Open Channel Flow Calculator - Q, Velocity, and Froude Number

An open channel flow calculator solves Manning's equation for uniform flow in an open channel such as a canal, flume, spillway, drainage ditch, or natural stream, reporting discharge Q from the channel cross section, the Manning roughness coefficient n, and the bed slope S.

• • Irrigation canal capacity checks: Estimate the discharge a trapezoidal earth canal can carry at a given depth before designing an irrigation turnout.
• • Stormwater and drainage design: Sanity-check the flow capacity of a trapezoidal ditch or grassed waterway during a design storm.
• • Lab and classroom hydraulics: Convert a measured depth in a flume or teaching channel into discharge for a fluid-mechanics lab or homework set.
• • Stream gauging by slope-area method: Get a defensible discharge estimate from a surveyed cross section, slope, and a roughness pick when no gauge is available.

Open channel flow is gravity-driven flow with a free surface. The most common steady-state form is uniform flow, where depth, area, and velocity stay roughly constant along a reach.

When the open channel flow you are checking ends at a control structure, Broad crested weir calculator turns the upstream head on a flat-crested weir into the same kind of discharge number that this calculator returns.

The calculator uses Manning's equation Q = (1/n) * A * R^(2/3) * S^(1/2), where A is the cross-section area, R is the hydraulic radius, and S is the bed slope. The cross section is trapezoidal: bottom width b, side slope z, and flow depth y.

• Q: Volumetric discharge in m^3/s (SI) or ft^3/s (US).
• n: Manning roughness coefficient. Smooth concrete is about 0.012, earth canals 0.022 to 0.025, natural streams 0.030 to 0.040.
• A: Cross-section flow area. For a trapezoid: A = (b + z*y) * y.
• R: Hydraulic radius R = A / P. For a trapezoid, P = b + 2 y sqrt(1 + z^2).
• S: Bed slope as a decimal. For uniform flow this equals the energy slope.
• k: Unit constant. k = 1 in SI, k = 1.486 in U.S. customary.

When the unit toggle is set to US customary, the calculator uses k = 1.4859 and reports lengths in feet, Q in cfs, and velocity in ft/s.

The Froude number is computed as Fr = V / sqrt(g * A / T), with A / T acting as the hydraulic depth D. Values below 1 indicate subcritical flow; above 1 is supercritical.

According to Wikipedia - Open-channel flow, Manning's equation Q = (1/n) A R^(2/3) S^(1/2) is the most common empirical method in the United States for uniform open channel flow, where A is the cross-section flow area, R is the hydraulic radius, S is the channel bed slope (equal to the energy slope for uniform flow), and n is the Manning roughness coefficient.

Confirming that the channel stays in the fully rough turbulent regime that Manning's equation assumes is much easier with Reynolds number calculator in hand so you can see the actual flow regime behind the picked n value.

Four ideas come up in every practical Manning's equation problem. Understanding them keeps the formula from being used outside the conditions where it is calibrated.

Where the open channel flow is not uniform and the water surface has visible drawdown or rise, Bernoulli equation calculator gives you the same two-section energy balance the energy-slope assumption in this calculator relies on.

Use the calculator in five steps. The defaults match a typical small earth canal, so you can usually just enter the cross section, depth, and slope.

1. 1 Pick the unit system: Use SI for meters and m^3/s, or US customary for feet and cfs.
2. 2 Choose how to enter roughness: Use Manning n for direct entry. Use k_s to derive n from the Strickler relation.
3. 3 Enter the cross-section geometry: Type bottom width b, side slope z, and flow depth y.
4. 4 Set the bed slope S: Enter the slope as a decimal. For uniform flow this equals the energy slope.
5. 5 Read Q, V, R, and Fr: Primary output is Q in m^3/s, with supporting outputs in L/s, cfs, and gpm.

For a 3 m wide earth trapezoidal canal with z = 2, y = 0.8 m, S = 0.0005, and n = 0.025, the calculator returns Q ≈ 2.23 m^3/s, V ≈ 0.61 m/s, R ≈ 0.56 m, Fr ≈ 0.25 (subcritical).

If you need to cross-check Manning n against a Darcy-Weisbach friction factor for a closed conduit flowing partially full, friction factor calculator lets you convert between the two without leaving the page.

The calculator is built for the kind of decisions that come up in a hydraulics course, an irrigation audit, or a stormwater review.

• • Full Manning equation with cross-section geometry: Enter bottom width, side slope, depth, slope, and roughness, and the calculator handles A, P, R, Q, V, and Fr.
• • Froude number regime flag: A Froude number and a 0/1/2 regime code tell you whether the flow is subcritical, critical, or supercritical.
• • SI and US customary in one form: A unit toggle switches between k = 1 (SI) and k = 1.4859 (US customary) and converts inputs and outputs together.
• • Roughness selector and direct n entry: Preset Manning n values for concrete, earth, and natural streams speed up common picks.
• • Discharge in four units at once: Q is shown in m^3/s, L/s, cfs, and gpm, and V in m/s and ft/s.

If your downstream spec is in liters per second, gallons per minute, or acre-feet per day instead of m^3/s, flow rate converter takes the Q this calculator outputs and turns it into the unit your report needs.

Manning's equation is short, but several conditions move the real discharge away from the calculator value.

• • The calculator uses a trapezoidal cross section. Circular pipes, parabolic channels, compound sections, and natural cross sections with overbank flow need different formulas.
• • Manning's equation assumes fully rough turbulent flow. At low Reynolds numbers (small flumes, viscous fluids) it over-predicts and a laminar correction is required.
• • The Froude number flag is for uniform flow only. Rapidly varied flow near a sluice gate or free overfall needs an energy-momentum analysis.

According to Wikipedia - Manning formula, Manning n is a dimensionless empirical roughness coefficient that lumps bed material, surface irregularities, vegetation, channel alignment, and obstructions into a single resistance parameter, and the hydraulic radius R is defined as the flow cross-section area divided by the wetted perimeter.

According to ISO 18481:2017 - Hydrometry, end depth method at a free overfall, critical depth in an open channel is given by yc = (q^2 / g)^(1/3) at a free overfall, and the Froude number Fr = V / sqrt(g D) with D = A / T separates subcritical flow (Fr < 1) from supercritical flow (Fr > 1).

The mean velocity V = Q / A that this calculator reports pairs naturally with velocity calculator when you also need a separate approach-velocity or downstream channel-velocity number in the same units.