Open channel hydraulics

See how water flows in a channel

Flume is a desktop app for open channel flow: normal and critical depth, the hydraulic jump, and water surface profiles, worked out as you type, drawn as you go, and written up as a PDF report.

gate-and-jump.flume
Flume showing a hydraulic jump located 11 m downstream of a sluice gate, with the water surface profile and its table

Uniform flow

Any section, any unknown

Describe the channel and solve Manning's equation for whichever value you don't have: discharge, normal depth, slope, roughness or bottom width.

  • Rectangular, trapezoidal, triangular, circular and parabolic sections
  • Surveyed sections, with a roughness for each part of the bed and banks
  • Froude number, critical depth and slope, bed shear, and a rating curve
river-floodplain.flume
A river with flood plains: its cross-section with the water level, and its rating curve

Energy and momentum

The hydraulic jump, on one screen

Enter one depth. Flume gives the depth on the other side of a jump, the energy it loses and the kind of jump it is, with the specific energy and specific force diagrams beside them.

  • Alternate and sequent depths for every section shape
  • Energy loss, efficiency and approximate length
  • Works from either side of the jump
stilling-basin.flume
Specific energy and specific force diagrams for a jump in a rectangular stilling basin

Gradually varied flow

Water surface profiles, classified

Start from a depth, a sluice gate or a weir. Flume follows the profile by the direct step method, names it (M1, S2, H3…), and draws the long section with the normal and critical depth lines.

  • Mild, steep, critical, horizontal and adverse slopes
  • Sharp- and broad-crested weirs, and sluice gates, as controls
  • A PDF report of the whole analysis, plus CSV tables and PNG figures
backwater-weir.flume
An M1 backwater profile running two kilometres upstream of a broad-crested weir

Two controls

It finds the jump for you

Give a reach a gate at one end and a tailwater at the other. Flume follows both profiles and puts the hydraulic jump where their specific forces balance, or tells you it's drowned or swept out.

  • Where the jump starts and ends, its depths and its energy loss
  • Both candidate profiles shown, dotted, behind the result
  • Raise the tailwater and watch the jump move
Flume
A hydraulic jump on a steep slope, between an S3 profile and an S1 profile backed up from the downstream control

Built to teach

A guide and tutorials inside the app

Every analysis is explained in a guide that opens beside your work, with four tutorials to follow along and the methods behind each number. A question mark next to a heading explains just that part.

  • Step-by-step tutorials with the results you should see
  • SI and US customary units, converted when you switch
  • Light and dark appearance
Flume
A question mark popover listing which control depths give which profile

What it works out

One channel, three analyses. Change a number and everything follows.

Q = (k/n) A R^(2/3) √S

Uniform flow

Normal depth, discharge, slope, roughness or width; area, wetted perimeter, hydraulic radius, top width; velocity and bed shear.

Fr = 1

Critical flow

Critical depth and critical slope for every section, and whether the channel is mild or steep.

E = y + V²/2g

Specific energy

The energy diagram, the minimum energy and the alternate depth for any depth of flow.

M = Q²/gA + Aȳ

Hydraulic jump

Sequent depth, energy loss, efficiency, kind and length, from the specific force.

dy/dx = (S₀ − S_f)/(1 − Fr²)

Profiles

Twelve kinds of gradually varied profile by the direct step method, as a long section and a table.

gate · weir · jump

Controls

Sluice gates and sharp- or broad-crested weirs as boundary conditions, and the jump between two controls.

Methods, stated plainly

Flume says what it assumes. The same list is in the app, under Help.

  • Manning's equation, with k = 1 (SI) or 1.486 (US)
  • An energy coefficient α you can set; momentum coefficient 1
  • Compound sections by the divided channel method
  • Profiles by the direct step method, in a prismatic channel
  • Jumps from the balance of specific force and weight along the bed
  • Gates free or submerged; weirs flowing free

The hydraulics are checked against hand calculations and Chow's Open-Channel Hydraulics examples each time the app is built.

Flume Guide
The in-app guide, open on a tutorial about a gate and a hydraulic jump
Status. Flume is written in Tessel and developed on macOS. Version 0.1.0 is a free download for Macs with Apple silicon (2.2 MB), signed and notarized; the samples are channels to open in it. Results are for study and preliminary design: check anything that matters by another method.