Hydraulic Radius
Calculate hydraulic radius for rectangular channels, trapezoidal channels, triangular channels, and circular pipes with interactive charts and breakdowns for engineering applications.
About This Calculator
The Hydraulic Radius Calculator computes the hydraulic radius (R), cross-sectional area (A), and wetted perimeter (P) for five common channel shapes used in open channel flow and pipe flow analysis. Engineers, hydrologists, and students use the hydraulic radius as a fundamental parameter in Manning's equation, the Chezy formula, and the Darcy-Weisbach equation to determine flow velocity, discharge capacity, and friction losses.
The hydraulic radius is defined as R = A / P, where A is the cross-sectional area of flow and P is the wetted perimeter (the length of channel boundary in contact with the fluid). This calculator supports rectangular channels (R = by / (b + 2y)), full circular pipes (R = r/2), partially filled pipes with central angle method, trapezoidal channels with side slopes, and triangular channels.
Key Applications
Open Channel Design: Civil and environmental engineers use hydraulic radius to design drainage channels, irrigation canals, and stormwater systems. The Manning equation V = (1/n)R^(2/3)S^(1/2) relates hydraulic radius to flow velocity, where n is Manning's roughness coefficient and S is the channel slope.
Pipe Flow Analysis: For sanitary and storm sewer design, the hydraulic radius of partially full pipes determines flow capacity at different fill depths, critical for avoiding surcharge conditions.
Hydrology and Water Resources: Hydrologists apply hydraulic radius in river and stream flow analysis, flood routing, and culvert design to predict water surface profiles and conveyance capacity.
How to Use
Select a channel shape from the dropdown menu — Rectangular, Circular Pipe (Full), Circular Pipe (Partially Filled), Trapezoidal, or Triangular. Enter the required dimensions in meters for width, depth, radius, and side slope as applicable. Click Calculate to instantly view the hydraulic radius, cross-sectional area, and wetted perimeter. The breakdown table and charts help visualize how each parameter contributes to the result.
Frequently Asked Questions
What is the hydraulic radius and how is it calculated?
The hydraulic radius (R) is the ratio of the cross-sectional area of flow (A) to the wetted perimeter (P), expressed as R = A / P. It is a key parameter in open channel flow analysis used in Manning's equation and the Chezy formula to determine flow velocity and discharge.
How do you calculate the hydraulic radius of a rectangular channel?
For a rectangular channel, the hydraulic radius is R = (b × y) / (b + 2y), where b is the channel width and y is the flow depth. The cross-sectional area is A = b × y and the wetted perimeter is P = b + 2y.
What is the hydraulic radius of a full circular pipe?
For a circular pipe flowing full, the hydraulic radius is R = r / 2 = D / 4, where r is the pipe radius and D is the pipe diameter. This follows from the area A = πr² and wetted perimeter P = 2πr, giving R = πr² / 2πr = r / 2.
How do you find the hydraulic radius of a trapezoidal channel?
For a trapezoidal channel, the area is A = by + y²z where b is the bottom width, y is the depth, and z is the side slope (horizontal:vertical). The wetted perimeter is P = b + 2y√(1 + z²). The hydraulic radius is R = A / P.
Why is hydraulic radius important in fluid mechanics?
Hydraulic radius is essential for calculating flow in open channels and pipes using Manning's equation (V = (1/n)R^(2/3)S^(1/2)) and the Darcy-Weisbach equation. It directly affects flow velocity, discharge capacity, and energy losses in hydraulic engineering design.
Can hydraulic radius be used for partially filled pipes?
Yes, for a partially filled pipe the central angle is θ = 2 × arccos((r - h) / r), where h is the fill depth. The area is A = r²(θ - sin(θ)) / 2 and wetted perimeter is P = rθ. The hydraulic radius is then R = A / P = r(θ - sin(θ)) / (2θ).
What units are used for hydraulic radius?
Hydraulic radius is expressed in units of length, typically meters (m) in SI units or feet (ft) in US customary units. Since it is the ratio of area to perimeter, it always has a dimension of length, similar to the radius of a pipe.