Hydraulic Radius Calculator
Enter channel bottom width and depth to compute the hydraulic radius R = A/P for a rectangular open channel.
Input Data
Results
At a glance:The hydraulic radius R = A/P is the ratio of the flow cross-sectional area A to the wetted perimeter P (the length of the boundary in contact with the fluid). It appears in open-channel resistance laws: Manning Q = (1/n)·A·R^(2/3)·S^(1/2) and Chezy Q = A·C·√(R·S). For a rectangular channel, A = b·y and P = b + 2y, so R = b·y/(b+2y). For a full circular pipe, R = D/4. A larger R means less relative boundary friction for the same area — wide shallow channels approach R ≈ y, while narrow deep ones have smaller R. This tool computes R and A for a rectangle.
Formula
Hydraulic radius: R = A/P
Rectangular: A = b·y, P = b+2y, R = b·y/(b+2y)
$$R = \dfrac{A}{P} = \dfrac{b\,y}{b + 2y}$$How to Use
- Enter the bottom width b (m).
- Enter the flow depth y (m).
- The calculator returns R and A.
Case Studies
Rectangular ditch
b = 2 m, y = 0.5 m.
A = 1 m², P = 3 m, R = 1/3 ≈ 0.333 m.
Used in Manning to get velocity.
FAQ
What does hydraulic radius tell you?
It scales how much 'open' area the flow has relative to the friction boundary; larger R → less boundary drag per unit flow, so higher velocity for given slope.
Why is it not a true radius?
It is an area/perimeter ratio (units of length), not a geometric radius; the name reflects its role analogous to radius in pipe-flow friction.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.