In fluid dynamics, laminar flow is characterized by fluid particles following smooth paths in layers, with each layer moving smoothly past the adjacent layers with little or no mixing. At low velocities, the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross-currents perpendicular to the direction of flow, nor eddies or swirls of fluids. In laminar flow, the motion of the particles of the fluid is very orderly with particles close to a solid surface moving in straight lines parallel to that surface. Laminar flow is a flow regime characterized by high momentum diffusion and low momentum convection.
Rheology is the study of the flow of matter, primarily in a liquid or gas state, but also as "soft solids" or solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an applied force. Rheology is a branch of physics, and it is the science that deals with the deformation and flow of materials, both solids and liquids.
In dimensional analysis, a dimensionless quantity is a quantity to which no physical dimension is assigned, also known as a bare, pure, or scalar quantity or a quantity of dimension one, with a corresponding unit of measurement in the SI of the unit one, which is not explicitly shown. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Dimensionless quantities are distinct from quantities that have associated dimensions, such as time. However, the symbols rad and sr are written explicitly where appropriate, in order to emphasize that, for radians or steradians, the quantity being considered is, or involves the plane angle or solid angle respectively. For example, etendue is defined as having units of meters times steradians.
In dimensional analysis, the Strouhal number is a dimensionless number describing oscillating flow mechanisms. The parameter is named after Vincenc Strouhal, a Czech physicist who experimented in 1878 with wires experiencing vortex shedding and singing in the wind. The Strouhal number is an integral part of the fundamentals of fluid mechanics.
The Grashof number (Gr) is a dimensionless number in fluid dynamics and heat transfer which approximates the ratio of the buoyancy to viscous force acting on a fluid. It frequently arises in the study of situations involving natural convection and is analogous to the Reynolds number. It's believed to be named after Franz Grashof. Though this grouping of terms had already been in use, it wasn't named until around 1921, 28 years after Franz Grashof's death. It's not very clear why the grouping was named after him.
In fluid dynamics, the Darcy–Weisbach equation is an empirical equation that relates the head loss, or pressure loss, due to friction 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 and Julius Weisbach. Currently, there is no formula more accurate or universally applicable than the Darcy-Weisbach supplemented by the Moody diagram or Colebrook equation.
In viscous fluid dynamics, the Archimedes number (Ar), is a dimensionless number used to determine the motion of fluids due to density differences, named after the ancient Greek scientist and mathematician Archimedes.
The Ekman number (Ek) is a dimensionless number used in fluid dynamics to describe the ratio of viscous forces to Coriolis forces. It is frequently used in describing geophysical phenomena in the oceans and atmosphere in order to characterise the ratio of viscous forces to the Coriolis forces arising from planetary rotation. It is named after the Swedish oceanographer Vagn Walfrid Ekman.
A Bingham plastic is a viscoplastic material that behaves as a rigid body at low stresses but flows as a viscous fluid at high stress. It is named after Eugene C. Bingham who proposed its mathematical form.
In fluid dynamics, the capillary number (Ca) is a dimensionless quantity representing the relative effect of viscous drag forces versus surface tension forces acting across an interface between a liquid and a gas, or between two immiscible liquids. For example, an air bubble in a liquid flow tends to be deformed by the friction of the liquid flow due to viscosity effects, but the surface tension forces tend to minimize the surface area. The capillary number is defined as:
In fluid dynamics, drag is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid. This can exist between two fluid layers or a fluid and a solid surface. Unlike other resistive forces, such as dry friction, which are nearly independent of velocity, drag force depends on velocity.
In fluid dynamics, the Taylor number (Ta) is a dimensionless quantity that characterizes the importance of centrifugal "forces" or so-called inertial forces due to rotation of a fluid about an axis, relative to viscous forces.
In fluid dynamics the Eötvös number (Eo), also called the Bond number (Bo), is a dimensionless number measuring the importance of gravitational forces compared to surface tension forces and is used to characterize the shape of bubbles or drops moving in a surrounding fluid. The two names commemorate the Hungarian physicist Loránd Eötvös (1848–1919) and the English physicist Wilfrid Noel Bond (1897–1937), respectively. The term Eötvös number is more frequently used in Europe, while Bond number is commonly used in other parts of the world.
The Womersley number is a dimensionless number in biofluid mechanics and biofluid dynamics. It is a dimensionless expression of the pulsatile flow frequency in relation to viscous effects. It is named after John R. Womersley (1907–1958) for his work with blood flow in arteries. The Womersley number is important in keeping dynamic similarity when scaling an experiment. An example of this is scaling up the vascular system for experimental study. The Womersley number is also important in determining the thickness of the boundary layer to see if entrance effects can be ignored.
The term friction loss has a number of different meanings, depending on its context.
The Reynolds number helps predict flow patterns in different fluid flow situations. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers flows tend to be turbulent. The turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow. These eddy currents begin to churn the flow, using up energy in the process, which for liquids increases the chances of cavitation. Reynolds numbers are an important dimensionless quantity in fluid mechanics.
In fluid mechanics, dynamic similarity is the phenomenon that when there are two geometrically similar vessels with the same boundary conditions and the same Reynolds and Womersley numbers, then the fluid flows will be identical. This can be seen from inspection of the underlying Navier-Stokes equation, with geometrically similar bodies, equal Reynolds and Womersley Numbers the functions of velocity (u’,v’,w’) and pressure (P’) for any variation of flow.
The Kapitza number (Ka) is a dimensionless number named after the prominent Russian physicist Pyotr Kapitsa. He provided the first extensive study of the ways in which a thin film of liquid flows down inclined surfaces. Expressed as the ratio of surface tension forces to inertial forces, the Kapitza number acts as an indicator of the hydrodynamic wave regime in falling liquid films. Liquid film behavior represents a subset of the more general class of free boundary problems. and is important in a wide range of engineering and technological applications such as evaporators, heat exchangers, absorbers, microreactors, small-scale electronics/microprocessor cooling schemes, air conditioning and gas turbine blade cooling.
Dimensionless numbers in fluid mechanics are a set of dimensionless quantities that have an important role in analyzing the behavior of fluids. Common examples include the Reynolds or the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, flow speed, etc.
In the field of fluid mechanics, kinematic similarity means, when the velocity at any point in the model flow is proportional by a constant scale factor to the velocity at the homologous point in the prototype flow, while considering it is maintaining the same flow streamline shape. This is one of the three necessary conditions for complete similarities between a model and a prototype. The kinematic similarity is the similarity of motion of the fluid. Since motions can be expressed with distance and time, it implies the similarity of lengths and, in addition, a similarity of the time interval. To achieve kinematic similarity in a scaled model, dimensionless numbers in fluid dynamics come into consideration. For example, Reynolds number of the model and the prototype must match. There are other dimensionless numbers that will also come into consideration, such as Womersley number
