Froude Number Calculator

The Froude number ($Fr$) is a dimensionless parameter that describes the ratio of a fluid's inertial forces to its gravitational forces. The calculation is performed in two primary steps. First, compute the hydraulic mean depth ($D$) by dividing the cross-sectional area of the flow ($A$) by the channel width ($T$): $D = A / T$. Second, substitute this hydraulic depth alongside the flow velocity ($V$) and the acceleration due to gravity ($g$) into the governing Froude equation: $Fr = V / \sqrt{g \times D}$. When $Fr < 1$, the flow is subcritical (tranquil); when $Fr = 1$, it is critical; and when $Fr > 1$, the flow is supercritical (rapid).

Consider an open rectangular irrigation channel with a flow velocity ($V$) of 2.5 meters per second and an acceleration due to gravity ($g$) of 9.81 meters per second squared. The cross-sectional area of the flow ($A$) is 4.0 square meters, and the channel width ($T$) is 2.0 meters. First, calculate the hydraulic mean depth: $D = 4.0 / 2.0 = 2.0$ meters. Next, calculate the denominator by multiplying gravity by the hydraulic depth and taking the square root: $\sqrt{9.81 \times 2.0} = \sqrt{19.62} \approx 4.429$ meters per second. Finally, divide the flow velocity by this value: $Fr = 2.5 / 4.429 \approx 0.564$. Because the resulting Froude number is less than 1, the flow is classified as subcritical.

Always ensure your input units are consistent before running the calculation, preferably using the metric system (meters and seconds) to avoid scaling errors with standard gravity ($9.81 \, \text{m/s}^2$). Pay close attention when $Fr$ is close to 1.0, as transitional critical flow can cause severe hydraulic instability and standing waves known as standing hydraulic jumps. Cross-verify your channel width and cross-sectional area inputs, especially when dealing with trapezoidal or natural irregular channels where top width differs from bottom width.