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

# Define spatially varied flow

Hydraulics · Chapter 5: Basics of Open channel flow

- Asked in: 2082 Kartik, 0.5 marks; 2081 Chaitra, 1 marks; 2076 Baisakh, 1 marks; 2072 Magh, 1 marks; 2072 Asoj, 1 marks (asked 5 times)
- Video: [Spatially varied flow||SVF|ocf|types of varied flow||open channel flow||SVF||varied flow figure](https://www.youtube.com/watch?v=KX3JKXD8qnM) — ENGINEER MIND
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/hydraulics/define-spatially-varied-flow
- Whole chapter: https://www.bctengineer.com/md/semester_4/hydraulics/chapter-5

## Question

Define spatially varied flow.

## Short answer

Spatially varied flow is steady, non-uniform open channel flow where discharge changes with distance due to lateral inflow or outflow. Examples include side channel spillways (increasing flow) and side weirs (decreasing flow).

## Answer

**Spatially varied flow (SVF)** is steady, non-uniform open channel flow in which the discharge changes along the length of the channel because water is added or removed along the way, as lateral inflow or outflow. Since $Q$ changes with distance, $dQ/dx\neq0$.

#### Types
- **Increasing discharge** (water added along the length): side channel spillway, roadside gutter, drainage channel collecting water from a field, wash-water trough.
- **Decreasing discharge** (water removed along the length): side weir or lateral spillway, irrigation channel with outlets, bottom rack (trench weir), perforated or porous channel.

```text
 Increasing Q (lateral inflow)      Decreasing Q (side weir)
     |  |  |  |                          ^  ^  ^  (outflow)
 ~~~~~~~~~~~~~~~~~~>  Q grows        ~~~~~~~~~~~~~~~~~~>  Q falls
 ____________________________        _____|side weir|______
```
The usual momentum or energy equation for gradually varied flow is modified to include the lateral discharge term. In a side channel spillway, for example, the depth changes along the channel as the flow increases.

## Check yourself

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

1. Spatially varied flow is steady non-uniform flow in which
   A. Discharge changes along the channel due to lateral inflow or outflow
   B. Flow is laminar
   C. Discharge changes with time only
   D. Depth is constant
   Answer: A. So dQ/dx is not zero. (Key point: Definition)

2. Which is an example of increasing discharge?
   A. Irrigation outlets
   B. Bottom rack
   C. Side weir
   D. Side channel spillway
   Answer: D. Water is added along a side channel spillway. (Key point: Increasing example)

3. Which is an example of decreasing discharge?
   A. Roadside gutter
   B. Side channel spillway
   C. Side weir
   D. Wash-water trough
   Answer: C. A side weir removes water along the length. (Key point: Decreasing example)

## 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×
- [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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