New Tool Release: Gradually Varied Flow (Water Surface Profiles)
We are taking open channel hydraulics to the next level today with the release of the Gradually Varied Flow (GVF) Worksheet! 🌊📉
In our Standard Open Channel Tool, we calculate Normal Depth ($y_n$). But Normal Depth assumes "Uniform Flow"—meaning the water depth stays perfectly constant forever. In the real world, this rarely happens. Dams, bridges, culverts, and free overfalls force the water surface to constantly change as it backs up or draws down.
This new interactive worksheet utilizes the rigorous Direct Step Method to calculate exactly how far a backwater curve will extend upstream, or how quickly a drawdown curve will accelerate downstream. It instantly classifies your flow profile (M1, M2, S1, S2, etc.) and plots a beautiful, CAD-style longitudinal profile of your channel.
Why Do We Need Gradually Varied Flow?
If you drop a leaf in a perfectly straight, infinitely long concrete canal, it will eventually settle into a steady state called Normal Depth ($y_n$). However, natural rivers and engineered channels are rarely infinite.
Consider a dam across a river. At the dam face, the water depth is forced to be very high (a "Control Point"). From the dam, the water surface must gradually curve backward, extending upstream for miles until it eventually blends back into the river's Normal Depth. This is called a Backwater Curve (M1 Profile). Knowing the exact length and shape of this curve is legally required to map out floodplains and buy out affected landowners.
Similarly, if a channel ends at a free waterfall, the water will accelerate and drop toward Critical Depth ($y_c$). This is a Drawdown Curve (M2 Profile). You need to know this curve to design the height of your concrete training walls.
How to Use the GVF Engine
This worksheet uses the numerical Direct Step Method. Instead of solving for depth at a specific distance (which is mathematically painful), it sets a specific depth and calculates the exact distance ($\Delta x$) required to reach it. Here is how to use it:
Define Channel Geometry & Flow
Enter your baseline parameters in Sections 1 and 2: Discharge ($Q$), Bed Slope ($S_0$), Manning's Roughness ($n$), and your cross-sectional dimensions.
Advanced Shapes: Just like our standard Open Channel tool, this GVF engine supports complex geometries including Compound Berms, Parabolic ditches, and Round-Bottom Trapezoids. The internal engine will calculate the exact Area, Wetted Perimeter, and Top Width for any given depth on the curve automatically!
Set the Boundary Conditions
This is where the magic happens. You need to define where your water profile begins ($y_1$) and where it ends ($y_2$).
- Control Depth ($y_1$): Enter the known physical depth at your constraint. If the channel empties into a lake, enter the lake's water depth. If it's a free overfall, the control depth is actually Critical Depth ($y_c$).
- Target Depth Type: A backwater curve theoretically never touches normal depth; it approaches it asymptotically at infinity. To prevent the math from exploding (dividing by zero), you must offset $y_2$ slightly from $y_n$. Use the dropdown to automatically snap your target depth to a mathematically safe offset!
Analyze Classification & CAD Drawing
The tool instantly computes the entire profile using $N$ number of calculation steps. Look at the top stats bar to see your automated Profile Classification.
The tool compares your channel slope (Mild vs Steep) against the relationship between the actual water depth ($y$), normal depth ($y_n$), and critical depth ($y_c$) to confidently stamp your profile as an M1, M2, S1, S2, C1, or even Horizontal/Adverse profile.
Finally, review the Longitudinal Profile Schematic. It utilizes a CAD-style architectural hatching and visualizes the Water Surface (HGL), the Energy Grade Line (EGL), and the mathematical limits ($y_n$, $y_c$).
Pro Tips for Modelers
The Direct Step method is mathematically continuous. It cannot naturally step through a Hydraulic Jump (where flow violently snaps from supercritical to subcritical, crossing Critical Depth). If you accidentally set boundary conditions that force the profile to cross $y_n$ or $y_c$, the tool will immediately flash a red warning banner alerting you that the continuous equation is invalid!
Standard plotting software often ruins GVF curves because it forces the Y-axis to scale to the absolute drop of the channel bed over a massive distance, squashing the water surface to a flat line. I engineered the schematic chart in this tool to use a Fixed Visual Slope. The bed always drops a fixed amount on-screen, allowing the relative variations in the water surface to remain perfectly visible and proportional, exactly like textbook diagrams!
Export Your Tables
Scroll to the bottom of the tool to review the actual step-by-step mathematical matrix ($\Delta E$, Average Friction Slope $\bar{S_f}$, $\Delta x$, and Cumulative $X$).
Click the Export Profile Data button in the toolbar to instantly download this entire matrix as a clean CSV file, ready to be attached to your drainage report or plugged into CAD to draft your final profile lines.
Head over to the tool page and try routing a backwater curve. If you find this useful, or if you want to request a feature (like adding the Standard Step method for non-prismatic natural river cross-sections), drop a comment below!
Happy Modeling!
- CivilSheets
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