Examples#
This gallery walks through every public feature of
engineeringkit.fluid_engineering, one breakthrough per script:
hydrostatics, flow meters, orifices and weirs, the momentum of jets, pipe
friction from Hagen and Poiseuille to Swamee and Jain, Couette flow, drag
on spheres, ship models and dimensional analysis, open channels, water
hammer, turbomachines, pump cavitation and pipe networks.
Units, assumptions and numerical validation
gives the physical validity limits. Each script is self-contained and can be
run directly with python examples/fluid_engineering/<section>/<script>.py.
Sections#
hydrostatics – Archimedes’s principle and Stevin’s hydrostatic paradox.
measurement – Pitot’s tube, Venturi’s meter, Torricelli’s orifice and Thomson’s V-notch weir.
momentum – Pelton’s water wheel.
pipe_flow – Hagen-Poiseuille, Darcy-Weisbach, Reynolds’s transition, Nikuradse’s roughness, Colebrook’s equation, Moody’s diagram and Swamee-Jain.
viscous – Couette’s rotating-cylinder viscometer.
drag – Stokes’s drag on a sphere.
similarity – Froude’s ship models and Buckingham’s Pi theorem.
open_channel – Manning’s formula, Bélanger’s hydraulic jump and Bakhmeteff’s specific energy.
transients – Joukowsky’s water hammer.
pumps – Thoma’s cavitation parameter and Euler’s turbine equation.
networks – Hardy Cross’s method for pipe networks.
Drag#
The drag on a sphere, from creeping flow to the drag crisis.
Hydrostatics#
Pressure in a fluid at rest, buoyancy and forces on submerged surfaces.
Measurement#
Flow speed and flow rate from pressure differences, orifices and weirs.
Momentum#
Forces from turning a stream: jets, vanes and pipe bends.
Networks#
Looped pipe networks.
Open channels#
Flow with a free surface: uniform flow, specific energy and the hydraulic jump.
Pipe flow#
Laminar and turbulent flow in pipes, head losses and friction factors.
Hagen and Poiseuille: laminar pipe flow (1839-1840)
Weisbach and Darcy: head loss in pipes (1845-1857)
Pumps#
Turbomachine head, pump power and cavitation.
Similarity#
Dimensionless groups, model testing and dimensional analysis.
Transients#
Pressure waves in pipelines.
Viscous flow#
Exact laminar solutions between moving walls.
