 A full scale X-43 Wind tunnel test. The test is designed to have dynamic similitude with the real application to insure valid results. Similitude is a concept used in the testing of engineering models. A model is said to have similitude with the real application if the two share geometric similarity, kinematic similarity and dynamic similarity. Similarity and similitude are interchangeable in this context. Download high resolution version (1056x842, 102 KB) Wikipedia does not have an article with this exact name. ...
Download high resolution version (1056x842, 102 KB) Wikipedia does not have an article with this exact name. ...
NASA technicians working on the X-43A at the tip of a Pegasus rocket attached to a Boeing B-52B prior to launch (March 27, 2004) The X-43 is an unmanned experimental hypersonic aircraft design with multiple planned scale variations meant to test different aspects of highly supersonic flight. ...
A wind tunnel is a research tool developed to assist with studying the effects of air moving over or around solid objects. ...
A physical model is used in various contexts to mean a physical representation of some thing. ...
Several equivalence relations in mathematics are called similarity. ...
The term dynamic similitude is often used as a catch-all because it implies that geometric and kinematic similitude have already been met.
Similitude's main application is in hydraulic and aerospace engineering to test fluid flow conditions with scaled models. It is also the primary theory behind many textbook formulas in fluid mechanics. Hydraulics is a branch of science and engineering concerned with the use of liquids to perform mechanical tasks. ...
The study, the science and the technology of travel in the space above the Earth. ...
In mathematics and in the sciences, a formula is a concise way of expressing information symbolically (as in a mathematical or chemical formula), or a general relationship between quantities. ...
Fluid mechanics or fluid dynamics is the study of the macroscopic physical behaviour of fluids . ...
Overview Engineering models are used to study complex fluid dynamics problems where calculations and computer simulations aren't reliable. Models are usually smaller than the final design, but not always. Scale models allow testing of a design prior to building, and in many cases are a critical step in the development process.
Construction of a scale model, however, must be accompanied with an analysis to determine what conditions it is tested under. While the geometry may be simply scaled, other parameters, such as pressure, temperature or the velocity and type of fluid may need to be altered. Similitude is achieved when testing conditions are created such that the test results are applicable to the real design. Pressure is the application of force to a surface, and the concentration of that force in a given area. ...
Temperature is the physical property of a system which underlies the common notions of hot and cold; the material with the higher temperature is said to be hotter. ...
Velocity (symbol: v) is a vector measurement of the rate and direction of motion. ...
A subset of the phases of matter, fluids include liquids, gases, plasmas and, to some extent, plastic solids. ...
 The three conditions required for a model to have similitude with an application. The following criteria are required to achieve similitude; Wikipedia does not have an article with this exact name. ...
Wikipedia does not have an article with this exact name. ...
- Geometric similarity - The model is the same shape as the application, usually scaled.
- Kinematic similarity - Fluid flow of both the model and real application must undergo similar time rates of change motions. (fluid streamlines are similar)
- Dynamic similarity - Ratios of all forces acting on corresponding fluid particles and boundary surfaces in the two systems are constant.
To satisfy the above conditions the application is analyzed; Several equivalence relations in mathematics are called similarity. ...
- All parameters required to describe the system are identified using principals from Continuum mechanics.
- Dimensional analysis is used to express the system with as few independent variables and as many dimensionless parameters as possible.
- The values of the dimensionless parameters are held to be the same for both the scale model and application. This can be done because they are dimensionless and will insure dynamic similitude between the model and the application. The resulting equations are used to derive scaling laws which dictate model testing conditions.
It is often impossible to achieve strict similitude during a model test. The greater the departure from the application's operating conditions, the more difficult achieving similitude is. In these cases some aspects of similitude may be neglected, focusing on only the most important parameters.-1...
Dimensional analysis is a conceptual tool often applied in physics, chemistry, and engineering to understand physical situations involving a mix of different kinds of physical quantities. ...
In the physical sciences, a dimensionless number (or more precisely, a number with the dimensions of 1) is a quantity which describes a certain physical system and which is a pure number without any physical units; it does not change if one alters ones system of units of measurement...
The design of marine vessels remains more of an art than a science in large part because dynamic similitude is especially difficult to attain for a vessel that is partially submerged: a ship is affected by wind forces in the air above it, by hydrodynamic forces within the water under it, and especially by wave motions at the interface between the water and the air. The scaling requirements for each of these phenomena differ, so models cannot replicate what happens to a full sized vessel nearly so well as can be done for an aircraft or submarine -- each of which operates entirely within one medium.
An example Consider a submarine modeled at 1/40th scale. The application operates in sea water at 0.5 °C, moving at 5 m/s. The model will be tested in fresh water at 20 °C. Find the power required for the submarine to operate at the stated speed. USS Los Angeles A submarine is a specialized watercraft that can operate underwater. ...
A free body diagram is constructed and the relevant relationships of force and velocity are formulated using techniques from continuum mechanics. The variables which describe the system are; Drawing a free body diagram is a method often used by physicists working out kinetics or other mechanics problems to show all the mechanical vector forces acting on the given free body (or bodies) at any given time. ...
| Variable | Application | Scaled model | Units | | L (diameter of submarine) | 1 | 1/40 | (unit length) | | V (Speed) | 5 | Calculate | (m/s) | | ρ (Density) | 1028 | 998 | (kg/m3) | | μ (Dynamic Viscosity) | 1.88 | 1.00 | Pa·s (N s/m2) | | F (force) | Calculate | To be measured | N (kg m/s2) | This example has five independent variables and three fundamental units. The fundamental units are Meter,Kilogram,Second. (In the SI system of units newtons can be expressed in terms of kg m/s2.) In general English usage, length (symbols: l, L) is but one particular instance of distance – an objects length is how long the object is – but in the physical sciences and engineering, the word length is in some contexts used synonymously with distance. Height is vertical distance; width (or breadth...
Speed (symbol: v) is the rate of motion, or equivalently the rate of change of position, expressed as distance d moved per unit of time t. ...
Density (symbol: ρ - Greek: rho) is a measure of mass per unit of volume. ...
The Pitch Drop Experiment at the University of Queensland. ...
The pascal (symbol Pa) is the SI unit of pressure. ...
In physics, as defined by Asimov, a force is that which can impose a change of velocity on a material body. ...
In physics, the newton (symbol: N) is the SI unit of force, named after Sir Isaac Newton in recognition of his work on classical mechanics. ...
In the language of measurement, quantities are quantifiable aspects of the world, such as time, distance, velocity, mass, and weight, and units measure them. ...
The metre, symbol: m, is the basic unit of distance (or of length, in the parlance of the physical sciences) in the International System of Units. ...
The international prototype, made of platinum-iridium, which is kept at the BIPM under conditions specified by the 1st CGPM in 1889. ...
The second (symbol s) is a unit for time, and one of seven SI base units. ...
The International System of Units (abbreviated SI from the French phrase, Système International dUnités) is the most widely used system of units. ...
In physics, the newton (symbol: N) is the SI unit of force, named after Sir Isaac Newton in recognition of his work on classical mechanics. ...
Invoking the Buckingham Pi theorem shows that the system can be described with two dimensionless numbers and one independent variable (5 variables - 3 fundamental units => 2 dimensionless numbers). The Buckingham π theorem is a key theorem in dimensional analysis. ...
Dimensional analysis is used to re-arrange the units to form the Reynolds number (Re) and Pressure coefficient (Cp)). These dimensionless numbers account for all the variables listed above except F, which will be the test measurement. Since the dimensionless parameters will stay constant for both the test and the real application, they will be used to formulate scaling laws for the test. The Reynolds number is the most important dimensionless number in fluid dynamics and provides a criterion for determining dynamic similitude. ...
The pressure coefficient is a dimensionless number used in aerodynamics. ...
Scaling Laws;
This gives a required test velocity of;
 .
The force measured from the model at that velocity is then scaled to find the force that can be expected for the real application;
The power required by the submarine is then;
Note that even though the model is scaled smaller, the water velocity needs to be increased for testing. This remarkable result shows how similitude in nature is often counterintuitive.
Typical applications Similitude has been well documented for a large number of engineering problems and is the basis of many textbook formulas and dimensionless quantities. These formulas and quantities are easy to use without having to repeat the laborious task of dimensional analysis and formula derivation. Simplification of the formulas (by neglecting some aspects of similitude) is common, and needs to be reviewed by the engineer for each application.
Similitude can be used to predict the performance of a new design based on data from an existing, similar design. In this case, the model is the existing design. Another use of similitude and models is in validation of computer simulations with the ultimate goal of eliminating the need for physical models altogether. A computer simulation or a computer model is a computer program which attempts to simulate an abstract model of a particular system. ...
Another application of similitude is to replace the operating fluid with a different test fluid. Wind tunnels, for example, have trouble with air liquefying in certain conditions so helium is sometimes used. Other applications may operate in dangerous or expensive fluids so the testing is carried out in a more convenient substitute. General Name, Symbol, Number helium, He, 2 Chemical series noble gases Group, Period, Block 18, 1, s Appearance colorless Atomic mass 4. ...
Some common applications of similitude and associated dimensionless numbers;
The Reynolds number is the most important dimensionless number in fluid dynamics and provides a criterion for determining dynamic similitude. ...
The pressure coefficient is a dimensionless number used in aerodynamics. ...
In fluid dynamics, the Froude number (named after William Froude) is the reciprocal of the square root of the Richardson number. ...
Weber number is a dimensionless quantity that is often useful in analysing fluid flows where there is an interface between two different fluids, especially for multiphase flows with strongly curved surfaces. ...
The Reynolds number is the most important dimensionless number in fluid dynamics and provides a criterion for determining dynamic similitude. ...
Mach number (Ma) is defined as a ratio of speed to the speed of sound in the medium in case. ...
Prandtl Number is a dimensionless number approximating the ratio of momentum diffusivity and thermal diffusivity, It is defined as: where is the kinematic viscosity and α is the thermal diffusivity. ...
In dimensional analysis, the Strouhal number is a dimensionless number describing oscillating flow mechanisms. ...
The Reynolds number is the most important dimensionless number in fluid dynamics and provides a criterion for determining dynamic similitude. ...
Mach number (Ma) is defined as a ratio of speed to the speed of sound in the medium in case. ...
The pressure coefficient is a dimensionless number used in aerodynamics. ...
See also In the physical sciences, a dimensionless number (or more precisely, a number with the dimensions of 1) is a quantity which describes a certain physical system and which is a pure number without any physical units; it does not change if one alters ones system of units of measurement...
The Buckingham π theorem is a key theorem in dimensional analysis. ...
Dimensional analysis is a conceptual tool often applied in physics, chemistry, and engineering to understand physical situations involving a mix of different kinds of physical quantities. ...
The International System of Units (abbreviated SI from the French phrase, Système International dUnités) is the most widely used system of units. ...
References - Binder, Raymond C.,Fluid Mechanics, Fifth Edition, Prentice-Hall, Englwood Cliffs, N.J., 1973.
- Howarth, L. (editor), Modern Developments in Fluid Mechanics, High Speed Flow, Oxford at the Clarendon Press, 1953.
- Kline, Stephen J., "Similitude and Approximation Theory", Springer-Verlag, New York, 1986. ISBN 0387165185
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