Manning's equation calculator for pipes and open channels
Calculate discharge, velocity or normal depth with Manning's equation for partially full circular pipes and rectangular, trapezoidal and triangular channels. Includes Froude number, boundary shear and SI or US customary units.
- Free, no sign-up
- Pipes and channels
- SI and US units
Manning's equation calculator
Results
- Normal depth
- 0.082 m
- y/D = 41.0 %
- Velocity
- 1.24 m/s
- Froude number
- 1.59
- Supercritical (rapid)
- Boundary shear
- 4.28 Pa
- Discharge
- 15.00 L/s
- Flow area
- 0.0121 m²
- Wetted perimeter
- 0.278 m
- Hydraulic radius
- 0.0436 m
- Top width
- 0.197 m
- Full-pipe discharge
- 42.64 L/s
- Full-pipe velocity
- 1.36 m/s
- Capacity used (Q/Qfull)
- 35.2 %
Uniform free-surface flow. Water at 1000 kg/m³, g = 9.81 m/s². Channel sketches are not to scale.
In short
Manning's equation gives the mean velocity of uniform free-surface flow: V = (1/n) · R2/3 · S1/2, where n is the roughness coefficient of the material, R the hydraulic radius (flow area divided by wetted perimeter) and S the slope. Discharge is Q = V · A. In US customary units the factor is 1.49 instead of 1. It is used to design sewers, storm drains and channels; it does not apply to pressurized pipes, which use Hazen-Williams or Darcy-Weisbach.
Manning's equation
V = (1/n) · R2/3 · S1/2
Q = V · A
- V: mean velocity (m/s).
- n: Manning's roughness coefficient; it depends on the material.
- R: hydraulic radius = A / P, in metres (A: flow area; P: wetted perimeter).
- S: slope of the channel bed or pipe (m/m).
- Q: discharge (m³/s).
V = (1.49/n) · R2/3 · S1/2
The same equation in US customary units (feet and seconds). The calculator works in SI internally and converts, so you can use either system.
Manning's n values by material
Typical design values. The range reflects surface condition: use the high end for aged surfaces, joints or sediment.
| Material or surface | Typical n | Range |
|---|---|---|
| PVC or smooth HDPE | 0.010 | 0.009 – 0.011 |
| Concrete pipe | 0.013 | 0.011 – 0.015 |
| Cast or ductile iron | 0.013 | 0.010 – 0.014 |
| Corrugated metal pipe | 0.024 | 0.021 – 0.030 |
| Concrete channel, float finish | 0.015 | 0.013 – 0.016 |
| Cemented rubble masonry | 0.025 | 0.017 – 0.030 |
| Earth channel, clean | 0.022 | 0.018 – 0.025 |
| Earth channel, short grass | 0.027 | 0.022 – 0.033 |
| Rock cut | 0.035 | 0.025 – 0.040 |
| Natural stream, clean | 0.030 | 0.025 – 0.033 |
Source: Ven Te Chow, Open-Channel Hydraulics (1959); for PVC and HDPE, common manufacturer values. If your governing standard sets a design n, use that one.
Partially full pipes: maximum flow is not at full depth
In a circular pipe, maximum discharge occurs at a depth of about 94 % of the diameter and is roughly 7.6 % higher than full-pipe flow. Maximum velocity occurs at about 81 % of the diameter. The reason: near the crown, the wetted perimeter grows faster than the flow area, so the hydraulic radius drops.
That is why, between full-pipe flow and the maximum, the same discharge has two possible depths. The calculator returns the lower one, which is the design depth, and warns you if the discharge exceeds the maximum: the pipe would then flow under pressure and Manning's equation no longer applies.
Worked example: 200 mm (8 in) PVC sewer
A 200 mm (about 8 in) PVC sewer (n = 0.010) at 1 % slope must carry 15 L/s (0.53 cfs). At what depth and velocity does it run?
- Full-pipe discharge: 42.6 L/s (1.51 cfs), so it runs at 35 % of capacity.
- Normal depth: 82 mm (3.2 in), that is y/D = 0.41.
- Velocity: 1.24 m/s (4.06 ft/s).
- Boundary shear: 4.28 Pa (0.089 lb/ft²).
- Froude number: 1.59, supercritical flow, common in small sewers on a slope.
These are the calculator's default inputs: replace them with your own pipe run.
Common sewer design criteria
Manning's equation gives you the hydraulics; your standard sets the limits. As a reference, the Ten States Standards (Recommended Standards for Wastewater Facilities) require sewers to reach at least 2.0 ft/s (0.6 m/s) when flowing full, computed with n = 0.013.
Standards in Latin America and Brazil often check self-cleansing with a minimum boundary shear of 1.0 Pa and limit the flow depth to 75 % of the diameter. Always check the current version of your local standard and utility requirements. If you lay out the network in Civil 3D, see how to model pipe networks with their fittings.
Designing whole networks? We automate the drafting in Civil 3D.
We build plugins that turn your layout into a 3D pipe network with its fittings (bends, tees and wyes) and check it against your design criteria, for water, sewer and storm drainage.
Free initial diagnosis · No commitment · We reply the same day
Frequently asked questions
What is Manning's n?
A number that represents the roughness of the surface the water flows over: the higher it is, the more friction and the lower the velocity. It ranges from about 0.010 for PVC to 0.035 or more for channels cut in rock.
What is the hydraulic radius?
The flow area divided by the wetted perimeter (R = A/P). It measures how efficient the section is: for the same area, more perimeter in contact with the water means more friction.
Can Manning's equation be used for pressurized pipes?
No. Manning's equation is for free-surface flow: channels and partially full pipes such as sewers. Pressurized water mains are designed with Hazen-Williams or Darcy-Weisbach.
Why is maximum pipe flow not at full depth?
Because near the crown the wetted perimeter grows faster than the flow area. The maximum occurs at about 94 % of the diameter and is roughly 7.6 % higher than full-pipe flow.
What is normal depth?
The depth the water reaches when flow is uniform: slope, roughness and discharge are in balance. It is what the tool computes in “Normal depth” mode.
What does the Froude number tell me?
It compares the flow velocity with the speed of a surface wave. Below 1 the flow is subcritical (tranquil); above 1 it is supercritical (rapid). Near 1 the flow is unstable, which designs should avoid.
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