Critical Depth in Rectangular Channel
Calculate the critical depth of a rectangular channel, y_c = (q² ÷ g)^(1/3), from the unit discharge q (flow per unit width, m³/s/m) and gravity g. Critical depth is the depth at which specific energy is minimum, marking the boundary between the two open-flow regimes: above it the flow is subcritical (slow, deep, Fr < 1, downstream-controlled); below, supercritical (fast, shallow, Fr > 1, upstream-controlled); exactly at it, Fr = 1. Critical depth is central to channel and structure hydraulics: it defines the control section at spillways, weirs and flumes (Parshall), where flow passes through the critical regime stably and the stage-discharge relation is unique — allowing flow measurement from head. It also determines whether a hydraulic jump can form and guides water-surface profiles. Enter the channel's unit discharge.
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Critical depth in a rectangular channel
The critical depth of a rectangular channel is y_c = (q² ÷ g)^(1/3), a function of the specific discharge q (flow per unit width) and of gravity g alone. It is the depth at which the specific energy of the flow reaches its minimum, and it marks the boundary between the two regimes of open-channel flow: above it the flow is subcritical (slow, deep, Froude < 1, controlled from downstream — like a placid river); below it, supercritical (fast, shallow, Froude > 1, controlled from upstream — like a rapid); exactly at it, Froude = 1. Critical depth is one of the pillars of open-channel hydraulics. It defines the control section at spillways, weirs and flow-measuring devices (Parshall flumes, measuring weirs): at those points the flow passes through the critical regime in a stable way and the relationship between discharge and stage becomes single-valued — which is what allows the flow to be measured simply by reading the depth of the water surface. Critical depth also decides whether a hydraulic jump can form (a jump only occurs in the transition from supercritical to subcritical) and guides the plotting of water-surface profiles in backwater curves, free overfalls and changes of bed slope. It is the reference around which the whole of open-channel hydraulics is organised. Enter the specific discharge of the channel.
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