Manning's Equation Calculator
A 2 m wide concrete channel flowing 0.5 m deep on a 0.1 % slope carries 1.01351 m³/s, at about 1 m/s.
Concrete 0.012–0.015, earth channel 0.022–0.030, PVC 0.009.
1.01350968812679 m³/s
Full answer, then cut to fewer decimals (not rounded):
- 1.01350968812679 m³/s
- 1.0135096881267 m³/s
- 1.013509688126 m³/s
- 1.01350968812 m³/s
- 1.0135096881 m³/s
- 1.013509688 m³/s
- 1.01350968 m³/s
- 1.0135096 m³/s
- 1.013509 m³/s
- 1.01350 m³/s
- 1.0135 m³/s
- 1.013 m³/s
- 1.01 m³/s
- 1.0 m³/s
- Mean velocity V
- 1.013509688 m/s
- Flow area A
- 1 m²
- Wetted perimeter P
- 3 m
- Hydraulic radius R = A/P
- 0.3333333333 m
- Froude number V/√(gA/T)
- 0.4577017411
- Flow is
- subcritical (tranquil)
Step-by-step solution
- A = 1 m², P = 3 m, R = A/P = 0.3333333333 m
- V = (1/n) R^(2/3) S^(1/2) = (1/0.015) × 0.4807498568 × 0.0316227766 = 1.013509688 m/s
- Q = VA = 1.013509688 m³/s
Manning's Equation Formula
V = (1/n) R^(2/3) S^(1/2), Q = VA
R = A/P hydraulic radius; SI units (multiply by 1.49 in US units)
Worked Example
A 2 m wide concrete rectangular channel flowing 0.5 m deep at a slope of 0.001:
- A = 1 m², P = 3 m, R = A/P = 0.3333333333 m
- V = (1/n) R^(2/3) S^(1/2) = (1/0.015) × 0.4807498568 × 0.0316227766 = 1.013509688 m/s
- Q = VA = 1.013509688 m³/s
Flow area A: 1 m² · Wetted perimeter P: 3 m · Hydraulic radius R = A/P: 0.3333333333 m · Froude number V/√(gA/T): 0.4577017411 · Flow is: subcritical (tranquil)
GATE tip
The most efficient rectangular section has b = 2y (R = y/2); the most efficient trapezoid is half a hexagon. Sewer design checks self-cleansing velocity (about 0.6–0.75 m/s) at minimum flow.
More Hydraulics and Groundwater Calculators
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Critical Depth Calculator
y_c = (q²/g)^(1/3), E_c = 1.5 y_c
specific energy E = y + q²/(2gy²); V_c = √(g y_c)
Example: A rectangular channel carrying 2 m²/s per metre width: Critical depth y_c = 0.741617 m.
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Hydraulic Jump Calculator
y₂/y₁ = ½(√(1 + 8F₁²) − 1)
F₁ = V₁/√(gy₁); head loss h_L = (y₂ − y₁)³/(4y₁y₂)
Example: Flow 0.3 m deep at 6 m/s entering a 3 m wide stilling basin: Sequent depth y₂ = 1.34167 m.
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Darcy's Law Calculator
Q = K i A, i = Δh/L
Darcy velocity q = Ki; seepage (linear) velocity = q/nₑ
Example: An aquifer with K = 10 m/day, 2 m head drop over 100 m and 50 m² cross-section: Discharge Q = 10 m³/day.
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Well Yield Calculator
Confined: Q = 2πKb(h₂ − h₁)/ln(r₂/r₁)
unconfined: Q = πK(h₂² − h₁²)/ln(r₂/r₁)
Example: A confined aquifer, K = 20 m/day, 30 m thick, with heads 40 m at the 0.15 m well and 45 m at 300 m: Well discharge Q = 2479.91 m³/day.
Frequently asked questions
What value of n should I use?
Finished concrete 0.012–0.013, unfinished 0.015, clean earth channels 0.022–0.030, natural streams 0.030–0.050.
Why is a pipe’s maximum flow below full?
Near the crown the wetted perimeter grows faster than the area, so peak discharge occurs at about 94 % depth in a circular pipe.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Manning's Equation Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/manning-equation-calculator/
IEEE
Scientific Converters, "Manning's Equation Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/manning-equation-calculator/