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Vector field which is used to mathematically describe the motion of a continuum
continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is
Flow_velocity
Volume of fluid which passes per unit time
in particular fluid dynamics, the volumetric flow rate (also known as volume flow rate, or volume velocity) is the volume of fluid which passes per unit
Volumetric_flow_rate
Equations of motion for viscous fluids
viscous term (proportional to the gradient of velocity) and a pressure term—hence describing viscous flow. The Navier–Stokes equations generalize the Euler
Navier–Stokes_equations
Compressible flow velocity limiting effect
Choked flow is a compressible flow effect. The parameter that becomes "choked" or "limited" is the fluid velocity. Choked flow is a fluid dynamic condition
Choked_flow
Fluid flow in which density remains constant
incompressible flow is a flow in which the material density does not vary over time. Equivalently, the divergence of an incompressible flow velocity is zero
Incompressible_flow
Aspects of fluid mechanics involving fluid flow
involves the calculation of various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space and time
Fluid_dynamics
Flow velocity larger than wave velocity
A supercritical flow is a flow whose velocity is larger than the wave velocity.[clarification needed] The analogous condition in gas dynamics is supersonic
Supercritical_flow
Quantification of bulk fluid movement
flow. Flow may be measured by measuring the velocity of fluid over a known area. For very large flows, tracer methods may be used to deduce the flow rate
Flow_measurement
Motion characterized by chaotic changes in pressure and flow velocity
turbulent flow is fluid motion exhibiting chaotic changes in pressure and flow velocity. It is in contrast to laminar flow, which occurs when a fluid flows in
Turbulence
Speed that exceeds five times the speed of sound (Mach 5 and above)
(pressure, temperature, adiabatic index), and a moving gas by four (flow velocity), a hot gas in chemical equilibrium also requires state equations for
Hypersonic_speed
Average velocity of a fluid parcel in a gravity wave
dynamics, the Stokes drift velocity is the average velocity when following a specific fluid parcel as it travels with the fluid flow. For instance, a particle
Stokes_drift
Measure of arterial stiffness
Pulse wave velocity (PWV) is the velocity at which the blood pressure pulse propagates through the circulatory system, usually an artery or a combined
Pulse_wave_velocity
Average velocity of particles mainly moving randomly
at the Fermi velocity, resulting in an average velocity of zero. Applying an electric field adds to this random motion a small net flow in one direction;
Drift_velocity
Law describing the pressure drop in an incompressible and Newtonian fluid
no acceleration of fluid in the pipe. For velocities and pipe diameters above a threshold, actual fluid flow is not laminar but turbulent, leading to larger
Hagen–Poiseuille_equation
Hypothetical flow velocity
velocity (or superficial flow velocity), in engineering of multiphase flows and flows in porous media, is a hypothetical (artificial) flow velocity calculated
Superficial_velocity
Fluid flow revolving around an axis of rotation
Vortices are a major component of turbulent flow. The distribution of velocity, vorticity (the curl of the flow velocity), as well as the concept of circulation
Vortex
Scalar potential used in fluid dynamics
fluid dynamics and continuum mechanics, a velocity potential is a scalar potential used in potential flow theory. It was introduced by Joseph-Louis Lagrange
Velocity_potential
Field lines in a fluid flow
lines in a fluid flow. They differ only when the flow changes with time, that is, when the flow is not steady. Considering a velocity vector field in three-dimensional
Streamlines, streaklines, and pathlines
Streamlines,_streaklines,_and_pathlines
Equation for the velocity of a body in viscous fluid
object (meters); v → {\displaystyle {\vec {v}}} is the body velocity vector, not the flow velocity relative to the object (meters per second). Note the minus
Stokes's_law
Reaction using laminar dynamics
product/sample is taken, or by adjusting the velocity of the gas/fluid. Therefore the benefit of a laminar flow reactor is that the different factors that
Laminar_flow_reactor
Ratio of inertial to viscous forces acting on a liquid
}}} where: ρ is the density of the fluid (SI units: kg/m3) u is the flow velocity (m/s) L is a characteristic length (m) μ is the dynamic viscosity of
Reynolds_number
Dimensionless quantity in fluid dynamic
dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound. It is named after Austrian
Mach_number
Concept in physics
refer to a velocity profile (variation in velocity across layers of flow in a pipe), it is often used to mean the gradient of a flow's velocity with respect
Strain-rate_tensor
Component of stress coplanar with a material cross section
viscosity, u is the flow velocity, and y is the distance from the wall. It is used, for example, in the description of arterial blood flow, where there is
Shear_stress
Type of fluid
fluid's rate of flow cannot be altered by shaking, pumping, or stirring the fluid. Stresses are proportional to magnitude of the fluid's velocity vector. A
Newtonian_fluid
Equation in fluid dynamics
viscous shear forces along a given length of pipe to the average velocity of the fluid flow for an incompressible fluid. The equation is named after Henry
Darcy–Weisbach_equation
Technique for managing measurement of fluid flows
measure aspects of flow measurement are flow conditions within a pipe upstream of a meter. Flow conditions mainly refer to the flow velocity profile, irregularities
Flow_conditioning
Dimensionless number; ratio of a fluid's flow inertia to the external field
open channel flows, Belanger 1828 introduced first the ratio of the flow velocity to the square root of the gravity acceleration times the flow depth. When
Froude_number
Mass of a substance which passes per unit of time
{\displaystyle Q} = volume flow rate, ρ {\displaystyle \rho } = mass density of the fluid, v {\displaystyle \mathbf {v} } = flow velocity of the mass elements
Mass_flow_rate
Branch of dynamics concerned with studying the motion of air
fundamental relationship between pressure, density, and flow velocity for incompressible flow known today as Bernoulli's principle, which provides one
Aerodynamics
Type of fluid motion where all flow velocities are parallel to a fixed plane
a two-dimensional flow is a form of fluid flow where the flow velocity at every point is parallel to a fixed plane. The velocity at any point on a given
Two-dimensional_flow
Dynamics of blood flow
the vessel wall. In most cases, the mean velocity is used. There are many ways to measure blood flow velocity, like videocapillary microscoping with frame-to-frame
Hemodynamics
Velocity field as the gradient of a scalar function
The flow of a fluid of low viscosity, in regions that do not contain a boundary layer. See Prandtl hypothesis. Potential flow describes the velocity field
Potential_flow
Layer of fluid in the immediate vicinity of a bounding surface
condition (zero velocity at the wall). The flow velocity then monotonically increases above the surface until it returns to the bulk flow velocity. The thin
Boundary_layer
Branch of fluid mechanics
than 0.3 (since the density change due to velocity is about 5% in that case). The study of compressible flow is relevant to high-speed aircraft, jet engines
Compressible_flow
Flow where fluid particles follow smooth paths in layers
types of flow may occur depending on the velocity and viscosity of the fluid: laminar flow or turbulent flow. Laminar flow occurs at lower velocities, below
Laminar_flow
Force perpendicular to flow of surrounding fluid
with the velocity based on an incorrect assumption (the constriction of the flow produces the velocity field). We can calculate a velocity based on this
Lift_(force)
Equations of fluid dynamics
necessary assumption is that all the fields of interest including pressure, flow velocity, density, and temperature are at least weakly differentiable. The equations
Derivation of the Navier–Stokes equations
Derivation_of_the_Navier–Stokes_equations
Low-pressure voids formed in liquids
between the impeller and the pump housing at extremely high flow velocity. This flow velocity causes a vacuum to develop at the housing wall (similar to
Cavitation
Set of quasilinear hyperbolic equations governing adiabatic and inviscid flow
of momentum, together with the incompressibility condition that the flow velocity is divergence-free. The compressible Euler equations consist of equations
Euler equations (fluid dynamics)
Euler_equations_(fluid_dynamics)
Highest velocity attainable by a falling object
Terminal velocity is the maximum speed attainable by an object as it falls through a fluid (air is the most common example). It is reached when the sum
Terminal_velocity
Flow rate of water that is transported through a given cross-sectional area
is the volumetric flow rate (volume per time, in units of m3/h or ft3/h) of a stream. It equals the product of average flow velocity (with dimension of
Discharge_(hydrology)
Device which measures fluid flow velocity, typically around an aircraft or boat
A pitot tube (/ˈpiːtoʊ/ PEE-toh; also pitot probe) measures fluid flow velocity. It was invented by French engineer Henri Pitot during his work with aqueducts
Pitot_tube
Constraints to computational problems
inlet flow velocity is known. In outlet boundary conditions, the distribution of all flow variables needs to be specified, mainly flow velocity. This
Boundary conditions in fluid dynamics
Boundary_conditions_in_fluid_dynamics
Pinched tube generating supersonic flow
called choked flow. As the nozzle cross-sectional area increases, the gas begins to expand, and the flow increases to supersonic velocities, where a sound
De_Laval_nozzle
Equation for the force of drag
direction of the flow velocity, ρ {\displaystyle \rho } is the mass density of the fluid, u {\displaystyle u} is the flow velocity relative to the object
Drag_equation
Bedform in channeled environments
supercritical flow, meaning that the Froude number is greater than 1.0 or the flow velocity exceeds the wave velocity; this is also known as upper flow regime
Antidune
Equation for force on an object in sea waves
phase with the local flow acceleration and a drag force proportional to the (signed) square of the instantaneous flow velocity. The inertia force is
Morison_equation
Computational fluid dynamics tools
mass is a good parameterization of the flow velocity u of the parcel.) In the Lagrangian description, the flow is described by a function X ( x 0 , t
Lagrangian and Eulerian specification of the flow field
Lagrangian_and_Eulerian_specification_of_the_flow_field
Time rate of change of some physical quantity of a material element in a velocity field
continuum deformation. For example, in fluid dynamics, the velocity field is the flow velocity, and the quantity of interest might be the temperature of
Material_derivative
Function in fluid dynamics
function is used to describe the streamlines and flow velocity in a three-dimensional incompressible flow with axisymmetry. A surface with a constant value
Stokes_stream_function
Retarding force on a body moving in a fluid
relative velocity for low-speed flow and is proportional to the velocity squared for high-speed flow. This distinction between low and high-speed flow is measured
Drag_(physics)
Study of forces and their effect on motion
involves the calculation of various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space and time
Dynamics_(mechanics)
Form of shear stress
compare true velocities, such as the velocity of a flow in a stream, to a velocity that relates shear between layers of flow. Shear velocity is used to
Shear_velocity
Device for testing internal aerodynamics of engine parts
Once velocity has been calculated, the volume can be calculated by multiplying the velocity by the orifice area times its flow coefficient. A flow bench
Air_flow_bench
Mathematical expression for the stability of rocks in water currents
\Delta d=0.7{\frac {u^{2}}{2g}}} Here, the variables represent: uc = flow velocity in proximity to the stone Δ = relative density of the stone, calculated
Izbash_formula
Equation describing the evolution of the vorticity of a fluid particle as it flows
it moves with its flow; that is, the local rotation of the fluid (in terms of vector calculus this is the curl of the flow velocity). The governing equation
Vorticity_equation
Filtration by force through a semipermeable membrane
adjustments of cross-flow velocity to dislodge them. UF systems can either operate with cross-flow or dead-end flow. In dead-end filtration the flow of the feed
Ultrafiltration
Theoretical model of shear fluid flow
)-U''\varphi =0,} with U ( z ) {\displaystyle U(z)} the flow velocity of the steady base flow whose stability is to be studied and z {\displaystyle z}
Rayleigh's equation (fluid dynamics)
Rayleigh's_equation_(fluid_dynamics)
Topics referred to by the same term
above its liquid-vapor critical point Supercritical flow, where flow velocity is larger than wave velocity Supercritical, above the critical mass in nuclear
Supercritical
Principle relating to fluid dynamics
to apply: the flow must be steady, that is, the flow parameters (velocity, density, etc.) at any point cannot change with time, the flow must be incompressible—even
Bernoulli's_principle
Water turbine
two flow components (i.e. the vector sum), yields the net total "Apparent flow velocity" as shown in the next figure. The action of this apparent flow on
Gorlov_helical_turbine
Diagram of the component velocities of a turbomachine's working fluid
rotor. Vw = tangential component of V (absolute velocity), called Whirl velocity. Vf = flow velocity (axial component in case of axial machines, radial
Velocity_triangle
Pressure surge when a fluid is forced to stop or change direction suddenly
regulator. Lower fluid velocities. To keep water hammer low, pipe-sizing charts for some applications recommend flow velocity at or below 1.5 m/s (4.9 ft/s)
Hydraulic_shock
Equation used to calculate the electromigration of ions in a fluid
affected by an ionic concentration gradient ∇ c {\displaystyle \nabla c} , flow velocity v {\displaystyle {\bf {v}}} , and an electric field E {\displaystyle
Nernst–Planck_equation
Function for incompressible divergence-free flows in two dimensions
based on the following assumptions: The flow field can be described as two-dimensional plane flow, with velocity vector u = [ u ( x , y , t ) v ( x , y
Stream_function
Type of water turbine
(yellow) at minimum flow setting Cut-away view, with wicket gates (yellow) at full flow setting Usually the flow velocity (velocity perpendicular to the
Francis_turbine
Equation describing the flow of a fluid through a porous medium
Darcy flux or Darcy velocity, is not the velocity at which the fluid is travelling through the pores. It is the volumetric flux, or flow rate per unit area
Darcy's_law
Geological feature resulting from the movement of bed material by fluid flow
Bedforms are often characteristic to the flow parameters, and may be used to infer flow depth and velocity, and therefore the Froude number. Bedforms
Bedform
Hydrodynamic distortions of tides
of the flood flow velocities, while increasing the ebb flow velocities. Since the friction scales quadratically with the flow velocities, the increase
Nonlinear_tides
Pseudovector field describing the local rotation of a continuum near some point
vorticity ω {\displaystyle {\boldsymbol {\omega }}} is the curl of the flow velocity v {\displaystyle \mathbf {v} } : ω ≡ ∇ × v , {\displaystyle {\boldsymbol
Vorticity
Dimensionless parameter to quantify fluid resistance
in the direction of the flow velocity; ρ {\displaystyle \rho } is the mass density of the fluid; u {\displaystyle u} is the flow speed of the object relative
Drag_coefficient
Estimate of velocity in open channel flows
equation is an empirical formula estimating the average velocity of a liquid in an open channel flow (flowing in a conduit that does not completely enclose
Manning_formula
Fluid dynamics calculation
formula is a semi-empirical resistance equation which estimates mean flow velocity in open channel conduits. The relationship was conceptualized and developed
Chézy_formula
Study of the flow of matter, primarily in a fluid state
rate (the relative flow velocity) are called non-Newtonian fluids. Key Rheological Models Different materials exhibit diverse flow behaviors that can
Rheology
Branch of physics which studies the behavior of materials modeled as continuous media
derivative is the instantaneous flow velocity v {\displaystyle \mathbf {v} } of the particle. Therefore, the flow velocity field of the continuum is given
Continuum_mechanics
Flight faster than Mach 5 below 90 km
=\sin ^{-1}(a/v)} where a is the speed of the sound wave and v is the flow velocity. Since M=v/a, the equation becomes μ = sin − 1 ( 1 / M ) {\displaystyle
Hypersonic_flight
Curved propagating disturbance wave
non-isentropic and the shock decreases the flow velocity from supersonic velocity upstream to subsonic velocity downstream. The bow shock significantly increases
Bow_shock_(aerodynamics)
Entropy production in Newtonian fluids
} is the second Lamé parameter, v {\displaystyle {\bf {v}}} is the flow velocity, ∇ {\displaystyle \nabla } is the del operator used to characterize
General equation of heat transfer
General_equation_of_heat_transfer
Class of computational fluid dynamics methods
Velocity = a.field[y][x][v] FirstTerm = Velocity # The Flow Velocity FlowVelocity = velocityField[y][x] Dotted = ( FlowVelocity[0] * DiscreteVelocityVectors[v][0]
Lattice_Boltzmann_methods
Simultaneous flow of materials with two or more thermodynamic phases
fluids and their flow rates. As velocity and gas-liquid ratio is increased, "bubble flow" transitions into "mist flow". At high liquid-gas ratios, liquid
Multiphase_flow
Movement of air
and turbulent flow patterns. Laminar flow occurs when air can flow smoothly, and exhibits a parabolic velocity profile; turbulent flow occurs when there
Airflow
Far from the surface the flow velocity must be a constant, so C = 0 {\displaystyle C=0} . We have imposed zero flow velocity at z = 0 {\displaystyle z=0}
Diffusiophoresis and diffusioosmosis
Diffusiophoresis_and_diffusioosmosis
Ratio between local shear stress and bulk dynamic pressure within a flow
u^{2}} ρ is the density of the fluid (kg/m3 or lbm/ft3) u is the bulk flow velocity (m/s or ft/s) In particular the shear stress at the wall can, in turn
Fanning_friction_factor
Propagating disturbance
shock wave the properties of the fluid (density, pressure, temperature, flow velocity, Mach number) change almost instantaneously. Measurements of the thickness
Shock_wave
Millennium Prize Problem
now consider the flow near the circular obstacle. In this region, the velocity of the fluid will be higher than the uniform flow velocity v 0 {\displaystyle
Navier–Stokes existence and smoothness
Navier–Stokes_existence_and_smoothness
Rate at which air moves from high- to low-pressure areas
and cyclones as freak weather conditions can drastically affect the flow velocity of the wind.[citation needed] The fastest wind speed not related to
Wind_speed
CSF Flow MRI overview, methodology, and application
fluid (CSF) flow MRI is used to assess pulsatile CSF flow both qualitatively and quantitatively. Time-resolved 2D phase-contrast MRI with velocity encoding
Cerebrospinal_fluid_flow_MRI
Device for measuring flow of a fluid
proportional to the flow velocity perpendicular to the flux lines. The physical principle at work is electromagnetic induction. The magnetic flow meter requires
Magnetic_flow_meter
Dimensionless metric in fluid dynamics
\rho } is the mass density, u {\displaystyle u} is a representative flow velocity, and z {\displaystyle z} is depth. The Richardson number given above
Richardson_number
Mathematical algorithm
motion of a continuum. The length of the flow velocity vector is the flow speed and is a scalar. The flow velocity u {\displaystyle \mathbf {u} } of a fluid
Lambda2_method
Machine for continuous flow gas compression
absolute velocities at the inlet and outlet respectively. V f 1 {\displaystyle V_{f1}\,} and V f 2 {\displaystyle V_{f2}\,} are the axial flow velocities at
Axial_compressor
Phenomenon of fluid mechanics
a fluid instability that occurs when there is velocity shear in a single continuous fluid or a velocity difference across the interface between two fluids
Kelvin–Helmholtz_instability
Method for determining sediment motion in rivers
does not show that sedimentation is caused by flow velocity deceleration and erosion is caused by flow acceleration. The dimensionless Shields Diagram
Hjulström_curve
{m}}|\nabla G|} where ρ {\displaystyle \rho } is the flow density, v {\displaystyle v} is the flow velocity and m ˙ = m ˙ ( x , t ) {\displaystyle {\dot {m}}={\dot
G_equation
Equation describing evolution of waves in shallow water
surface elevation η ( x , t ) {\displaystyle \eta (x,t)} and horizontal flow velocity u ( x , t ) , {\displaystyle u(x,t),} with x {\displaystyle x} the horizontal
Green's_law
Imbalance of electric charges within or on the surface of a material
prescribes pipe flow velocity limits. Because water content has a large impact on the fluids dielectric constant, the recommended velocity for hydrocarbon
Static_electricity
Fluid dynamics theory on gravity waves
wavelength (for waves in deep water). Airy wave theory uses a potential flow (or velocity potential) approach to describe the motion of gravity waves on a fluid
Airy_wave_theory
Movement of solid particles, typically by gravity and fluid entrainment
flow, and moves at a large fraction of the mean flow velocity in the stream. A common characterization of suspended sediment concentration in a flow is
Sediment_transport
Abnormal sound from turbulent arterial blood flow
frequency dependent on the heart rate. Anything increasing the blood flow velocity such as fever, anemia, hyperthyroidism, or physical exertion, can increase
Bruit
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