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Manning's Open Channel Flow Calculator

Calculate the exact volumetric flow rate of a rectangular open channel, trench, or aqueduct using Manning's Equation. Essential for civil stormwater and agricultural irrigation design.

Manning's Open Channel Flow Calculator

Manning's Equation is the fundamental formula for calculating flow in any open channel — roadside ditches, irrigation canals, stormwater trenches, and rivers. The key insight is that channel shape drives efficiency: a narrow, deep channel has a smaller wetted perimeter per unit area, meaning less friction and dramatically higher flow rates than a wide, shallow channel of the same cross-section.

Manning's Roughness (n) Presets

Slope Presets (ft/ft or m/m)

Bottom Width (b) — ft

Rectangular base

Water Depth (y) — ft

y < channel depth

Channel Slope (S) — ft/ft

Rise ÷ horizontal run

Manning's Roughness (n)

Concrete ≈ 0.013

A = b × y = 10 × 3 = 30.0000 ft²

P = b + 2y = 10 + 2×3 = 16.0000 ft

R_h = A/P = 30.0000/16.0000 = 1.87500 ft

Q = (1.49/0.013) × 30.0000 × R_h^(2/3) × S^(1/2)

Q = 114.6154 × 30.0000 × 1.52055 × 0.044721 = 233.8191 CFS

Hydraulic Radius (R_h)

1.8750

ft = A/P

Cross-Section Area (A)

30.00

ft²

Volumetric Flow Rate (Q)

233.82

CFS

High Flow — Major stormwater conveyance

Flow Rate vs. Water Depth (b=10.0 ft, n=0.013, S=0.002)

0.5 ft

15.15 CFS

1 ft

45.39 CFS

2 ft

130.03 CFS

3 ft

233.82 CFS

4 ft

349.15 CFS

6 ft

600.34 CFS

8 ft

867.48 CFS

Practical Example

A civil engineer designs a concrete drainage channel for a suburban development. The channel is 10 ft wide, carries water at 3 ft depth, slopes at 0.2% (S = 0.002), and is lined with smooth concrete (n = 0.013).

A = 10 × 3 = 30 ft²
P = 10 + (2 × 3) = 16 ft
R_h = 30 / 16 = 1.875 ft
Q = (1.49/0.013) × 30 × (1.875)^(2/3) × (0.002)^(1/2)
Q = 114.6 × 30 × 1.538 × 0.04472 = ~237 CFS

This single channel conveys the equivalent of 107,000 gallons per minute — enough to drain a 50-acre watershed during a 100-year storm event, a typical design requirement for most municipal stormwater systems.

💡 Field Notes

Hydraulic Radius vs. Depth: R_h is NOT the same as water depth for a rectangular channel. A wide, shallow channel (b=20, y=1) has R_h = 20/22 = 0.91 ft even though water is 1 ft deep. A narrow, deep channel (b=4, y=5) flowing the same area (20 ft²) has R_h = 20/14 = 1.43 ft — 57% larger — meaning dramatically higher velocity and flow despite identical cross-sectional area. This is why deep, narrow channels are hydraulically superior.
Manning's n sensitivity: The roughness coefficient n is in the denominator — it has a massive effect. Doubling n (from concrete 0.013 to a weedy earth channel 0.025) halves the flow rate entirely. Concrete-lining a dirt channel is not cosmetic; it approximately doubles conveyance capacity. Even algae or biofilm growth on concrete channels can meaningfully raise n from 0.013 to 0.016+.
Normal depth design: Engineers use Manning's equation in reverse to find the normal depth (y) required to pass a design storm flow Q. This requires iterative solving (trial and error) or Newton-Raphson convergence — calculators like this one let you bracket y quickly by varying the depth input until Q equals your design storm value.

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What is Fluid Mechanics and Open Channel Flow?

Manning's Equation is the foundational formula for all open channel hydraulics — from roadside gutters to major aqueducts. Unlike pressure-driven pipe flow, open channels are driven purely by gravity acting on water with a free surface. The key variable that separates efficient channels from slow-flowing ditches is not the cross-sectional area, but the Hydraulic Radius.

Mathematical Foundation

Cross-Sectional Area (A)

A = b \times y

b

= Bottom width of the rectangular channel in feet or meters.

y

= Depth of water flowing in the channel in feet or meters.

Wetted Perimeter (P)

P = b + 2y

P

= The total Length of the channel boundary that is in contact with flowing water — the source of all frictional resistance.

Hydraulic Radius (R_h)

R_h = \frac{A}{P}

R_h

= The ratio of flow area to wetted perimeter. A larger Hydraulic Radius means less friction per unit of area — the core measure of channel hydraulic efficiency.

Manning's Equation — Volumetric Flow (Q)

Q = \frac{k}{n} \times A \times R_h^{2/3} \times S^{1/2}

k

= Unit coefficient: 1.49 for Imperial (CFS), 1.00 for Metric (m³/s).

n

= Manning's Roughness Coefficient — dimensionless. Smooth concrete ≈ 0.013; excavated rock ≈ 0.035; natural rivers can reach 0.060+.

S

= Longitudinal slope of the channel, expressed as rise/horizontal run (dimensionless). A 0.2% grade = S = 0.002.

Laws & Principles

The Hydraulic Radius (R_h) is the single most important shape parameter in open channel design. A wide, shallow river flowing at the same total area as a narrow, deep canal has a much larger wetted perimeter — meaning more friction against the bottom per unit of flow area. The deep channel has a larger R_h and flows significantly faster, despite identical A and S values.
Manning's n is extremely sensitive: it appears in the denominator, so doubling n (from 0.013 concrete to 0.025 gravelly earth) halves the flow rate entirely. Concrete lining a dirt channel is not merely cosmetic — it approximately doubles the conveyance capacity of the same geometric channel.
The 2/3 power on R_h arises from the physics of turbulent flow. Velocity scales as R_h^(2/3) — not linearly. This means deepening a channel gives diminishing returns: doubling the depth does not double the flow rate, because wetted perimeter also grows as depth increases.
Normal Depth Design: In practice, engineers use Manning's equation in reverse — they know the design storm flow Q, choose n and S, then iterate on y until Q is matched. This is called finding the 'normal depth' for a given discharge.

Step-by-Step Example Walkthrough

" A civil engineer designs a concrete-lined stormwater conveyance channel: 10 ft wide, 3 ft deep at normal flow, slope 0.002, Manning's n = 0.013 (smooth concrete). What is the design flow capacity? "

1. Compute cross-section area: A = 10 x 3 = 30 sq ft.
2. Compute wetted perimeter: P = 10 + (2 x 3) = 16 ft.
3. Compute hydraulic radius: R_h = A/P = 30/16 = 1.875 ft.
4. Apply Manning's: Q = (1.49/0.013) x 30 x (1.875)^(2/3) x (0.002)^(1/2).
5. Compute parts: (1.49/0.013) = 114.6. (1.875)^(2/3) = 1.538. (0.002)^(1/2) = 0.04472.
6. Q = 114.6 x 30 x 1.538 x 0.04472 = 237 CFS.

Final Result: 237 Cubic Feet per Second — equivalent to over 106,000 gallons per minute. This represents the total capacity of the channel at the design water depth of 3 feet. A 25-year design storm for a 50-acre watershed typically requires 150-350 CFS, confirming this channel is adequately sized.

Quick Answer: How do I calculate open channel flow rate?

Use Manning's Equation: Q = (k/n) × A × R_h^2/3 × S^1/2. Enter the channel width, water depth, slope, and roughness coefficient. A 10 ft wide concrete channel at 3 ft depth with 0.2% slope carries about 237 CFS (106,000+ gallons per minute). The roughness coefficient n is the most sensitive variable — concrete (0.013) vs bare earth (0.025) nearly doubles the flow capacity of the same channel.

Manning's Equation

Q = (k / n) × A × R_h^2/3 × S^1/2

Where k = 1.49 for Imperial (CFS) or 1.00 for Metric (m³/s), n is Manning's roughness coefficient, A is the cross-sectional flow area, R_h is the hydraulic radius (A divided by wetted perimeter), and S is the channel bed slope. The 2/3 exponent on R_h reflects how turbulent friction scales with channel geometry.

Manning's Roughness Coefficient (n) Reference

Channel Material	n Value	Flow Rate (10 ft × 3 ft, S=0.002)	Typical Use
Glass / PVC pipe	0.010	308 CFS	Lab flumes, smooth culverts
Smooth concrete	0.013	237 CFS	Lined drainage channels
Unfinished concrete	0.017	181 CFS	Cast-in-place channels
Gravel bottom	0.025	123 CFS	Excavated drainage ditches
Natural stream (clean)	0.035	88 CFS	Maintained waterways
Weedy / overgrown	0.050	62 CFS	Unmaintained channels

All values use k=1.49 (Imperial). A five-fold increase in roughness (0.010 to 0.050) reduces flow capacity by 80% in the same channel geometry.

Design Scenarios

Stormwater Detention Outlet

A 6 ft wide concrete channel with 0.5% slope carries stormwater from a detention pond to a creek. At 2 ft normal depth (n = 0.013): A = 12 sq ft, P = 10 ft, R_h = 1.2 ft. Q = 114.6 × 12 × 1.131 × 0.0707 = 110 CFS. This handles a 10-year storm for a 30-acre residential subdivision.

Agricultural Irrigation Canal

An unlined earthen canal (n = 0.025), 8 ft wide, carries irrigation water at 1.5 ft depth with 0.1% slope. A = 12 sq ft, P = 11 ft, R_h = 1.09 ft. Q = 59.6 × 12 × 1.060 × 0.0316 = 24 CFS. Lining this canal with concrete (n = 0.013) would increase capacity to 46 CFS — nearly double — without changing the channel geometry.

Pro Tips

Do This

✓Design for the 25-year or 100-year storm event. Local regulations specify the design storm return period. Under-sizing a channel for a 10-year storm means it overtops during a 25-year event — causing erosion, flooding, and potential liability.
✓Add freeboard to the channel depth. Design the channel walls 20-30% higher than the calculated normal depth. Freeboard accounts for wave action, debris blockage, and flow surges that would otherwise overtop a channel designed to the exact capacity.
✓Check velocity limits, not just flow rate. High velocities erode unlined channels. Maximum safe velocity: 2 ft/s for sandy soil, 4 ft/s for firm clay, 6 ft/s for grass-lined channels, 20+ ft/s for concrete. Calculate velocity as V = Q / A.

Avoid This

✗Don't confuse slope with grade percentage. A "2% grade" means S = 0.02, not 2.0. Entering 2.0 instead of 0.02 gives a result 10x too high. Always convert: divide the percentage by 100 to get the dimensionless slope ratio.
✗Don't use Manning's for pressurized flow. Manning's Equation applies only to gravity-driven open channel flow with a free water surface. For full-pipe pressurized flow, use the Darcy-Weisbach or Hazen-Williams equation instead.
✗Don't assume n stays constant over time. Vegetation growth, sediment deposits, and algae can increase n by 50-100% in unlined channels within a few years. Design with the aged roughness value, not the as-built value.

Frequently Asked Questions

What is Manning's roughness coefficient and how do I choose it?

Manning's n is a dimensionless coefficient that represents the frictional resistance of the channel surface to water flow. Smoother surfaces have lower n values and carry more water. Typical values: smooth concrete = 0.013, corrugated metal pipe = 0.024, clean natural stream = 0.030-0.040, heavily vegetated floodplain = 0.050-0.150. Published tables (FHWA HEC-15, Chow's Open-Channel Hydraulics) provide n values for every common channel material. When in doubt, use the higher end of the published range for conservative design.

What is the hydraulic radius and why does it matter?

The hydraulic radius R_h = A / P (flow area divided by wetted perimeter). It measures how efficiently a channel shape delivers water. A semicircular channel has the largest possible R_h for a given area — it's the most hydraulically efficient shape. A wide, shallow channel has a small R_h because so much of the water is in contact with the bottom, creating friction. Increasing R_h by 50% (deepening but narrowing a channel) increases flow velocity by about 31% due to the 2/3 power relationship.

What is the difference between CFS and GPM?

CFS (cubic feet per second) is the standard unit for open channel and river flow measurement. GPM (gallons per minute) is used for pipe flow and pumping. To convert: 1 CFS = 448.8 GPM. Civil engineers use CFS for stormwater design because the numbers are more manageable at large scale — a typical urban drainage channel might carry 200 CFS, which is 89,760 GPM. The metric equivalent is m³/s (cubic meters per second).

Can Manning's Equation be used for partially full pipes?

Yes — Manning's Equation works for any gravity-driven flow with a free surface, including partially full circular pipes. The key difference is that the cross-sectional area and wetted perimeter must be calculated using the circular segment geometry (based on the central angle of the water surface), not the simple rectangular b × y formula. Most stormwater sewer design uses Manning's for pipe sizing. A circular pipe flowing 80% full actually carries more flow than a 100% full pipe because the hydraulic radius is larger at partial depth.

Manning's Open Channel Flow Calculator

Manning's Open Channel Flow Calculator