Mannings Flow Calculator

Mannings Flow Calculator solves flow, normal depth, slope, pipe size or roughness n for gravity pipes, box culverts and open channels, and reports Froude number and critical depth.

How the Mannings Flow Calculator Works

The Mannings Flow Calculator applies Manning's equation to uniform gravity flow, where water runs with a free surface at a steady depth. It covers circular pipes, closed box culverts, and rectangular, trapezoidal and triangular open channels.

Solve For decides which value you get back. Flow Rate is the usual starting point, while Normal Depth finds how deep a known flow runs. Required Slope finds the grade that carries a flow at a chosen depth, and Pipe Diameter or Width sizes the section. Manning's n works backward from a measured flow to the roughness the channel really has.

Pipe depth goes in as a percent of the diameter, so 75 means the pipe runs three-quarters full. Slope accepts percent, ft/ft, per thousand or feet per mile. Result Units switches every output between US units (cfs, ft/s, ft) and SI units (m³/s, m/s, m).

Manning's Flow Equation

Manning's equation gives the mean velocity from the channel's roughness, shape and slope. Multiplying that velocity by the flow area gives the discharge.

$$V=\frac{k}{n}\cdot R^{2/3}\cdot S^{1/2}$$

$$Q=\frac{k}{n}\cdot A\cdot R^{2/3}\cdot S^{1/2}$$

Here V is mean velocity, Q is flow, n is Manning's roughness coefficient and S is the slope as a decimal. The hydraulic radius R is the flow area divided by the wetted perimeter, the length of channel wall the water touches.

$$R=\frac{A}{P}$$

The constant k is 1.0 in SI units and 1.486 in US units. The 1.486 comes from converting meters to feet, since the cube root of 3.2808 is 1.4859. Some references round it to 1.49, which raises the flow by about a quarter of a percent.

Worked Example in a 24 in Pipe

The Mannings Flow Calculator opens on a 24 in precast concrete pipe (n 0.012) laid at 0.5 percent and running 75 percent full. At that depth the flow area is 2.53 ft², the wetted perimeter is 4.19 ft and the hydraulic radius is 0.603 ft.

$$Q=\frac{1.486}{0.012}\cdot 2.53\cdot 0.603^{2/3}\cdot 0.005^{1/2}=15.80\text{cfs}$$

That is 7,093 gpm, or 10.21 million gallons per day. The water moves at 6.25 ft/s, and its velocity head of 0.608 ft adds to the 1.50 ft depth for a specific energy of 2.11 ft. The Froude number is 0.91, so the flow is subcritical, with the 1.50 ft depth sitting just above the 1.43 ft critical depth.

Gravity Pipe Flow at Partial Depth

A round pipe does not carry the most water when it runs full. Near the top, the crown adds wetted perimeter faster than the water adds area, so friction rises and flow falls. A circular pipe peaks at about 93.8 percent depth, carrying 7.6 percent more than it does full.

The fourth card in the Mannings Flow Calculator shows this for your pipe. In the default case, the 15.80 cfs is 91.2 percent of the 17.33 cfs full-pipe capacity, and the peak is 18.64 cfs at 93.8 percent depth. Design checks usually use full-pipe capacity, because the extra above 93.8 percent depth disappears the moment the pipe fills.

The Hydraulic Radius card also gives the freeboard left above the water. At 75 percent depth in a 24 in pipe, that is 25.0 percent of the diameter, or 6.00 in to the crown. For a box it measures to the top slab, and for an open channel to the bank.

The partial-depth ratios below hold for any circular pipe with a constant n. Half full carries exactly half the full flow at the same velocity as full, which makes 50 percent a handy check.

The Depth Rating Table under the results runs the same idea for your actual pipe, listing flow, velocity and Froude number from 10 percent depth to full. The cross-section diagram draws your depth to scale with critical depth as a dashed line. The Partial Pipe Flow Calculator also finds flow and velocity for a pipe running partly full.

Sewer Slopes and Self-Cleaning Velocity

A gravity sewer needs enough speed to carry solids along. Mississippi DEQ's wastewater design criteria require at least 2.0 ft/s when flowing full, using n 0.013, and list a minimum slope for each size. Running those slopes through Manning's equation shows they all land at about 2 ft/s. Enter any row in the Mannings Flow Calculator at 100 percent depth with n 0.013 to see the same result.

Illinois sets the same 2.0 ft/s rule at n 0.013 in 35 IAC 370.320, with steeper minimums for small sewers, such as 0.40 percent for 8 in pipe. The Mannings Flow Calculator applies that check to every circular pipe and warns when the full-flow velocity at n 0.013 falls under 2.0 ft/s (0.61 m/s).

Both rules call for special protection against erosion and shock where velocity passes 15 ft/s. To turn a slope into the fall over a run, the Sewer Line Slope Calculator and Pipe Slope Calculator handle the layout side.

Open Channel Shapes

For an open channel, the Mannings Flow Calculator takes the bottom width, the flow depth and, for sloped sides, the side slope as horizontal run per 1 vertical. Each shape changes only the area and wetted perimeter, and the rest of the equation stays the same.

$$A_{\text{trap}}=y\cdot (b+z\cdot y)$$

$$P_{\text{trap}}=b+2\cdot y\cdot \sqrt{1+z^2}$$

A rectangle is the same formula with z set to 0, and a V-channel is the same with b set to 0. The table compares the three at a 2 ft depth on a 0.1 percent slope, using a 6 ft bottom, 2:1 side slopes and n 0.015 for float-finished concrete, the tool's starting value for channels.

For channels, the fourth card reports bed shear instead of pipe capacity. Mean shear is γRS and maximum shear is γyS, so the trapezoid above puts 0.084 lb/ft² on average and 0.125 lb/ft² at the deepest point on its lining. Compare those with the allowable shear of the lining you plan to use.

Channels also take a Bank Height, set to 4 ft to start. The tool reports the freeboard between the water and the bank, and it warns that the channel overtops when the normal depth runs higher than the bank.

Froude number and critical depth

The third card compares the flow with the speed of a surface wave. A Froude number below 1 is subcritical, slow and deep, while above 1 the flow is supercritical, fast and shallow. Steep concrete channels often run supercritical, and the Mannings Flow Calculator warns when they do.

Critical depth is the depth where the Froude number equals 1. When supercritical flow meets flatter grade or slower water, it jumps back up past critical depth in a hydraulic jump. The critical slope on the same card is the grade that would make your flow run at exactly critical depth.

Box Culvert Flow

The Box Culvert option in the Mannings Flow Calculator treats the box as a closed section with a span and a rise. While the water stays below the top slab, it behaves like a rectangular channel. Once water touches the slab, the wetted perimeter jumps to the full box and the flow drops, so the box carries the most just below full height.

A 6 ft by 4 ft concrete box (n 0.013) at 3 ft depth on a 0.5 percent slope carries 190.6 cfs. Manning's equation sets the barrel's own capacity, but a culvert can also be limited by its inlet. For headwater and inlet control, the Culvert Flow Calculator covers the entrance side.

Manning's n Values

The roughness coefficient has more effect on the answer than any other input, because flow scales with 1/n. Moving from n 0.012 to 0.013 cuts flow by 7.7 percent. The Mannings Flow Calculator ships with pipe values from Caltrans Highway Design Manual Table 851.2, which gives a design value and a range for each material.

For PVC sewer pipe specifically, the PVC pipe industry's Uni-Bell hydraulic testing found n 0.009 to be a conservative design value. The Mississippi DEQ sewer criteria above use n 0.013 for every material, so check which value your reviewing agency expects.

Open channels vary far more than pipes. The channel presets in the Mannings Flow Calculator use the normal figures from Chow's Open-Channel Hydraulics Table 5-4, the standard reference for channel roughness.

When a channel is already built, the Manning's n mode gives a better answer than any table. Measure the flow and depth on a straight, uniform reach, enter the slope, and the tool backs out the roughness the channel really has, then names the closest material.

Manning Equation in Excel

The Step-by-Step Math panel prints each geometry step and an Excel or Google Sheets formula built from your numbers. For the 24 in example, the flow formula reads as below and returns 15.80 cfs.

=(1.486/0.012)*2.52741*0.603374^(2/3)*0.005^(1/2)

To reuse it, put n in A2, area in B2, hydraulic radius in C2 and slope as a decimal in D2. The formula below then returns cfs, and replacing 1.486 with 1 returns m³/s for SI inputs.

=(1.486/A2)*B2*C2^(2/3)*D2^(1/2)

Depth and size can't be solved in one cell, because the area and radius both depend on the unknown. Spreadsheets handle those with Goal Seek, which the Mannings Flow Calculator replaces with a direct search in its Normal Depth and Pipe Diameter or Width modes.

Manning vs Hazen-Williams

Both equations predict friction, but they fit different flows. Manning's equation is for gravity flow with a free surface, such as storm drains, sewers, culverts and ditches. Hazen-Williams is for water pushed through full, pressurized pipe by a pump or a tank.

A pipe flowing full under gravity can use either, but pressure mains belong with the Hazen Williams Equation Calculator. To size a storm drain, start with the peak flow from the Storm Water Runoff Calculator and enter it in the Mannings Flow Calculator under Pipe Diameter or Width.