Calculator Inputs
Example Data Table
| Section | Inputs | Area | Wetted Perimeter | Hydraulic Radius |
|---|---|---|---|---|
| Rectangular | b = 4 m, y = 1.2 m | 4.8000 m² | 6.4000 m | 0.7500 m |
| Trapezoidal | b = 3 m, y = 1 m, z = 1.5 | 4.5000 m² | 6.6056 m | 0.6812 m |
| Full circular pipe | D = 1.2 m | 1.1310 m² | 3.7699 m | 0.3000 m |
Formula Used
Hydraulic radius: R = A / P, where A is flow area and P is wetted perimeter.
Hydraulic diameter: Dh = 4R. This is often used when comparing noncircular sections.
Rectangular channel: A = by and P = b + 2y.
Trapezoidal channel: A = y(b + zy), P = b + 2y√(1 + z²), and T = b + 2zy.
Triangular channel: A = zy² and P = 2y√(1 + z²).
Full pipe: A = πD² / 4, P = πD, and R = D / 4.
Partly full pipe: θ = 2 cos⁻¹((r - y) / r), A = r²(θ - sinθ) / 2, and P = rθ.
Manning estimate: V = kR2/3S1/2 / n, where k is 1 for metric and 1.486 for US customary units.
How to Use This Calculator
- Select the section type that matches the channel or pipe.
- Choose metric or US customary units before entering dimensions.
- Enter only the dimensions needed for that geometry.
- Use direct mode when area and wetted perimeter are already known.
- Add Manning roughness and slope when velocity and discharge are needed.
- Press Calculate to show results below the header and above the form.
- Use CSV for spreadsheet work or PDF for a compact report.
Hydraulic Radius in Channel Physics
Hydraulic radius is a compact measure of flow section efficiency. It links the water area to the wetted boundary. A larger value often means less boundary resistance for the same area. Engineers use it in open channel studies, pipe checks, culvert sizing, and drainage reports.
Why the Value Matters
Water loses energy when it rubs against a boundary. The wetted perimeter represents that contact length. The flow area represents the space carrying water. The ratio between them gives hydraulic radius. It helps compare shapes that may carry similar flow but have different contact surfaces.
Common Section Types
Rectangular channels are simple and common. Their wetted perimeter includes the bed and two water sides. Trapezoidal channels add side slopes, so their wetted sides become longer. Triangular channels are useful for small ditches and V drains. Circular pipes need a special segment method when partly full. A full circular pipe has a simple radius equal to one fourth of the diameter.
Design Use
Hydraulic radius feeds Manning based velocity estimates. It also supports hydraulic diameter checks. When slope and roughness are known, the calculator estimates velocity and discharge. These results help during early sizing. They should still be checked against local standards, site controls, freeboard rules, sediment limits, and safety needs.
Input Quality
Use consistent units. Area and wetted perimeter must describe the same water section. Depth should be the actual flow depth, not total wall height. For trapezoids, side slope is horizontal to vertical. For partial pipes, depth must stay between zero and the diameter. Bad geometry creates misleading results.
Practical Review
Compare the calculated hydraulic radius with sample cases. A sudden jump may show a wrong perimeter or depth entry. Export the CSV for spreadsheets. Download the PDF for quick record keeping. The tool is best for transparent physics review, class work, and preliminary hydraulic design. It makes the formula visible, so each result can be traced and checked.
Limitations
The result does not replace detailed hydraulic modeling. Real channels may include bends, debris, transitions, vegetation, and uneven beds. Roughness may change with depth. Treat the output as a clear calculation step. Use surveyed geometry and verified coefficients for final decisions. Review assumptions before approval.
FAQs
What is hydraulic radius?
Hydraulic radius is the flow area divided by the wetted perimeter. It shows how efficiently a channel section carries water compared with its boundary contact.
Is hydraulic radius the same as pipe radius?
No. For a full circular pipe, hydraulic radius equals one fourth of the diameter. It is not the physical radius of the pipe.
What is wetted perimeter?
Wetted perimeter is the length of the channel or pipe boundary touching water. It excludes the free water surface in open channel flow.
Can I use direct mode?
Yes. Use direct mode when you already know the flow area and wetted perimeter from drawings, surveys, or a separate geometry calculation.
What does side slope z:1 mean?
It means horizontal distance per one vertical distance. A side slope of 1.5 means the bank extends 1.5 units sideways for every 1 unit upward.
Why enter Manning roughness?
Manning roughness lets the tool estimate velocity and discharge. Without roughness and slope, it only reports geometry based hydraulic values.
Can this design a final drainage system?
It supports preliminary calculations. Final design should consider codes, rainfall data, inlet controls, tailwater, freeboard, sediment, maintenance, and professional review.
Why is top width sometimes unavailable?
A full pipe has no open water surface. Direct mode also lacks top width unless you enter it. Mean hydraulic depth needs top width.