10.3 Manning, Open Channel, and Critical Flow

Uniform Flow, Control, and Flow Regime

Open-channel hydraulics is different from pressure-pipe hydraulics because the water surface is exposed to the atmosphere and can adjust its depth. The current NCEES WRE specification includes open-channel flow, hydraulic grade lines, energy dissipation, stormwater drainage, and subcritical and supercritical flow. The exam often asks which hydraulic model applies before it asks for a number.

Manning's Equation

For US customary units, Manning's equation is commonly written as Q = (1.49/n) A R^(2/3) S^(1/2). In SI units, the coefficient is 1.0. Here, A is wetted flow area, R is hydraulic radius A/P, P is wetted perimeter, S is the energy slope for uniform flow, and n is Manning roughness.

A common PE mistake is using flow depth as hydraulic radius. For a rectangular channel, A = by and P = b + 2y, so R = by/(b + 2y). Only in a very wide channel does R approach depth.

Normal Depth Workflow

Normal depth is the depth that makes Manning capacity equal the given flow in a prismatic channel under uniform-flow assumptions. To solve a normal-depth problem:

1. Identify the channel shape and write A, wetted perimeter, and hydraulic radius as functions of depth.
2. Use the given n and slope S.
3. Substitute into Manning's equation.
4. Iterate or test answer choices until computed Q matches required Q.
5. Check whether the resulting depth is physically possible within the channel.

Normal depth is not automatically the water depth at a culvert entrance, spillway, bridge opening, or abrupt slope change. Those locations are controls. A control section fixes a depth-flow relationship and causes nonuniform flow upstream or downstream.

Critical Flow and Specific Energy

Specific energy is the energy per unit weight measured relative to the channel bottom: E = y + V^2/(2g). For a given flow and channel shape, critical depth occurs at the minimum specific energy. The Froude number identifies the regime. If Fr < 1, flow is subcritical: deep, slower, and influenced by downstream conditions. If Fr > 1, flow is supercritical: shallow, faster, and controlled from upstream. At Fr = 1, flow is critical.

For a rectangular channel, critical depth has a convenient form: y_c = (q^2/g)^(1/3), where q = Q/b. This equation is high value because it appears in weir, spillway, culvert, and channel-transition problems.

Hydraulic Jumps and Energy Dissipation

A hydraulic jump occurs when supercritical flow transitions to subcritical flow. Depth increases sharply, velocity decreases, and energy is dissipated as turbulence. Momentum, not simple Bernoulli energy conservation, is used across the jump because energy is lost. The WRE exam can ask for a conceptual interpretation, such as why a stilling basin, drop structure, plunge pool, or riprap apron is needed downstream of a culvert or spillway.

Exam-Ready Checks

• Use Manning only when uniform-flow assumptions are reasonable or explicitly requested.
• Compare normal depth and critical depth to classify slope behavior and likely controls.
• Remember that subcritical water-surface profiles respond to downstream controls.
• Expect supercritical flow near steep outlets and energy-dissipation structures.
• Check units: cfs with ft, or m^3/s with m, not a mixture.

Open-channel questions become manageable when you label the depth being requested. Normal depth, critical depth, actual depth at a control, and conjugate depth after a jump are different quantities.