Calculator
Example data table
Use these example inputs to confirm your workflow and units.
| Shape | Inputs | Area expression |
|---|---|---|
| Trapezoidal | b=3.00 m, y=1.20 m, z=1.50 | A=(b+T)*y/2 |
| Rectangular | b=2.50 m, y=1.10 m | A=b*y |
| Triangular (V) | y=1.00 m, z=1.00 | A=(T*y)/2, T=2*z*y |
| Circular segment | D=2.00 m, y=0.80 m | A=(r^2/2)(theta-sin(theta)) |
| Parabolic (approx.) | T=6.00 m, y=1.20 m | A=(2/3)Ty |
Formula used
- Rectangular: A = b·y, P = b + 2y, T = b.
- Trapezoidal: T = b + 2zy, A = (b+T)·y/2, P = b + 2y√(1+z²).
- Triangular (V): T = 2zy, A = T·y/2, P = 2y√(1+z²).
- Circular segment: with r=D/2, theta = 2·acos((r−y)/r), A = (r²/2)(theta−sin(theta)), P = r·theta.
- Parabolic (approx.): A = (2/3)·T·y.
- Hydraulic radius: R = A/P.
How to use this calculator
- Select the canal cross-section shape that matches your design.
- Choose a unit system and enter geometric inputs.
- Click Calculate to display area and related parameters.
- Review top width and wetted perimeter for hydraulic checks.
- Use Download CSV or Download PDF for documentation.
Professional article
1) Why cross-section area matters
Cross-section area controls conveyance capacity, velocity, and freeboard decisions in open-channel design. It is the first geometric input for Manning-based checks, sediment transport screening, and lining selection. When the area is underestimated, velocities rise and erosion risk increases; when it is oversized, excavation and lining costs grow without benefit.
2) Selecting the canal shape
Rectangular sections suit lined canals and constrained corridors, because walls are near-vertical and widths are predictable. Trapezoidal sections are common for earth canals, where side slopes improve stability and simplify construction. V sections are used for small drains and temporary channels. Circular segments represent part-full conduits or prefabricated linings. Parabolic shapes approximate some efficient irrigation canal profiles.
3) Using top width and wetted perimeter
Top width influences hydraulic depth and surface exposure. Wetted perimeter represents the boundary in contact with water and is required to compute the hydraulic radius, R=A/P. A larger perimeter for the same area lowers R, which can reduce conveyance. For trapezoids and V channels, the side slope parameter directly affects both area and perimeter through the sloped face length.
4) Units and field inputs
Use one unit system for every input, then keep it consistent through output reporting. Typical design checks record depth, bottom width, and side slope as measured values or survey targets. For circular segments, depth must remain between zero and the diameter. The built-in precision control supports quick comparisons during design iterations and reviews.
5) Practical workflow and documentation
Start by choosing a shape that matches the construction method and geotechnical constraints. Enter candidate dimensions, review area and R, then adjust geometry until capacity and velocity targets are satisfied. Export CSV for calculation logs and PDF for submittals, including inputs, outputs, and the selected section type for traceable approvals for field teams.
FAQs
Q1. Which canal shape should I select?
Select the shape that matches the built profile. Lined canals often use rectangles, earth canals use trapezoids, small drains use V sections, and circular segments represent part-full conduits.
Q2. What does side slope z mean?
z is the horizontal-to-vertical ratio of the side. For example, z=1.5 means 1.5 units horizontal for each 1 unit vertical. Larger z creates wider, flatter sides and a larger perimeter.
Q3. Why is hydraulic radius included?
Hydraulic radius R equals area divided by wetted perimeter. It is a key term in Manning-style capacity checks and helps compare how efficiently different shapes convey flow at a given roughness and slope.
Q4. Can I mix metric and imperial inputs?
Avoid mixing units. Enter all dimensions in one unit system so area, perimeter, and radius remain consistent. If you must convert, convert all length inputs first, then calculate.
Q5. How is the circular segment computed?
Depth is limited between zero and diameter. The method uses a central angle based on depth, then applies standard segment relations to compute area and wetted perimeter, plus the water-surface width.
Q6. Why does the parabolic option say approximate?
Parabolic canals vary by field shaping and lining practice. The area relation is a common approximation using top width and depth, while the perimeter estimate is simplified for quick screening and comparisons.
Q7. What should I include in reports?
Record section type, unit system, inputs, and the resulting area, top width, perimeter, and hydraulic radius. Use the CSV for logs and the PDF for submittal attachments and internal reviews.
Notes for engineering use
- Inputs represent water section geometry, not excavation quantities.
- For circular segments, depth is clamped between 0 and D.
- Parabolic perimeter is an estimate; verify if required.