How to calculate hydraulic radius
Hydraulic radius is flow area divided by wetted perimeter. In an open channel, the water surface touches air and is not part of the wetted perimeter.
What the formula is saying
Find the area occupied by water and the length of solid boundary in contact with it. Divide A by P. For a rectangular open channel, A = by and P = b + 2y.
Read the symbols in plain language
- A
- Flow aream²
- P
- Wetted perimeterm
Sort out the units first
Use m² for area and m for wetted perimeter to get m. Example: width 3 m and depth 1 m give A = 3 m² and P = 5 m.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
- A · Flow area
- 3 m²
- P · Wetted perimeter
- 5 m
Count only the wetted boundary
Exclude the air–water surface in an open channel.
(5) = 5 mDivide water area by wetted perimeter
m² / m gives an ordinary length.
(3) ÷ (5) = 0.6 m
Does this worked answer make sense?
The rectangular example gives 0.6 m. Including the 3 m free surface in P would incorrectly reduce it to 0.375 m.
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Use these new values. Work it out first, then check your answer.
- A · Flow area
- 2 m²
- P · Wetted perimeter
- 6 m
Find: hydraulic radius
A hint, not the answer
Find the area occupied by water and the length of solid boundary in contact with it. Divide A by P. For a rectangular open channel, A = by and P = b + 2y.
Use m² for area and m for wetted perimeter to get m. Example: width 3 m and depth 1 m give A = 3 m² and P = 5 m.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Count only the wetted boundary
Exclude the air–water surface in an open channel.
(6) = 6 mDivide water area by wetted perimeter
m² / m gives an ordinary length.
(2) ÷ (6) ≈ 0.3333333333 m
Avoid the common trap
R is not generally the geometric radius. For a full circular pipe, hydraulic radius is D/4, while hydraulic diameter is 4R.
When this method applies — and when it does not
Geometric definition only. It does not determine discharge without an additional flow relationship and its assumptions.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
One idea understood. Keep going.
This optional checkmark is saved only in this browser. It is your own progress note, not a certificate.
Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Lesson updated: · Worked examples checked against the implemented formula; not an independent engineering certification.