Hydraulic Radius Calculator

At its core, the hydraulic radius (R_h) represents the ratio of a flow channel's cross-sectional area to its wetted perimeter. The fundamental mathematical formula is expressed as R_h = A / P, where A is the area of the flow cross-section and P is the wetted perimeter in direct contact with the fluid. Depending on the geometry selected—whether a full circular pipe, a rectangular duct, a triangular channel, or a trapezoidal ditch—the calculator applies specific geometric formulas to resolve both area and perimeter before computing the final ratio. For instance, a full circular pipe computes area via pi times the radius squared and perimeter via two times pi times the radius, simplifying to R_h = r / 2.

Consider a rectangular open channel or drainage duct designed with a rectangle width of 4 meters and a rectangle height of 2 meters, operating under fully wetted conditions. First, compute the cross-sectional area by multiplying height by width: A = 2 meters * 4 meters = 8 square meters. Next, calculate the wetted perimeter using the formula P = 2 * height + width, which gives P = (2 * 2) + 4 = 8 meters. Finally, divide the area by the wetted perimeter to find the hydraulic radius: R_h = 8 / 8 = 1.0 meter. This step-by-step evaluation ensures your channel dimensions meet optimal hydraulic efficiency standards.

When inputting dimensions into the calculator, always maintain consistent units—such as meters or feet—to avoid skewed results. For partially filled circular pipes, ensure your fill depth measurement is precise, as minor input variations near the pipe invert can noticeably impact the central angle (phi) and resulting wetted perimeter. Always cross-reference your calculated hydraulic radius with Manning's equation parameters when estimating open-channel flow velocities.