Steady flow
Steady flow is fluid motion in which properties such as velocity, pressure, and density at each fixed location remain constant over time.
Continuity equation: A conservation equation stating that mass entering and leaving a flow region must balance, accounting for accumulation within it. In steady flow, no mass accumulates at a fixed location, simplifying the mass balance.
Fluid mechanics: The study of fluids at rest and in motion, including forces, transport, and deformation. Steady flow is one regime within the broader study of fluid motion.
Open-channel flow: Liquid flow with a free surface exposed to a gas, driven primarily by gravity. Steady conditions let channel depth and discharge be analyzed as constant at each section.
Laminar flow: Fluid motion in which nearby layers move smoothly with limited cross-layer mixing. Laminar describes motion structure, not whether properties change with time.
Leonhard Euler: An eighteenth-century mathematician and physicist whose work helped establish mathematical fluid mechanics. Euler's equations provide a foundational description of ideal fluid motion, including steady cases.
Bernoulli's principle: A relation among pressure, speed, and elevation for ideal fluid motion along a streamline. For steady, inviscid flow, it relates changing speed and elevation to pressure.
Velocity field: A description assigning a fluid velocity vector to each position and time. Steadiness means this field has no time dependence at any fixed position.
Pipe flow: Fluid motion through a closed conduit, commonly driven by pressure differences or pumps. Steady pipe-flow analysis predicts pressure loss and flow rate in operating systems.
Turbulent flow: Irregular fluid motion with fluctuating velocity and strong mixing across scales. Turbulence can be statistically steady even though instantaneous properties fluctuate.
Claude-Louis Navier: A French engineer and physicist who formulated equations accounting for viscosity in fluid motion. The Navier–Stokes framework describes viscous flows that may reach steady conditions.