friction plus mixing of the lateral flow |
| Analysis | Energy equation $dy/dx=(S_0-S_f)/(1-Fr^2)$ | Momentum, specific energy, empirical | Momentum equation (increasing Q) or energy equation (decreasing Q), with a $dQ/dx$ term |
| Examples | Backwater behind a dam, drawdown to an overfall | Hydraulic jump, flow over a spillway crest, flow below a sluice gate | Side weir, side channel spillway, roadside gutter |

```text
GVF: backwater            RVF: hydraulic jump
     ___                   
 ~~~~    ~~~~|  dam          ~~~~\___/\~~~~~
 ___________|                 ___________

SVF: increasing Q            SVF: decreasing Q
   | | |  lateral inflow       ~~~~~~~~~~\
 ~~~~~~~~~~~~~~>                ~~~~~~~~~~~~~> 
 ___________________            _____/weir___
```

## Check yourself

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

1. Which flow has an abrupt depth change over a short reach with strongly curved streamlines?
   A. Gradually varied flow
   B. Rapidly varied flow
   C. Spatially varied flow
   D. Uniform flow
   Answer: B. RVF, such as a hydraulic jump, has sudden depth change and strongly curved streamlines. (Key point: Depth change)

2. Which of the three types has discharge that varies along the length?
   A. Spatially varied flow only
   B. Gradually varied flow only
   C. Rapidly varied flow only
   D. All three
   Answer: A. GVF and RVF have constant Q; SVF has lateral inflow or outflow. (Key point: Discharge)

3. Which pressure distribution applies to rapidly varied flow?
   A. Hydrostatic
   B. Non-hydrostatic, because of streamline curvature
   C. Zero everywhere
   D. Always above hydrostatic in every case
   Answer: B. Strong streamline curvature makes the pressure non-hydrostatic in RVF. (Key point: Pressure)

4. Which pairing of flow type and example is correct?
   A. GVF - hydraulic jump
   B. RVF - backwater behind a dam
   C. SVF - side weir
   D. SVF - flow below a sluice gate
   Answer: C. A side weir changes Q along the reach (SVF). The jump and sluice gate are RVF; backwater is GVF. (Key point: Examples)

## Close variants set in other exams

- [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×

## 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×