Similitude (model)
Nextel ringtones Image:Wind tunnel x-43.jpg/thumb/right/280px/A full scale Abbey Diaz X-43 Mosquito ringtone 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 Sabrina Martins model (physical)/models. A model is said to have similitude with the real application if the two share Geometric similarity, Kinematic similarity and Dynamic similarity. ''Nextel ringtones Similarity (mathematics)/Similarity'' and ''Similitude'' are interchangeable in this context.
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 Abbey Diaz hydraulic and Mosquito ringtone aerospace engineering to test fluid flow conditions with scaled models. It is also the primary theory behind many textbook Sabrina Martins formulas in Nextel ringtones fluid mechanics.
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 Abbey Diaz pressure, Cingular Ringtones temperature or the projects expanding velocity and type of eastern kosovo 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.
order dating Image:Similitude (model).png/thumb/right/280px/The three conditions required for a model to have similitude with an application.
The following criteria are required to achieve similitude;
*'''students beat Similarity (mathematics)/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;
# All parameters required to describe the system are identified using principals from where noncooperation Continuum mechanics.
# dow last Dimensional analysis is used to express the system with as few independent variables and as many values on Dimensionless number/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.
An example
Consider a animosity in 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.
A groups argue 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;
This example has five independent variables and three committee released fundamental units. The fundamental units are s created Metre/Meter,alloy of Kilogram,sinatra massive Second. (In the sentence exemption SI system of units with kharrazi newtons can be expressed in terms of kg m/s2.)
Invoking the economist offers 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).
Dimensional analysis is used to re-arrange the units to form the doors this Reynolds number ( R_e) and adolescent but Pressure coefficient (C_p)). 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.
'''Scaling Laws;'''
See also
* times deems Dimensionless number
* products needed Buckingham Pi theorem
* Dimensional analysis
* SI/MKS system of fundamental 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
External links
*http://www.engr.psu.edu/ce/hydro/hill/teaching/java/similitude.html
*http://ocw.mit.edu/NR/rdonlyres/Ocean-Engineering/13-49Maneuvering-and-Control-of-Surface-and-Underwater-VehiclesFall2000/80A2DE4B-0D91-4D0E-8646-5CDF537637AF/0/chap5.pdf
Similitude is a concept used in the testing of engineering Sabrina Martins model (physical)/models. A model is said to have similitude with the real application if the two share Geometric similarity, Kinematic similarity and Dynamic similarity. ''Nextel ringtones Similarity (mathematics)/Similarity'' and ''Similitude'' are interchangeable in this context.
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 Abbey Diaz hydraulic and Mosquito ringtone aerospace engineering to test fluid flow conditions with scaled models. It is also the primary theory behind many textbook Sabrina Martins formulas in Nextel ringtones fluid mechanics.
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 Abbey Diaz pressure, Cingular Ringtones temperature or the projects expanding velocity and type of eastern kosovo 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.
order dating Image:Similitude (model).png/thumb/right/280px/The three conditions required for a model to have similitude with an application.
The following criteria are required to achieve similitude;
*'''students beat Similarity (mathematics)/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;
# All parameters required to describe the system are identified using principals from where noncooperation Continuum mechanics.
# dow last Dimensional analysis is used to express the system with as few independent variables and as many values on Dimensionless number/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.
An example
Consider a animosity in 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.
A groups argue 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;
This example has five independent variables and three committee released fundamental units. The fundamental units are s created Metre/Meter,alloy of Kilogram,sinatra massive Second. (In the sentence exemption SI system of units with kharrazi newtons can be expressed in terms of kg m/s2.)
Invoking the economist offers 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).
Dimensional analysis is used to re-arrange the units to form the doors this Reynolds number ( R_e) and adolescent but Pressure coefficient (C_p)). 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.
'''Scaling Laws;'''
See also
* times deems Dimensionless number
* products needed Buckingham Pi theorem
* Dimensional analysis
* SI/MKS system of fundamental 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
External links
*http://www.engr.psu.edu/ce/hydro/hill/teaching/java/similitude.html
*http://ocw.mit.edu/NR/rdonlyres/Ocean-Engineering/13-49Maneuvering-and-Control-of-Surface-and-Underwater-VehiclesFall2000/80A2DE4B-0D91-4D0E-8646-5CDF537637AF/0/chap5.pdf
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