Try a Common Scenario
Click to pre-fill the calculator with realistic values.
Calculate flow rate (Q) and velocity (V) for a circular gravity pipe with a known diameter, slope and Manning's n. Compare full and partially full flow in US customary or metric units. For a ditch, swale, or noncircular cross-section, use the open channel flow calculator.
Need a diameter for a design flow? Use the storm drain pipe sizing calculator (US). Need a roughness value? Open the Manning's n table by material.
Manning’s equation for circular pipe flow
Manning’s equation is Q = (k/n)AR2/3S1/2, with V = Q/A. For a full circular pipe, A = πD2/4 and P = πD, so R = A/P = D/4. Use k = 1.486 in US customary units or 1.0 in SI. It applies to uniform gravity/free-surface flow, not a pressurized or surcharged pipe.
Sources: FHWA HEC-22, FHWA HDS-4, and EPA SWMM.
For educational purposes only. Not a substitute for professional engineering judgment.
Manning's equation is empirical and assumes uniform, steady flow conditions
Not valid for pressurized (surcharged) pipe flow - use pressure flow equations instead
Accuracy decreases for very smooth pipes (n < 0.010) or very rough pipes (n > 0.035)
Does not account for entrance/exit losses or other minor losses
Partial flow calculations assume free surface (atmospheric pressure at water surface)
Maximum Q/Qfull occurs at approximately y/D = 0.94, not at full flow
Air entrainment effects near the pipe crown are not considered
References formatted in APA 7th Edition style.
- Chow, V. (1959). Open-Channel Hydraulics. New York, NY: McGraw-Hill.textbook
- Federal Highway Administration (2009). Urban Drainage Design Manual (3rd ed.). Washington, DC: U.S. Department of Transportation. https://www.fhwa.dot.gov/engineering/hydraulics/pubs/10009/10009.pdfView Source manual
- United States Army Corps of Engineers (1994). Hydraulic Design of Flood Control Channels. Washington, DC: U.S. Army Corps of Engineers. https://www.publications.usace.army.mil/Portals/76/Publications/EngineerManuals/EM_1110-2-1601.pdfView Source manual
Interactive model
Interactive Manning partial-flow pipe geometry
Adjust diameter, roughness, slope, and y/D to see flow area, wetted perimeter, hydraulic radius, velocity, and discharge change together.
Open full model (opens in a new tab)How it works
Manning's equation relates gravity flow in a pipe or channel to its slope, roughness and cross-sectional geometry. This calculator applies it to a circular pipe for two cases: flowing full and flowing partly full.
Discharge and velocity (Manning's equation):
- Q = (k / n) · A · R2/3 · S1/2
- V = (k / n) · R2/3 · S1/2, and Q = V · A
where:
- Q = discharge (cfs or m³/s)
- V = average velocity (ft/s or m/s)
- n = Manning's roughness coefficient (dimensionless)
- A = flow cross-sectional area (ft² or m²)
- P = wetted perimeter (ft or m)
- R = hydraulic radius = A / P (ft or m)
- S = slope of the energy line (ft/ft or m/m)
- k = unit conversion factor = 1.486 for US customary units, 1.0 for SI units (Chow 1959; some US references use 1.49, a difference of under 0.3%)
Full-pipe geometry (diameter D):
- Flow area: A = πD² / 4
- Wetted perimeter: P = πD
- Hydraulic radius: R = A / P = D / 4
Partial-flow geometry uses the central angle θ subtended by the water surface for a flow depth y:
- θ = 2 · cos-1(1 − 2y/D) (radians)
- Flow area: A = (D² / 8)(θ − sinθ)
- Wetted perimeter: P = Dθ / 2
The calculator also reports the Froude number, Fr = V / √(g · Dh), where Dh is the hydraulic depth (A/T). Fr < 1 is subcritical flow, Fr = 1 is critical, and Fr > 1 is supercritical.
Manning's n for common pipe materials
Roughness coefficients for closed conduits. Use the typical value for design; the min-max range reflects condition and age. Sources: Chow (1959) Table 5-6, FHWA HEC-22, FHWA HDS-4.
| Material | Condition | n (min) | n (typical) | n (max) |
|---|---|---|---|---|
| PVC | Smooth interior | 0.009 | 0.010 | 0.011 |
| HDPE | Smooth interior | 0.009 | 0.011 | 0.012 |
| HDPE | Corrugated exterior, smooth interior | 0.010 | 0.012 | 0.013 |
| Concrete | Precast, good joints | 0.011 | 0.013 | 0.015 |
| Concrete | Aged / deteriorated | 0.015 | 0.017 | 0.020 |
| Vitrified Clay | Good condition | 0.011 | 0.013 | 0.015 |
| Ductile Iron | Cement-lined | 0.011 | 0.013 | 0.015 |
| Corrugated Metal | 2-2/3 × 1/2 in corrugations, unpaved | 0.022 | 0.024 | 0.026 |
| Corrugated Metal | 3 × 1 in corrugations, unpaved | 0.027 | 0.028 | 0.030 |
| Corrugated Metal | 6 × 2 in corrugations (structural plate) | 0.033 | 0.035 | 0.037 |
A fuller table including box culverts and lined CMP is available on the Manning's n reference page.
Worked example
A 24-inch (2 ft) precast concrete pipe (n = 0.013) laid at a 1% slope (S = 0.01), flowing full:
- Flow area A = π × 2² / 4 = 3.14 ft²
- Hydraulic radius R = D / 4 = 2 / 4 = 0.50 ft
- Velocity V = (1.486 / 0.013) × 0.502/3 × 0.011/2 ≈ 7.20 ft/s
- Discharge Q = V × A = 7.20 × 3.14 ≈ 22.6 cfs
The 7.2 ft/s velocity is above the 2 ft/s self-cleansing minimum and below the ~15 ft/s erosion threshold, so this pipe and slope are hydraulically sound.
Self-cleansing vs erosion velocity
Too slow (< ~2 ft/s)
Below about 2 ft/s (0.6 m/s) sediment and solids settle out and gradually clog the pipe. Fix it by increasing the slope or reducing the diameter so the same flow runs deeper and faster.
Too fast (> ~15 ft/s)
Above about 15 ft/s (4.5 m/s) high velocity can abrade the pipe wall and damage joints. Flatten the slope, increase the diameter, or add energy dissipation at the outlet.
Remember that peak discharge in a circular pipe occurs near y/D = 0.94, and peak velocity near y/D = 0.81 — not at full bore. Design for about 75-80% full to retain reserve capacity.
Frequently asked questions
What is Manning's equation for pipe flow?
Manning's equation is an empirical formula for uniform, steady open-channel flow. For a circular pipe it is written V = (k/n) R^(2/3) S^(1/2) for velocity and Q = (k/n) A R^(2/3) S^(1/2) for discharge, where n is the roughness coefficient, R is the hydraulic radius (A/P), S is the slope, and A is the flow area. The factor k is 1.486 in US customary units and 1.0 in SI units. It applies to gravity (free-surface) flow, not pressurized flow.
Does a pipe carry the most flow when it is exactly full?
No. Because the wetted perimeter increases faster than the flow area near the crown, the maximum discharge in a circular pipe actually occurs at a depth of about y/D = 0.94 (roughly 94% full), where capacity is a few percent higher than at full bore. Maximum velocity occurs at about y/D = 0.81. Designers typically size storm and sanitary pipes to flow no more than about 75-80% full so there is reserve capacity and the pipe stays in gravity flow.
What is a good flow velocity for a drainage pipe?
A minimum velocity of about 2 ft/s (0.6 m/s) is the common rule of thumb to keep solids and sediment moving (self-cleansing). On the high end, velocities above roughly 15 ft/s (4.5 m/s) raise the risk of abrasion and joint damage, so energy dissipation or a flatter slope may be needed. Many designs aim to keep velocity in the 2-10 ft/s range.
Which Manning's n should I use for my pipe material?
Use a value matched to the pipe material and condition. Smooth-wall PVC, polypropylene and HDPE are typically n = 0.010-0.012; precast concrete and vitrified clay with good joints are about n = 0.013; corrugated metal pipe ranges from about 0.024 up to 0.035 for large structural-plate corrugations. The roughness table below lists values from Chow (1959), HEC-22 and HDS-4. When in doubt, use the higher (rougher) value for a conservative capacity estimate.
Can I use this calculator for pressurized (surcharged) pipes?
No. Manning's equation assumes free-surface gravity flow at atmospheric pressure. Once a pipe surcharges and flows under pressure, you need pressure-flow (e.g., Hazen-Williams or Darcy-Weisbach with the energy grade line) instead. If the calculator shows the pipe flowing more than about 80% full, treat the result as a capacity warning rather than a steady design point.
What This Solves
Calculates the flow rate and velocity in a circular pipe using Manning's equation for gravity-driven (non-pressurized) conditions.
Best Used When
- You are sizing a storm sewer or drainage pipe for a known design flow
- You need to check whether an existing pipe has enough capacity
- You want to evaluate partial-flow depth and velocity in a circular pipe
Do NOT Use When
- The pipe is flowing under pressure (surcharged condition) — Use Culvert Outlet Control Calculator
- You are analyzing an open channel rather than a closed pipe — Use Manning's Channel Calculator
- You need to find the depth at which uniform flow occurs for a given discharge — Use Normal Depth Calculator
Key Assumptions
- Flow is uniform and steady (not rapidly changing)
- The pipe has a constant slope and cross-section along its length
- Flow is gravity-driven with a free water surface (not pressurized)
- Roughness is uniform throughout the pipe
- Fully developed turbulent flow conditions exist
Input Quality Notes
The Manning's n value has the largest effect on results. Use published values for the specific pipe material and condition (new vs. aged). Slope should be the actual energy grade line slope, not just the pipe invert slope, though they are equal for uniform flow.
Was this calculator helpful?
Last verified: February 2026