Pipe & Channel Flow Calculator

July 18, 2026

This tool computes uniform flow in partially full pipes and open channels using Manning's equation, with the standard section geometry relations from FHWA HDS-4 and HDS-5 (public domain US DOT publications). Five section types are supported: circular pipe, rectangular tube, rectangular channel, flat bottom (trapezoidal) channel, and vee channel. Four modes are available: solve for the flow rate at a given depth, solve for the normal depth at a target flow rate, compute volumes and weights, and estimate thermal length expansion.

Beyond the basic solution, the calculator reports the critical depth for the computed discharge, partial-flow ratios (Q/Qfull, V/Vfull) for closed conduits, and design velocity checks (self-cleansing minimum and permissible velocities for erodible channels per Fortier and Scobey, as tabulated in Chow, 1959), and plots the full discharge curve Q(y) with the current case, critical depth, and the depth of maximum discharge marked. The built-in reference database covers 12 pipe series, 37 Manning roughness values, 18 materials, and 56 fluids. Multiple cases can be collected into a data table, each with its own 3D schematic, and exported as a single PDF calculation sheet.

Pipe & Channel Flow Calculator

Partially Full Flow in Pipes and Channels (Manning's Equation)

Input

Project and computed / checked names are stamped on the PDF calculation sheet.
Nominal pipe size
Manning's coefficient n
Internal diameter, ID (in)
Pipe length (ft)
Slope (%)
1 % = 0.01 ft/ft; S = 0.01; drop = S x L = 0.4 ft
n (editable)
Water depth, y (in) - uniform flow

Results

Flow area A (ft²)
0.07065
Wetted perimeter P (in)
8.387
Hydraulic radius R (in)
1.213
Surface width T (in)
3.509
Velocity (ft/s)
2.69
Flow rate Q (cfs)
0.19
Froude number
0.964
Flow rate units:Flow regime: subcritical (tranquil)
Critical depth yc = 2.95 inPartial-flow ratios: y/D = 0.745, Q/Qfull = 0.905, V/Vfull = 1.132

Discharge curve Q(y)

00.060.130.190.2501.012.013.024.03y of Qmax (0.94 D) · selection limitcritical depth (Fr = 1)currentQ (cfs)y (in)click or drag on the curve to set the depth
Discharge over the full depth range at the current section, n and slope. Click or drag on the curve to set the water depth. The dashed line marks the critical depth for the computed discharge (Fr = 1); the red line is the depth of maximum discharge (y = 0.94 D) and the selection limit: the shaded region above it cannot be picked, since discharge falls beyond it). Depths above critical flow subcritical (tranquil), below it supercritical (rapid).

Schematic

y/D = 0.745 / V = 2.69 ft/s
Dashed line is the horizontal datum; the pipe and the water surface (parallel to the invert under uniform flow) tilt with the slope, exaggerated ×8 for visibility. Particle speed follows the computed velocity V.

Data table

No rows yet. Set up a case and press "+ Add to data table" in Results. Captured rows are included in the PDF report.

Formulas and sources

V = (Ku/n) R2/3S1/2, Q = VA
Manning's equation; Ku = 1.486 (US customary), 1.0 (SI). Source: FHWA HDS-5, Hydraulic Design of Highway Culverts (FHWA-HIF-12-026), public domain.
θ = 2 arccos(1 − 2y/D), A = (D²/8)(θ − sin θ), P = /2, R = A/P, T = D sin(θ/2)
Geometric elements of a circular section. Standard open-channel relations; see FHWA HDS-4, Introduction to Highway Hydraulics (public domain).
Fr = V / √(gA/T )
Froude number with hydraulic depth A/T. Fr < 1 subcritical (tranquil), Fr > 1 supercritical (rapid). Source: FHWA HDS-4/HDS-5.
Q² T / (gA³) = 1 ⇒ y = yc
Critical depth for the computed discharge, found numerically. Depths above critical flow subcritical (tranquil), below it supercritical (rapid). Source: FHWA HDS-4.
Assumes steady uniform flow (normal depth): friction slope equals bed slope.
References: FHWA Hydraulic Design Series No. 4 and No. 5 (US DOT, public domain). Material, fluid, pipe dimension and roughness tables: standard published reference data. For engineering use, verify against project-specific criteria.
How to citeShow

Author ORCID: 0009-0000-1316-1362

APA
Chernitsky, I. (2026). Pipe & Channel Flow Calculator [Computer software]. Chernitsky.net. https://chernitsky.net/blog/Pipe-and-Channel-Flow-Calculator
IEEE
I. Chernitsky, "Pipe & Channel Flow Calculator," Chernitsky.net, 2026. [Online]. Available: https://chernitsky.net/blog/Pipe-and-Channel-Flow-Calculator
BibTeX
@misc{chernitsky2026pipe,
  author       = {Chernitsky, Ilia},
  title        = {Pipe \& Channel Flow Calculator},
  year         = {2026},
  howpublished = {\url{https://chernitsky.net/blog/Pipe-and-Channel-Flow-Calculator}},
}