Open Channel Flow Calculator — Manning Equation Velocity & Discharge

What Is Open Channel Flow?

Transporting water from one place to another can be done in two ways — with the help of pressure or with the help of gravity. If we want to bring water up a building, we could do this with a powerful water pump that pushes the water up the pipes by applying a large amount of pressure, usually by centrifugal force. In this case water fills the pipes as it travels upward. Because the pipe cross-section is fully enclosed and not directly exposed to atmospheric pressure, this is called a closed channel.

On the other hand, we call it an open channel flow when gravity does the work of transporting the water — like in rivers or canals, where the water flows from a higher to a lower elevation and the surface of the water is "open", or exposed to atmospheric pressure. There are also cases where water flows due to gravity but the pipe is completely filled (see a pipe flow calculator for those).

This calculator deals with the simplest form of open channel flow: steady, uniform flow. In a steady uniform flow the flow rate does not change along a channel that has a uniform cross-sectional shape, slope, and roughness. We can then determine the velocity and discharge as long as we know the other characteristics of the channel.

Open Channel Flow Equations — What Affects Flow Rate?

In the late 19th century an accountant-turned-engineer named Robert Manning developed an equation describing how a channel's characteristics affect its water flow rate. Manning concluded that the flow rate depends on three things:

• The material of the channel surface (roughness). The rougher the surface, the slower the water flows. A smooth-finish concrete lining allows faster flow than a natural channel lined with river rocks and underwater vegetation.
• The channel's cross-sectional shape. The larger the cross-sectional area, the more water can flow. But friction between the water and the channel surface slows the flow. We quantify this contact surface with the wetted perimeter — the cross-sectional length of channel that the water touches. The larger the wetted perimeter, the more friction and the slower the flow.
• The channel's slope. The steeper the slope, the faster the water flows down the channel.

Manning Equation for Open Channel Flow

With those concepts in mind, Manning's formula for the average flow velocity is:

where:

• V — flow velocity (m/s or ft/s);
• n — Manning's roughness coefficient (dimensionless);
• R — the channel's hydraulic radius, found by dividing the cross-sectional area A by the wetted perimeter P (R = A / P); and
• s — the slope of the channel's bottom surface (m/m or ft/ft);
• k — a unit conversion factor: k = 1.0 for SI (metric) units and k = 1.486 for US customary (imperial) units.

Examining the equation, the area and slope are directly proportional to the flow rate — increasing them increases flow. The roughness coefficient and the wetted perimeter are inversely proportional — increasing them decreases flow.

Once we know the velocity, the volumetric flow rate (discharge) is simply the product of velocity and cross-sectional area:

Most Efficient Cross-Section of Open Channels

For a given cross-sectional area, slope, and roughness, a channel carries the most water when its wetted perimeter is the smallest possible. A smaller wetted perimeter means less friction, a larger hydraulic radius, and therefore a higher velocity and discharge. The geometrically most efficient open channel section is a semicircle. Among practical shapes:

• Rectangular channels are most efficient when the width is twice the flow depth (b = 2y).
• Trapezoidal channels are most efficient when they form half of a regular hexagon.
• Triangular channels are most efficient with a 90° vertex angle.

Using Our Open Channel Flow Calculator

1. Select your unit system — Metric (m, m²) or American (ft, ft²).
2. Pick a channel material from the list to auto-fill Manning's roughness coefficient n, or choose "Custom" and type your own value.
3. Enter the channel slope s as a decimal (for example, a 0.5% slope = 0.005).
4. Enter the cross-sectional area A of the flowing water.
5. Enter the wetted perimeter P — the length of channel boundary in contact with the water.
6. Click Calculate. You instantly get the hydraulic radius R, the flow velocity V, and the volumetric flow rate Q, each shown in several convenient units.

Manning's Roughness Coefficient (n) Reference

Worked Example

A finished-concrete rectangular channel (n = 0.012) is 4 m wide and carries water 0.5 m deep on a slope of 0.005.

1. Cross-sectional area: A = 4 × 0.5 = 2 m²
2. Wetted perimeter: P = 4 + 2 × 0.5 = 5 m (bottom + two sides)
3. Hydraulic radius: R = A / P = 2 / 5 = 0.4 m
4. Velocity: V = (1.0 / 0.012) × 0.4^2/3 × 0.005^1/2 ≈ 3.19 m/s
5. Discharge: Q = V × A ≈ 6.39 m³/s

Frequently Asked Questions

What is open channel flow?

Open channel flow is the gravity-driven flow of a liquid with a free surface exposed to the atmosphere, such as water in a river, canal, or partially filled pipe.

What is the hydraulic radius?

The hydraulic radius R is the cross-sectional flow area divided by the wetted perimeter (R = A / P). It is a measure of how efficiently the channel carries water — a larger hydraulic radius means less frictional resistance per unit of flow.

Why does the Manning coefficient k differ between unit systems?

Manning's equation is empirical. In SI (metric) units the conversion factor k equals 1.0, while in US customary units it equals 1.486 so the formula returns velocity in ft/s. This calculator applies the correct factor automatically based on the unit system you select.

What slope value should I use?

Use the channel bed slope as a decimal (rise over run). For example, a fall of 1 m over 200 m of channel length is a slope of 1/200 = 0.005.