Open Channel Flow Calculator

Q: How do you calculate the hydraulic radius of a channel?

Divide the wet area by the wetted perimeter: R = A / P The wetted perimeter is only the length of the bed and walls that water touches. The top water surface is not counted, because air causes almost no friction. Example: a rectangular channel 3 m wide with 1 m of water has A = 3 m² and P = 3 + 1 + 1 = 5 m. So R = 0.6 m. A bigger R means less friction per unit of water, so the channel carries more flow.

Q: What is the minimum velocity needed to keep a storm drain or sewer from clogging?

The usual rule is about 0.6 m/s (2 ft/s) for storm drains and 0.9 m/s (3 ft/s) for sanitary sewers. Below that speed, sand, grit and solids drop out and build up on the bottom. This is called the self-cleansing velocity. If your design speed is too low, steepen the slope or use a smaller pipe so the water runs deeper and faster.

Q: How do you find critical depth in a rectangular channel?

Use the flow per unit width, q = Q / b, then: y c = (q² / g) 1/3 Example: Q = 12 m³/s in a 4 m wide channel gives q = 3 m²/s. Then y c = (9 / 9.81) 1/3 = 0.97 m. For trapezoidal, triangular and round shapes there is no simple formula. You must solve A³/T = Q²/g by trial and error.

Q: Can two different depths carry the same flow rate?

Yes. In a circular pipe, the same discharge can happen at two depths, because flow rate peaks near 94 percent full and then drops slightly as the pipe fills. In specific energy problems, one energy value also matches two depths: a shallow supercritical depth and a deeper subcritical depth. These are called alternate depths. Which one is real depends on the slope and on what happens upstream and downstream.

Q: What slope should a drainage ditch or swale have?

A common range is 0.5 to 5 percent (0.005 to 0.05). Below about 0.5 percent, water sits and silt builds up. Above about 5 percent, a grass ditch usually erodes and needs riprap, check dams, or a hard lining. Roadside ditches often run 1 to 2 percent. Long irrigation canals may be as flat as 0.0005 because they must carry water far without losing much height.

Open Channel Flow Calculator

Introduction

Open channel flow is water that moves with a free top surface. Think of a canal, a ditch, a stream, or a pipe that is only part full. The air above the water pushes on it, and gravity pulls the water downhill. This Open Channel Flow Calculator works out how much water moves through the channel and how fast it goes.

The calculator uses Manning's equation, the standard formula in fluid mechanics for steady uniform flow. You pick a shape, type in the size, the bed slope, and the roughness of the lining. You get back the discharge (Q) and the mean velocity (V), plus flow area, wetted perimeter, hydraulic radius, top width, velocity head, and specific energy.

You can pick four cross-section shapes: trapezoidal, rectangular, triangular, and circular pipes or culverts. Trapezoidal channels let you set the left and right side slopes on their own, so sloped banks do not have to match.

You can also flip the problem around. Instead of solving for flow, you can solve for normal depth, critical depth, channel slope, Manning's n, bottom width, or side slope. Eleven solve modes are built in, so you can size a new channel or check one that already exists.

Every run also reports the Froude number and tells you the flow regime: subcritical, critical, or supercritical. This matters because it shows whether upstream or downstream conditions control the water surface, and whether a hydraulic jump may form.

A built-in Manning's roughness table lets you pick a material like concrete, earth, gravel, or corrugated metal. Step-by-step math shows each formula with your own numbers, in metric or imperial units. A rating curve graphs depth against flow, and a drawing of the cross-section updates as you move the sliders.

How to use our Open Channel Flow Calculator

Enter your channel shape, size, depth, bed slope, and roughness, and the calculator gives you the flow rate, velocity, flow area, hydraulic radius, Froude number, critical depth, and the flow regime, plus a step-by-step solution and a rating curve.

Global Unit System: Pick Metric (SI) or Imperial to set every unit menu at once. You can still change any single unit menu afterwards.

Channel Cross-Section Shape: Choose Trapezoidal, Rectangular, Triangular, or Circular. The calculator then shows only the inputs that shape needs.

Solve For: Pick the unknown you want, such as discharge and velocity, normal depth, critical depth, slope, Manning's n, bottom width, or a side slope. Fields marked "computed" are filled in for you.

Bottom Width (b): Type the flat width of the channel floor, then pick its unit.

Pipe Diameter (D): For circular pipes or culverts, type the inside diameter and pick its unit.

Water Depth (y): Type how deep the water is, measured up from the channel bottom. For a pipe, this must be less than the diameter.

Left Side Slope (z₁): Type the horizontal run for each 1 unit of rise on the left bank. It has no unit.

Right Side Slope (z₂): Type the same ratio for the right bank. It can be different from the left bank.

Symmetric Side Slope (z): Type one slope ratio when both banks are the same.

Channel Slope (S₀): Type the bed slope as a decimal, like 0.001 for a 1 m drop over 1000 m.

Manning's Roughness (n): Type the roughness value for your channel lining. Most values fall between 0.009 and 0.080.

Select Material: Pick a lining like concrete, earth, or corrugated metal to fill in Manning's n for you. Open the full reference table if you want to compare values.

Discharge (Q): Type the flow rate when it is a known input, and pick a unit such as m³/s, ft³/s, or gal/min.

Mean Velocity (V): Type the average flow speed when it is a known input, in m/s or ft/s.

Calculate: Press this to get your results. Use Try Example to load a sample channel, or Clear to start over.

Visual Explorer sliders: Drag the width, depth, side slope, bed slope, and roughness sliders to see how the cross-section and flow change. These sliders are just for viewing and do not change your answers above.

What Is Open Channel Flow?

Open channel flow is water that moves with a free surface open to the air. Rivers, canals, ditches, gutters, and partly full storm pipes all carry water this way. Gravity pulls the water downhill, and friction from the bed and walls slows it down. When those two forces balance, the depth stays the same along the channel. That steady state is called uniform flow.

Manning's Equation

Most open channel math starts with Manning's equation. It links flow speed to the shape of the channel, the slope of the bed, and how rough the surface is:

Q = (k / n) × A × R^2/3 × S₀^1/2

Q is discharge, the volume of water passing each second (m³/s or ft³/s)
n is Manning's roughness number; smooth concrete is low, weedy dirt is high
A is the wet cross-section area of the flow
R is the hydraulic radius, equal to A divided by the wetted perimeter P
S₀ is the bed slope, the drop in height per length of channel
k is 1.0 in metric units, 1.486 in US customary units

Mean velocity is V = Q / A.

Channel Shapes

The area A, wetted perimeter P, and top width T depend on the shape of the cross-section. Trapezoidal channels are common for earth canals because sloped banks do not cave in. Rectangular channels have vertical walls. Triangular channels work for small roadside ditches. Circular shapes cover pipes and culverts that run partly full. Side slope z means the bank moves z units sideways for every 1 unit up.

Normal Depth and Critical Depth

Normal depth (y_n) is the depth where gravity and friction balance for a given flow, slope, and roughness. Critical depth (y_c) is the depth where the flow has the least energy for that discharge. Comparing the two tells you if the channel is steep or mild.

Froude Number and Flow Regime

The Froude number compares water speed to wave speed: Fr = V / √(g × D_h), where D_h = A / T is the hydraulic depth.

Fr < 1, subcritical: deep, slow, calm flow. Things downstream control the water surface.
Fr = 1, critical: unstable, wavy flow at minimum energy.
Fr > 1, supercritical: shallow, fast flow. A hydraulic jump can form where it slows down.

Why Roughness Matters

Manning's n has a big effect on the answer. A smooth plastic pipe near 0.009 carries far more water than a weedy earth channel near 0.070 with the same size and slope. Picking the right value from a roughness table is one of the most important choices in any channel design.

Where Engineers Use It

Open channel flow math is used to size storm drains and culverts, design irrigation canals, check if a creek will flood, plan road ditches, and model sewer lines that are not full. Getting the depth, velocity, and discharge right keeps water moving without overflow or erosion.

Formulas used

Manning's equation for discharge

Q = \frac{K}{n}\,A\,R^{2/3}\,S_0^{1/2},\qquad K = 1.0\ (\mathrm{SI}),\ \ K = 1.486\ (\mathrm{US})

Hydraulic radius, mean velocity and hydraulic depth

R = \frac{A}{P},\qquad V = \frac{Q}{A},\qquad D_h = \frac{A}{T}

Trapezoidal section geometry (independent side slopes)

A = y\left(b + \frac{(z_1+z_2)\,y}{2}\right),\quad P = b + y\left(\sqrt{1+z_1^{2}} + \sqrt{1+z_2^{2}}\right),\quad T = b + (z_1+z_2)\,y

Circular (partly full) section geometry

\theta = 2\arccos\!\left(1-\frac{2y}{D}\right),\quad A = \frac{D^{2}}{8}\left(\theta - \sin\theta\right),\quad P = \frac{D\theta}{2},\quad T = D\sin\!\left(\frac{\theta}{2}\right)

Froude number and flow regime

Fr = \frac{V}{\sqrt{g\,D_h}},\qquad g = 9.80665\ \mathrm{m/s^2}

Critical depth condition and critical slope

\frac{A_c^{3}}{T_c} = \frac{Q^{2}}{g},\qquad S_c = \frac{g\,n^{2}\,(A_c/T_c)}{K^{2}\,R_c^{4/3}}

Velocity head and specific energy

h_v = \frac{V^{2}}{2g},\qquad E = y + \frac{V^{2}}{2g}

Slope and roughness solved from Manning's equation

S_0 = \left(\frac{Q\,n}{K\,A\,R^{2/3}}\right)^{2} = \left(\frac{V\,n}{K\,R^{2/3}}\right)^{2},\qquad n = \frac{K\,A\,R^{2/3}\,S_0^{1/2}}{Q} = \frac{K\,R^{2/3}\,S_0^{1/2}}{V}

Frequently asked questions

What is the difference between open channel flow and pipe flow?

Open channel flow has a free water surface open to the air. Gravity moves the water, and the depth can change along the channel.

Pipe flow fills the whole pipe. Pressure pushes the water, and it can even flow uphill.

A storm pipe running half full is open channel flow. The same pipe running full under pressure is pipe flow. That is why a partly full pipe is solved with Manning's equation and a wetted perimeter, not with a pressure drop.

How do you calculate the hydraulic radius of a channel?

Divide the wet area by the wetted perimeter:

R = A / P

The wetted perimeter is only the length of the bed and walls that water touches. The top water surface is not counted, because air causes almost no friction.

Example: a rectangular channel 3 m wide with 1 m of water has A = 3 m² and P = 3 + 1 + 1 = 5 m. So R = 0.6 m.

A bigger R means less friction per unit of water, so the channel carries more flow.

Why does a round pipe carry the most water when it is not completely full?

As a pipe fills past about 94 percent, the extra wall area added at the top adds more friction than the small bit of extra flow area gains.

Peak discharge happens near y/D = 0.94. Peak velocity happens near y/D = 0.81.

So a pipe flowing about 94 percent full carries roughly 7 percent more water than the same pipe flowing exactly full by gravity. Designers often size storm drains for 80 to 90 percent full to leave room for air.

What is the minimum velocity needed to keep a storm drain or sewer from clogging?

The usual rule is about 0.6 m/s (2 ft/s) for storm drains and 0.9 m/s (3 ft/s) for sanitary sewers.

Below that speed, sand, grit and solids drop out and build up on the bottom. This is called the self-cleansing velocity.

If your design speed is too low, steepen the slope or use a smaller pipe so the water runs deeper and faster.

What water speed starts to erode an earth channel?

It depends on the soil and lining. Rough limits for steady flow:

Fine sand: about 0.4 to 0.6 m/s (1.5 to 2 ft/s)
Firm loam: about 0.8 m/s (2.5 ft/s)
Stiff clay: about 1.2 to 1.5 m/s (4 to 5 ft/s)
Grass lined: about 1.5 to 1.8 m/s (5 to 6 ft/s)
Concrete: 4 m/s (13 ft/s) or more

If your velocity is above the limit, flatten the slope, widen the channel, or add riprap or a hard lining.

What is the most efficient channel shape?

The best shape gives the largest area with the smallest wetted perimeter, so friction is lowest.

A semicircle is the true best. For practical shapes:

Trapezoid: half a hexagon, with side slope z = 0.577 (about 1.73:1)
Rectangle: width equal to twice the depth (b = 2y)
Triangle: side slopes of 1:1

Real canals often use flatter banks than this, because soil will slump on steep sides.

How do you find critical depth in a rectangular channel?

Use the flow per unit width, q = Q / b, then:

y_c = (q² / g)^1/3

Example: Q = 12 m³/s in a 4 m wide channel gives q = 3 m²/s. Then y_c = (9 / 9.81)^1/3 = 0.97 m.

For trapezoidal, triangular and round shapes there is no simple formula. You must solve A³/T = Q²/g by trial and error.

What is a hydraulic jump and when does it form?

A hydraulic jump is a sudden rise in water level where fast, shallow flow slows down to deep, slow flow.

It forms when flow changes from supercritical (Fr > 1) to subcritical (Fr < 1). Common spots are the bottom of a spillway, below a sluice gate, or where a steep chute meets a flat channel.

The jump churns and loses energy, which is useful. Engineers build stilling basins on purpose so the jump happens there instead of scouring the streambed.

Can two different depths carry the same flow rate?

Yes. In a circular pipe, the same discharge can happen at two depths, because flow rate peaks near 94 percent full and then drops slightly as the pipe fills.

In specific energy problems, one energy value also matches two depths: a shallow supercritical depth and a deeper subcritical depth. These are called alternate depths.

Which one is real depends on the slope and on what happens upstream and downstream.

What slope should a drainage ditch or swale have?

A common range is 0.5 to 5 percent (0.005 to 0.05).

Below about 0.5 percent, water sits and silt builds up. Above about 5 percent, a grass ditch usually erodes and needs riprap, check dams, or a hard lining.

Roadside ditches often run 1 to 2 percent. Long irrigation canals may be as flat as 0.0005 because they must carry water far without losing much height.

How much freeboard should a canal or ditch have?

Freeboard is the extra bank height above the design water level. It stops waves, surges and extra storm flow from spilling over.

A common rule is 20 to 30 percent of the flow depth, with a minimum of about 0.15 to 0.3 m (6 to 12 in) on small channels. Big canals may use 0.6 to 1.2 m.

Add more freeboard on curves, where water rides up on the outside bank.

Why is there a 1.486 in Manning's equation for feet?

Manning's n was measured in metric units, so the base constant is 1.0 for meters. The number 1.486 is just the unit conversion baked into the formula.

It comes from (3.2808)^1/3, since one meter is 3.2808 feet and the equation has R to the 2/3 power.

The value of n itself stays the same in both systems. Only the constant changes: use 1.0 with meters, 1.486 with feet.

When does Manning's equation stop working?

Manning's equation assumes steady, uniform, fully turbulent flow in a channel with the same shape all along it. It gets unreliable when:

The slope is very steep, above about 10 percent
The flow is very shallow or very slow and not fully turbulent
The depth changes fast, as at a weir, drop, or hydraulic jump
The channel shape, roughness or slope changes along the reach

For those cases engineers use energy and momentum equations, or a step-by-step water surface profile method.

What is specific energy in open channel flow?

Specific energy is the energy of the water measured from the channel bottom:

E = y + V² / 2g

It adds the depth to the velocity head. For a given flow, E is smallest at critical depth.

It is useful for checking flow over a bump, under a gate, or through a narrowed section, where the bed height changes but total energy stays about the same.

How does a steep slope differ from a mild slope?

Compare normal depth (y_n) to critical depth (y_c) for the same flow.

Mild slope: y_n > y_c. Flow is subcritical, deep and calm. Downstream conditions control the surface.
Steep slope: y_n < y_c. Flow is supercritical, shallow and fast. Upstream conditions control it.

The slope where they are equal is the critical slope. Steep and mild are about the flow, not just the number, so the same bed slope can be mild for a big flow and steep for a small one.

Results

Rate this calculator

Introduction

How to use our Open Channel Flow Calculator

What Is Open Channel Flow?

Manning's Equation

Channel Shapes

Normal Depth and Critical Depth

Froude Number and Flow Regime

Why Roughness Matters

Where Engineers Use It

Formulas used

Frequently asked questions

What is the difference between open channel flow and pipe flow?

How do you calculate the hydraulic radius of a channel?

Why does a round pipe carry the most water when it is not completely full?

What is the minimum velocity needed to keep a storm drain or sewer from clogging?

What water speed starts to erode an earth channel?

What is the most efficient channel shape?

How do you find critical depth in a rectangular channel?

What is a hydraulic jump and when does it form?

Can two different depths carry the same flow rate?

What slope should a drainage ditch or swale have?

How much freeboard should a canal or ditch have?

Why is there a 1.486 in Manning's equation for feet?

When does Manning's equation stop working?

What is specific energy in open channel flow?

How does a steep slope differ from a mild slope?

Open Channel Flow Calculator

Results

Rate this calculator

Introduction

How to use our Open Channel Flow Calculator

What Is Open Channel Flow?

Manning's Equation

Channel Shapes

Normal Depth and Critical Depth

Froude Number and Flow Regime

Why Roughness Matters

Where Engineers Use It

Formulas used

Frequently asked questions

What is the difference between open channel flow and pipe flow?

How do you calculate the hydraulic radius of a channel?

Why does a round pipe carry the most water when it is not completely full?

What is the minimum velocity needed to keep a storm drain or sewer from clogging?

What water speed starts to erode an earth channel?

What is the most efficient channel shape?

How do you find critical depth in a rectangular channel?

What is a hydraulic jump and when does it form?

Can two different depths carry the same flow rate?

What slope should a drainage ditch or swale have?

How much freeboard should a canal or ditch have?

Why is there a 1.486 in Manning's equation for feet?

When does Manning's equation stop working?

What is specific energy in open channel flow?

How does a steep slope differ from a mild slope?

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