About Open-Channel Flow Calculator
The open-channel flow calculator evaluates uniform (normal) flow in a prismatic channel using Manning's equation. Choose a rectangular, trapezoidal, triangular, or partially full circular section, enter the geometry, Manning's roughness n, the bed slope S, and the flow depth y, and the tool returns the flow area, wetted perimeter, hydraulic radius, mean velocity, and discharge.
It also reports the Froude number Fr = V / sqrt(g A / T), where T is the free-surface top width, and classifies the flow as subcritical (Fr < 1), critical (Fr = 1), or supercritical (Fr > 1). An optional solver returns the normal depth that conveys a target discharge, and a rating curve plots discharge against depth so you can size channels and check serviceability.
How It Works
- Select the channel shape and enter its dimensions (bottom width b, side slope z, or pipe diameter D as required).
- Enter Manning's roughness coefficient n, the channel bed slope S (m/m), and the flow depth y (m).
- The calculator forms the section geometry (A, P, T), computes the hydraulic radius R = A/P, then applies Manning's equation Q = (k/n) A R^(2/3) S^(1/2) with k = 1.0 for SI units.
- It derives the mean velocity V = Q/A and the Froude number, classifies the flow regime, and plots the discharge-versus-depth rating curve.
Worked Example
A rectangular concrete channel has bottom width b = 3 m, flow depth y = 1 m, Manning's n = 0.013, and bed slope S = 0.001. The area A = b*y = 3 m^2, wetted perimeter P = b + 2y = 5 m, and hydraulic radius R = A/P = 0.6 m. Manning's equation gives Q = (1/0.013) * 3 * 0.6^(2/3) * 0.001^(1/2) = 5.19 m^3/s. The mean velocity is V = Q/A = 1.73 m/s, and the Froude number Fr = V / sqrt(g*A/T) = 1.73 / sqrt(9.81 * 3 / 3) = 0.55, so the flow is subcritical.
Formulas
- Manning's equation (uniform flow)
Q = (k / n) * A * R^(2/3) * S^(1/2)- Hydraulic radius and velocity
R = A / P, V = Q / A- Section geometry
Rect: A=b*y, P=b+2y, T=b | Trap: A=(b+zy)y, P=b+2y*sqrt(1+z^2), T=b+2zy | Tri: A=z*y^2, P=2y*sqrt(1+z^2), T=2zy- Circular (partially full)
theta = 2*acos(1 - 2y/D), A = (D^2/8)(theta - sin theta), P = (D/2) theta, T = D sin(theta/2)- Froude number and regime
Fr = V / sqrt(g * A / T); Fr < 1 subcritical, Fr = 1 critical, Fr > 1 supercritical
Standards & References
- Manning's equation (Gauckler-Manning-Strickler)
- Ven Te Chow, Open-Channel Hydraulics (1959)
- USACE / FHWA HDS-3 open-channel design guidance
Frequently Asked Questions
What is the difference between SI and US customary forms of Manning's equation?
The SI form uses the constant k = 1.0 (metres, seconds). The US customary form uses k = 1.49 to keep the same n values when lengths are in feet and discharge in cubic feet per second. This tool applies a consistent unit set and lets you switch the dimensional constant.
How does the calculator handle a partially full circular pipe?
It computes the central angle theta subtended by the water surface from theta = 2*acos(1 - 2y/D), then the area, wetted perimeter, and top width from the standard circular-segment formulas. Flow depth cannot exceed the pipe diameter.
What does the Froude number tell me?
The Froude number compares flow velocity to the speed of a surface wave. Fr < 1 is subcritical (deep, tranquil flow controlled downstream), Fr = 1 is critical, and Fr > 1 is supercritical (shallow, rapid flow controlled upstream). It governs whether hydraulic jumps and backwater effects occur.
Does this compute normal depth or critical depth?
The main calculation gives uniform (normal) flow for a depth you enter. The optional solver inverts Manning's equation to find the normal depth that carries a target discharge. The Froude number indicates proximity to critical depth but the tool does not solve critical depth directly.