What Is the Hydraulic Radius?
The hydraulic radius (\(R_h\)) is a key parameter in open-channel and pipe-flow hydraulics. It is defined as the ratio of the cross-sectional area of flow to the wetted perimeter — the length of the channel boundary that is in contact with the fluid. The hydraulic radius effectively describes how "efficient" a channel shape is at conveying flow: a larger hydraulic radius means less frictional resistance per unit of flow area.
How to Use This Calculator
Enter the cross-sectional area of flow (A) and the wetted perimeter (P) in consistent units (for example, square meters and meters). The calculator divides A by P to return the hydraulic radius in length units. Make sure both inputs use the same base length unit so the result is meaningful.
The Formula Explained
The governing equation is simply $$R_h = \frac{\text{Area (A)}}{\text{Wetted Perimeter (P)}}$$ Here A is the area of the fluid cross-section perpendicular to flow, and P is the wetted perimeter — only the portion of the boundary touching the fluid, not the free water surface. For a full circular pipe of diameter D, \(R_h = \frac{\pi D^2/4}{\pi D} = \frac{D}{4}\). This value feeds directly into the Manning and Chézy equations used to estimate flow velocity and discharge.
Worked Example
Consider a rectangular channel carrying water 2 m deep and 5 m wide. The flow area is \(A = 2 \times 5 = 10\ \text{m}^2\). The wetted perimeter is the bottom plus both sides: \(P = 5 + 2 + 2 = 9\ \text{m}\) (the top surface is open and not counted). Then $$R_h = \frac{10}{9} \approx 1.111\ \text{m}$$
FAQ
Does the water surface count toward the wetted perimeter? No. Only the solid boundary in contact with the fluid is included; the free surface is excluded.
What units should I use? Any, as long as area and perimeter share the same base length unit. The result carries that length unit.
What is hydraulic radius used for? It is a core input to the Manning and Chézy formulas for computing flow velocity and discharge in channels and partially filled pipes.
