Dimensionless quantities, also known as quantities of dimension one are implicitly defined in a manner that prevents their aggregation into units of measurement. Typically expressed as ratios that align with another system, these quantities do not necessitate explicitly defined units. For instance, alcohol by volume (ABV) represents a volumetric ratio. Its derivation remains independent of the specific units of volume used; any common unit may be applied. Notably, ABV is never expressed as milliliters per milliliter or ounces per ounce, underscoring its dimensionless nature.
In fluid mechanics, the Rayleigh number (Ra, after Lord Rayleigh) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free (or natural) convection. It characterises the fluid's flow regime: a value in a certain lower range denotes laminar flow; a value in a higher range, turbulent flow. Below a certain critical value, there is no fluid motion and heat transfer is by conduction rather than convection. For most engineering purposes, the Rayleigh number is large, somewhere around 106 to 108.
Bernoulli's principle is a key concept in fluid dynamics that relates pressure, speed and height. Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or the fluid's potential energy. The principle is named after the Swiss mathematician and physicist Daniel Bernoulli, who published it in his book Hydrodynamica in 1738. Although Bernoulli deduced that pressure decreases when the flow speed increases, it was Leonhard Euler in 1752 who derived Bernoulli's equation in its usual form.
An isentropic process is an idealized thermodynamic process that is both adiabatic and reversible. The work transfers of the system are frictionless, and there is no net transfer of heat or matter. Such an idealized process is useful in engineering as a model of and basis of comparison for real processes. This process is idealized because reversible processes do not occur in reality; thinking of a process as both adiabatic and reversible would show that the initial and final entropies are the same, thus, the reason it is called isentropic. Thermodynamic processes are named based on the effect they would have on the system. Even though in reality it is not necessarily possible to carry out an isentropic process, some may be approximated as such.
Fluid statics or hydrostatics is the branch of fluid mechanics that studies fluids at hydrostatic equilibrium and "the pressure in a fluid or exerted by a fluid on an immersed body".
Thermodynamics is expressed by a mathematical framework of thermodynamic equations which relate various thermodynamic quantities and physical properties measured in a laboratory or production process. Thermodynamics is based on a fundamental set of postulates, that became the laws of thermodynamics.
In physics and engineering, mass flow rate is the mass of a substance which passes per unit of time. Its unit is kilogram per second in SI units, and slug per second or pound per second in US customary units. The common symbol is , although sometimes μ is used.
The Fanning friction factor, named after John Thomas Fanning, is a dimensionless number used as a local parameter in continuum mechanics calculations. It is defined as the ratio between the local shear stress and the local flow kinetic energy density:
Fluid mechanics is that branch of physics concerned with the mechanics of fluids and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical, and biomedical engineering, as well as geophysics, oceanography, meteorology, astrophysics, and biology.
The heat capacity rate is heat transfer terminology used in thermodynamics and different forms of engineering denoting the quantity of heat a flowing fluid of a certain mass flow rate is able to absorb or release per unit temperature change per unit time. It is typically denoted as C, listed from empirical data experimentally determined in various reference works, and is typically stated as a comparison between a hot and a cold fluid, Ch and Cc either graphically, or as a linearized equation. It is an important quantity in heat exchanger technology common to either heating or cooling systems and needs, and the solution of many real world problems such as the design of disparate items as different as a microprocessor and an internal combustion engine.
In thermodynamics, vapor quality is the mass fraction in a saturated mixture that is vapor; in other words, saturated vapor has a "quality" of 100%, and saturated liquid has a "quality" of 0%. Vapor quality is an intensive property which can be used in conjunction with other independent intensive properties to specify the thermodynamic state of the working fluid of a thermodynamic system. It has no meaning for substances which are not saturated mixtures . Vapor quality is an important quantity during the adiabatic expansion step in various thermodynamic cycles. Working fluids can be classified by using the appearance of droplets in the vapor during the expansion step.
A compressed fluid is a fluid under mechanical or thermodynamic conditions that force it to be a liquid.
Chilton–Colburn J-factor analogy is a successful and widely used analogy between heat, momentum, and mass transfer. The basic mechanisms and mathematics of heat, mass, and momentum transport are essentially the same. Among many analogies developed to directly relate heat transfer coefficients, mass transfer coefficients, and friction factors Chilton and Colburn J-factor analogy proved to be the most accurate.
In fluid mechanics, pipe flow is a type of fluid flow within a closed conduit, such as a pipe, duct or tube. It is also called as Internal flow. The other type of flow within a conduit is open channel flow. These two types of flow are similar in many ways, but differ in one important aspect. Pipe flow does not have a free surface which is found in open-channel flow. Pipe flow, being confined within closed conduit, does not exert direct atmospheric pressure, but does exert hydraulic pressure on the conduit.
In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a formula in order to predict some characteristics of the system, and it is usually required by the construction of a dimensionless quantity, in the general framework of dimensional analysis and in particular applications such as fluid mechanics.
In fluid mechanics, non-dimensionalization of the Navier–Stokes equations is the conversion of the Navier–Stokes equation to a nondimensional form. This technique can ease the analysis of the problem at hand, and reduce the number of free parameters. Small or large sizes of certain dimensionless parameters indicate the importance of certain terms in the equations for the studied flow. This may provide possibilities to neglect terms in the considered flow. Further, non-dimensionalized Navier–Stokes equations can be beneficial if one is posed with similar physical situations – that is problems where the only changes are those of the basic dimensions of the system.
Equimolar counterdiffusion is an instance of molecular diffusion in a binary mixture, and occurs when equal numbers of molecules of the two substances are moving in opposite directions.
In fluid dynamics, the entrance length is the distance a flow travels after entering a pipe before the flow becomes fully developed. Entrance length refers to the length of the entry region, the area following the pipe entrance where effects originating from the interior wall of the pipe propagate into the flow as an expanding boundary layer. When the boundary layer expands to fill the entire pipe, the developing flow becomes a fully developed flow, where flow characteristics no longer change with increased distance along the pipe. Many different entrance lengths exist to describe a variety of flow conditions. Hydrodynamic entrance length describes the formation of a velocity profile caused by viscous forces propagating from the pipe wall. Thermal entrance length describes the formation of a temperature profile. Awareness of entrance length may be necessary for the effective placement of instrumentation, such as fluid flow meters.
In engineering and physics, gc is a unit conversion factor used to convert mass to force or vice versa. It is defined as
In fluid mechanics, kinematic similarity is described as “the velocity at any point in the model flow is proportional by a constant scale factor to the velocity at the same point in the prototype flow, while it is maintaining the flow’s streamline shape.” Kinematic Similarity is one of the three essential conditions to complete the similarities between a model and a prototype. The kinematic similarity is the similarity of the 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
