Manning normal depth · Critical depth · Froude-number flow regime in a trapezoidal channel
This simulator computes normal depth, critical depth, and Froude number for a trapezoidal open channel using Manning's equation — the same hydraulic relationships embedded in HEC-RAS and other professional channel analysis software. Civil and hydraulic engineers use it to classify flow regime and check channel stability during preliminary design.
Manning's equation in US customary units is Q = (1.49/n) · A · R^(2/3) · S^(1/2), where A is the cross-sectional flow area (ft²), R = A/P is the hydraulic radius (ft), and S is the longitudinal slope (ft/ft). For a given discharge Q, normal depth yn is the depth at which this equation is exactly satisfied; it is found here by bisection over 60 iterations.
Critical depth yc is the depth at which specific energy is minimized and Froude number Fr = 1. It satisfies Q²/g = A³/T, where T is the top water surface width. When yn > yc the channel slope is mild and flow is subcritical (Fr < 1); when yn < yc the slope is steep and flow is supercritical (Fr > 1). This regime classification drives freeboard requirements, energy dissipator design, and hydraulic jump location.
Channel hydraulic design in the United States follows ASCE 7 for design storm frequencies and HEC-RAS (USACE Hydrologic Engineering Center) for one- and two-dimensional water surface profile computations. FEMA requires HEC-RAS or equivalent analyses for NFIP flood insurance studies. Many state DOTs reference AASHTO drainage design standards that incorporate Manning's equation for roadside channels. The Federal Highway Administration (FHWA) Hydraulic Design Series No. 4 (HDS-4) covers culvert hydraulics using the same governing equations.
Minimum channel velocity to prevent sediment deposition is typically 2.0 ft/s for sandy channels and up to 3.0 ft/s for silt. Maximum non-erosive velocity depends on lining material: bare earth 3–5 ft/s, riprap 10–15 ft/s, concrete 20+ ft/s. Freeboard above normal depth should be at least 1 ft for small channels and up to 2–3 ft for large agricultural or flood-control channels.
For trapezoidal sections the side slope z (H:V) is governed by material: compacted earth 2:1 to 3:1, rock 0.5:1, concrete-lined 1:1 to 1.5:1. Manning's n values commonly used are 0.013 for smooth concrete, 0.025 for clean earth, 0.030 for gravelly earth, and 0.035 for riprap.
Enter discharge Q (cfs), bottom width b (ft), side slope z (z:1 H:V), Manning's n, and longitudinal slope S (ft/ft) using the sliders. The calculator instantly returns normal depth yn, critical depth yc, velocity, Froude number, flow area, top width, and hydraulic depth. The colored status banner identifies the flow regime. The cross-section SVG shows normal depth (teal line) and critical depth (orange dashed) at scale, letting you visualize freeboard and relative depths at a glance.
Use n = 0.025–0.030 for a well-maintained grass channel. Unmowed or weedy grass channels can reach n = 0.035–0.050. FHWA HDS-4 and USWRC provide tables by vegetation type and stand density.
A hydraulic jump forms when supercritical flow (Fr > 1) transitions to subcritical flow (Fr < 1), such as at the toe of a spillway or downstream of a culvert outlet. The jump dissipates kinetic energy and must be confined by a stilling basin to prevent scour.
Fr = V / sqrt(g · A/T) measures the ratio of inertial to gravitational forces. Fr < 1 is subcritical (stable, tranquil flow), Fr > 1 is supercritical (rapid, shoot flow), and Fr = 1 is critical (minimum specific energy). Most drainage channels are designed to operate subcritically to maintain predictable, controllable conditions.
Increasing z (flatter sides) increases the flow area and hydraulic radius for the same depth, raising channel capacity. However, flatter slopes require more right-of-way. Steeper slopes (smaller z) are used in rock cuts or lined channels where stability is not an issue.
No — this tool is limited to simple trapezoidal sections with uniform roughness. For compound sections (main channel plus overbank floodplain), use HEC-RAS or HEC-2 which split the section into sub-elements with separate Manning's n values and sum the conveyances.