Formula Used
Hydraulic radius is defined as the ratio of wetted flow area to wetted perimeter: Rh = A / P. The wetted area A is the cross-sectional area occupied by water, and the wetted perimeter P is the boundary length in contact with water.
- Rectangular open channel: A = b·y, P = b + 2y
- Trapezoidal open channel: A = y(b + z·y), P = b + 2y√(1 + z²)
- Circular full pipe: A = πD²/4, P = πD
- Circular partially full: θ = arccos((r − y)/r), A = r²(θ − sinθ·cosθ), P = 2rθ
How to Use This Calculator
- Select a calculation mode that matches your channel or pipe.
- Choose your preferred length unit, then enter geometry values.
- For custom mode, enter wetted area and wetted perimeter directly.
- Click Calculate to show results above the form.
- Use CSV or PDF buttons to save a copy for reports.
Example Data Table
| Case | Mode | Inputs | Wetted Area (m²) | Wetted Perimeter (m) | Hydraulic Radius (m) |
|---|---|---|---|---|---|
| 1 | Rectangular | b = 2.0 m, y = 0.8 m | 1.600 | 3.600 | 0.444 |
| 2 | Trapezoidal | b = 1.5 m, y = 1.0 m, z = 1.0 | 2.500 | 4.328 | 0.578 |
| 3 | Circular Full | D = 0.6 m | 0.283 | 1.885 | 0.150 |
Values are rounded for display and may vary with precision settings.
Hydraulic Radius in Flow Analysis
1) What the hydraulic radius represents
The hydraulic radius (Rh) condenses cross‑section geometry into one length scale by dividing wetted area by wetted perimeter. For open channels, it increases when the flow becomes wider or deeper, and it decreases when boundary contact grows faster than area. Designers use it to compare sections objectively.
2) Why wetted perimeter matters
Boundary contact drives shear and energy loss. For a fixed area, a larger wetted perimeter usually implies more friction and lower conveyance. This is why smoother linings and compact perimeters can raise capacity without changing slope. The calculator makes this tradeoff visible by reporting A and P alongside Rh.
3) Typical magnitude and scaling
In small laboratory flumes, Rh may be only a few millimeters. Irrigation channels often fall in the 0.05–0.30 m range, while large rivers can exceed 1 m depending on depth and width. Because Rh is a length, doubling all dimensions doubles Rh.
4) Connection to Manning and Chezy methods
Many open‑channel calculations combine Rh with slope and roughness. In Manning’s equation, discharge scales with Rh2/3, so modest geometric improvements can produce noticeable flow increases. Chezy formulations similarly link velocity to the hydraulic radius through a resistance coefficient.
5) Hydraulic diameter for closed conduits
In pipe and duct work, analysts often convert Rh into hydraulic diameter, Dh = 4Rh. Dh lets you apply standard friction‑factor correlations that were developed for circular pipes. Enable the “derived metric” option to display Dh in your chosen unit.
6) Partial‑flow circular sections
For partially full pipes, both area and wetted perimeter vary nonlinearly with depth. Near shallow depths, perimeter grows quickly relative to area, reducing Rh. As depth approaches full flow, Rh approaches the full‑pipe value, and Dh approaches the pipe diameter.
7) Using units and precision safely
Keep all input dimensions in the selected length unit. For custom mode, choose an area unit that matches your measurement source, then enter the wetted perimeter in the length unit. Increase precision when working with small channels, thin films, or near‑zero depths.
8) Practical workflow for design checks
Start with a candidate geometry and compute Rh. Compare alternatives by holding area or depth fixed and observing how the perimeter changes. Export a CSV for traceable calculations or a PDF for project files. Pair Rh with slope and roughness in your capacity model to finalize sizing.
FAQs
1) What is the hydraulic radius?
It is the wetted flow area divided by the wetted perimeter. It summarizes cross‑section geometry into one length that is widely used in resistance and capacity calculations.
2) Is hydraulic radius the same as hydraulic diameter?
No. Hydraulic diameter equals four times the hydraulic radius (Dh = 4Rh). Hydraulic diameter is commonly used in pipe friction‑factor and Reynolds number correlations.
3) For open channels, what counts in the wetted perimeter?
Only the boundary in contact with water counts: the bed and sidewalls. The free surface is not included because it does not create wall shear like solid boundaries.
4) Why does a larger hydraulic radius often increase capacity?
A larger hydraulic radius typically means less boundary contact per unit area, which reduces frictional losses. In Manning‑type methods, discharge increases with Rh2/3 for the same slope and roughness.
5) Can I use measured area and perimeter instead of a shape?
Yes. Choose the custom mode, select an area unit, then enter wetted area and wetted perimeter directly. This is useful for irregular sections or survey‑based channel shapes.
6) What happens if the wetted perimeter is zero?
The hydraulic radius is undefined because division by zero occurs. This can happen at zero depth in a channel or at an empty pipe. Increase depth to compute a valid result.
7) How accurate is the partially full pipe calculation?
It uses exact circular‑segment relations based on the depth and radius. Accuracy is high when your diameter and depth are measured correctly and you keep units consistent.