Pipe Flow Toolkit

July 18, 2026

This tool computes open-channel flow in a partially full circular pipe using Manning's equation and the standard circular-segment geometry from FHWA HDS-4 and HDS-5 (public domain US DOT publications). Four modes are available: solve for the flow rate at a given depth, solve for the normal depth at a target flow rate, compute pipe and fluid volumes and weights, and estimate thermal length expansion.

The built-in reference database covers 12 pipe series (ANSI Sch 10/40/80, BSP, copper Type L, PVC Sch 40/80/120, aluminium, and storm sewer sizes up to 60"), 37 Manning roughness values, 18 pipe materials, and 56 fluids with specific gravity at temperature. The interactive 3D schematic shows the water level, slope, and dimension annotations in real time, and the data table lets you collect multiple cases into a single PDF report.

Pipe Flow Toolkit

Partially Full Pipe Flow (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)
Pipe slope (%)
drop = S x L = 1.5 ft, S = 0.003
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)
1.47
Flow rate Q (cfs)
0.104
Froude number
0.528
Flow rate units:Flow regime: subcritical (tranquil)

Schematic

y/D = 0.745 / V = 1.47 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 = V A
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 = Dθ/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 / √(g A/T )
Froude number with hydraulic depth A/T. Fr < 1 subcritical (tranquil), Fr > 1 supercritical (rapid). Source: FHWA HDS-4/HDS-5.
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 Flow Toolkit [Computer software]. Chernitsky.net. https://chernitsky.net/blog/Pipe-Flow-Toolkit
IEEE
I. Chernitsky, "Pipe Flow Toolkit," Chernitsky.net, 2026. [Online]. Available: https://chernitsky.net/blog/Pipe-Flow-Toolkit
BibTeX
@misc{chernitsky2026pipe,
  author       = {Chernitsky, Ilia},
  title        = {Pipe Flow Toolkit},
  year         = {2026},
  howpublished = {\url{https://chernitsky.net/blog/Pipe-Flow-Toolkit}},
}