Gradually Varied Flow (GVF) – Water Surface Profile Analysis

A Jupyter notebook for computing and visualising the water surface profile of gradually varied flow in a rectangular open channel using the Direct Step Method (Manning's equation).

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What is Gradually Varied Flow?

Gradually Varied Flow (GVF) is a steady, non-uniform open channel flow where the depth changes slowly along the channel length. It occurs when there is a disturbance to uniform flow (e.g. a gate, a change in slope, a weir).

The governing differential equation is:

dy/dx = (So - Sf) / (1 - Fr²)

where Sₒ = bed slope, Sf = friction slope, Fr = Froude number.

Direct Step Method

Instead of solving the ODE directly, the Direct Step Method works backwards from a known boundary depth. For each step in depth Δy, it computes the corresponding distance Δx:

Δx = ΔE / (So − S̄f)

where ΔE is the change in specific energy and S̄f is the average friction slope between two sections.

Profile Types

Symbol	Slope	Condition	Description
M1	Mild	y > yn > yc	Backwater curve
M2	Mild	yn > y > yc	Drawdown curve
M3	Mild	yn > yc > y	Rising curve (supercritical)
S1	Steep	y > yc > yn	Backwater curve
S2	Steep	yc > y > yn	Drawdown curve
S3	Steep	yc > yn > y	Rising curve

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Project Structure

gvf-analysis/
│
├── data/
│   └── hydrau.xlsx          ← Input file (edit with your lab measurements)
│
├── GVF_clean.ipynb          ← Main notebook (run this)
│
├── requirements.txt         ← Python dependencies
├── .gitignore               ← Files Git should ignore
└── README.md                ← You are here

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Input File Format (data/hydrau.xlsx)

Fill in one row per measurement section, moving downstream:

Column	Unit	Description
distance_'x'(m)	m	Measured distance along channel
depth_'y'(m)	m	Measured water depth at this section
time:	s	Time for the volumetric measurement
Bed_slope	—	Channel bed slope (dimensionless, e.g. 0.005)

Example (11 sections from lab experiment):

distance_'x'(m)	depth_'y'(m)	time:	Bed_slope
0.00	0.017	12.5	0.005
0.02	0.023	12.5	0.005
0.04	0.031	12.5	0.005
…	…	…	…
0.20	0.060	12.5	0.005

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Getting Started

Option A – Google Colab (no installation)

1. Go to colab.research.google.com.
2. File → Upload notebook → upload GVF_clean.ipynb.
3. Upload hydrau.xlsx via the file panel (folder icon → upload).
4. Update EXCEL_PATH = "/content/hydrau.xlsx" in the notebook.
5. Runtime → Run all and enter values when prompted:
   • Volume (litres)
   • Manning's roughness n
   • Channel width (m)

Option B – Run locally

# 1. Clone the repository
git clone https://github.com/<your-username>/gvf-analysis.git
cd gvf-analysis

# 2. Create a virtual environment (recommended)
python -m venv venv
source venv/bin/activate        # Windows: venv\Scripts\activate

# 3. Install dependencies
pip install -r requirements.txt

# 4. Launch Jupyter
jupyter notebook GVF_clean.ipynb

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Output

The notebook produces three plots (all saved as .png):

File	Description
water_surface_profile.png	Water surface profile with yc and yn reference lines
energy_profile.png	Specific energy and depth along the channel
friction_slope.png	Friction slope Sf vs distance, compared with Sₒ

It also prints:

• All intermediate hydraulic quantities in a tabular format
• Critical depth yc, normal depth yn, and profile classification (e.g. M2)

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Requirements

Package	Purpose
pandas	Reading Excel input and tabular calculations
openpyxl	Excel engine for pandas
numpy	Numerical operations
matplotlib	Plotting
scipy	Solving Manning's equation for normal depth

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Limitations

• Assumes a rectangular channel with constant width.
• Bed slope and Manning's n are assumed uniform along the channel.
• The Direct Step Method is accurate only when depth increments are small.
• Does not handle hydraulic jumps (rapidly varied flow).

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Author

Uddipta Bhaskar Sarma(uddiptasarma361@gmal.com – open an issue or pull request to suggest improvements.