Hydraulic Radius Calculator
Calculate hydraulic radius for open channels and pipes using Rh = A/Pw with Froude number, mean depth, and flow classification for fluid mechanics analysis.
What is Hydraulic Radius?
The hydraulic radius (Rh) is a fundamental parameter in open-channel flow and pipe flow analysis. It is defined as the ratio of the cross-sectional area of flow (A) to the wetted perimeter (Pw): Rh = A / Pw. The wetted perimeter is the length of the channel boundary that is in contact with the fluid — notably, the free water surface is NOT included in the wetted perimeter.
The hydraulic radius appears in Manning's equation, Chezy's equation, and the Darcy-Weisbach equation for calculating flow velocity and capacity in channels, rivers, sewers, and pipes. A higher hydraulic radius means less friction per unit of flow area, which translates to more efficient flow. A semicircular channel has the highest hydraulic radius for a given cross-sectional area, making it the most hydraulically efficient shape.
Formulas and Calculations
Hydraulic Radius (Rh): Rh = A / Pw
Where A is the cross-sectional area of flow and Pw is the wetted perimeter (the length of channel boundary in contact with the fluid).
Full Circular Pipe (special case): Rh = D / 4
For a pipe flowing completely full, the area is πD²/4 and the wetted perimeter is πD, so Rh = D/4. Note that this is different from the physical radius (D/2).
Froude Number: Fr = v / √(g × hm)
The Froude number classifies open-channel flow as subcritical (Fr < 1), critical (Fr = 1), or supercritical (Fr > 1). Subcritical flow is slow and deep; supercritical flow is fast and shallow.
How to Use the Hydraulic Radius Calculator
Enter the cross-sectional area of flow (A) and the wetted perimeter (Pw). The calculator instantly computes the hydraulic radius using Rh = A / Pw. Remember that the free water surface should not be included in the wetted perimeter — only surfaces in contact with the channel boundary count.
Frequently Asked Questions
What does hydraulic radius represent physically?
Rh is the flow cross-sectional area divided by the wetted perimeter — it measures how efficiently a channel shape conveys water. It appears in Manning's and Chezy's equations as the geometric driver of flow capacity: higher Rh means less drag per unit of cross-section.
Why is a semicircular channel hydraulically efficient?
For a given flow area, a semicircle minimizes the wetted perimeter, maximizing Rh. This is why drainage culverts and irrigation ditches often approximate a half-pipe shape — they achieve the same flow rate at a smaller energy cost or in a smaller channel.
What is the hydraulic radius of a full circular pipe?
For a full pipe of diameter D, the area is πD²/4 and the wetted perimeter is πD, so Rh = D/4. A 200 mm full pipe has Rh = 0.05 m. This is different from the physical pipe radius (D/2 = 0.1 m), which is a common point of confusion.
Why isn't the free water surface part of the wetted perimeter?
Friction only develops where the fluid contacts a solid boundary. The free water surface is in contact with air, where shear stress is negligible compared to channel walls. Including it would overstate the wetted perimeter and under-predict the hydraulic radius.
How is the Froude number used in open-channel design?
Fr = v/√(g × hm) classifies flow regime. Fr < 1 is subcritical (slow, deep) — typical of rivers. Fr > 1 is supercritical (fast, shallow) — typical of steep flumes and downstream of spillways. Crossing Fr = 1 produces a hydraulic jump, useful for energy dissipation in stilling basins.
Where is hydraulic radius used in engineering?
Hydraulic radius is used in Manning's equation for open-channel flow (canals, rivers, sewers), Chezy's equation, Darcy-Weisbach pipe flow, storm sewer design, dam spillway analysis, and channel design optimization. It is a fundamental parameter in nearly all civil engineering hydraulic calculations.
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