Hydraulic Radius Calculator

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. Use it with our Manning Equation Calculator and Chezy Equation Calculator for complete open-channel flow analysis.

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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What is Hydraulic Radius?

Formulas and Calculations

How to Use the Hydraulic Radius Calculator

Frequently Asked Questions

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