Froude Number (Open Channel)

The Froude number compares how fast the water is moving to how fast a disturbance can travel across its surface. A shallow-water wave moves at $\sqrt{gD}$, so $Fr$ below 1 means a ripple can travel upstream and the flow downstream can influence the flow upstream. Above 1 it cannot, and the reach is hydraulically deaf to everything happening below it. Three metres a second at a hydraulic depth of 1.5 metres gives $3/\sqrt{9.81 \times 1.5} = 0.78$, comfortably subcritical, which is where you want a channel to sit.

That control question is the practical use. In subcritical flow the control is downstream, so a weir or a culvert at the end of a reach sets the water surface all the way back up it. In supercritical flow the control is upstream, and a backwater calculation must be marched in the opposite direction. Getting that backwards is the single most common error in a water-surface profile, and it produces a plausible-looking answer with the wrong shape.

Two details matter. The depth in the formula is the hydraulic depth, area divided by top width, not the maximum depth. In a rectangular channel they coincide; in a trapezoidal or circular one they very much do not, and using the deepest point instead makes the flow look more subcritical than it is. And flow near $Fr = 1$ is genuinely unstable, so designers avoid the band from roughly 0.8 to 1.2: small changes in depth there produce large changes in energy, the water surface hunts, and a channel built to run near critical will not hold a steady profile. If a design lands in that band, change the slope or the section rather than argue with the number.