Hydraulic Radius Calculator
If you want to find the hydraulic radius in your pipe flow calculations, then this hydraulic radius calculator is right up your alley. We gathered a total of five hydraulic radius equations for various channel shapes: a rectangle, a trapezoid, a triangle, and a pipe with a different level of fill — this tool is certainly not a pipe dream!
Come right in and discover what's the difference between a wetted perimeter and the hydraulic radius of a pipe, or any other channel shape for that matter.
What is the hydraulic radius?
The hydraulic radius, R, is defined as the ratio of the cross-sectional area of the flow, A, to the wetted perimeter of the channel, P:
R = A / P
For example, imagine that you have a rectangular channel. The area of the flow will be equal to the channel width, b, multiplied by the flow depth, y. The wetted perimeter, on the other hand, is simply the total length of channel walls which are in contact with the liquid. In the case of the rectangular channel, it's a sum of b + y + y.
How do you calculate the wetted perimeter of a pipe?
The wetted perimeter of the pipe is the portion of the total pipe perimeter that is in contact with the flowing liquid (for example, water). It's very simple to calculate this for a full pipe — it's equal to the total pipe perimeter:
P = 2πr
If your pipe is only half full, the wetted perimeter will be equal to half of the total perimeter:
P = πr
What happens if the pipe is not exactly full or half full? In that case, the wetted perimeter is equal to the arc length, corresponding to the central angle θ:
P = r × θ where θ = 2 × arccos[(r − h) / r]
Here r is the pipe radius and h is the height of the liquid (the fill level).
Hydraulic radius equations for rectangular, trapezoidal, and triangular channels
- Rectangle — area A = b · y, wetted perimeter P = b + 2y, so R = (b · y) / (b + 2y). Here b is the channel width and y is the flow depth.
- Trapezoid — area A = (b + z·y)·y, wetted perimeter P = b + 2y·√(1 + z²). Here z is the side slope (horizontal run per 1 unit of vertical rise, H:1V).
- Triangle — area A = z·y², wetted perimeter P = 2y·√(1 + z²) for a symmetric V-shaped channel with side slope z.
Hydraulic radius of a pipe
- Full pipe — area A = πr², wetted perimeter P = 2πr. This simplifies neatly to R = r / 2 (one quarter of the diameter).
- Partially filled pipe — first find the central angle θ = 2 × arccos[(r − h) / r], then the flow area A = (r²/2)(θ − sin θ) and the wetted perimeter P = r · θ. The hydraulic radius is again R = A / P.
Units
This calculator supports both the metric system (lengths in meters, areas in m²) and the American / imperial system (lengths in feet, areas in ft²). Whatever unit you choose for your inputs, the results are shown in both systems so you can compare instantly.
Hydraulic radius vs. hydraulic diameter
The hydraulic diameter is a closely related quantity used in many flow correlations. It equals four times the hydraulic radius:
DH = 4R
The hydraulic radius is widely used in open-channel flow formulas such as Manning's equation and the Chézy equation, while the hydraulic diameter appears in Reynolds-number and friction-factor calculations for pipe flow.