ch-7-similitude,dimensional analysis & modeling

Similitude,Dimensional analysis, and modeling

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Similitude, Dimensional Analysis, and Modeling


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Think of the variables, that affect the pressure drop in a unit length of pipe?


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Correlation of Experimental DataDimensional analysis greatly facilitates the efficient handling, interpretation,and correlation of experimental data.

If only one pi term is involved in a problem, it must be equal to a constant.


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For problems involving only two pi terms, results of an experiment can beconveniently presented in a simple graph.


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For problems involving more than two or three pi terms, it is often necessary to use a model to predict specific characteristics.


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Modeling and SimilitudeAn engineering model is used to predict the behavior of the physical systemof interest

A model is a representation of a physical system that may be used to predict the behavior of the system in some desired respect.

The physical system for which the predictions are to be made is called the prototype. Prototype can also be termed as a full scale experimental system, (thus a model).

Theory of Models

If then or

then with the presumption that the form of function (phi) is the same for model and prototype, it follows that

Above equation is the desired prediction equation and indicates that the measured value of obtained with the model will be equal to the corresponding for the prototype as long as the other pi terms are equal. The conditions specified by Eqs. 7.9 provide the model design conditions, also called similarity requirements or modeling laws.

7.9


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Model design conditions is also called similarity requirements or modeling laws. It includes following:

(a) Geometric similarity(b) Dynamic similarity(c) Kinematic similarity ----(Achieved by ensuring a&b)

Modeling Laws


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Some Typical Model Studies(a) Flow Through Closed Conduits (b) Flow around immersed bodies

Flow Through Closed Conduits

Examples of this type of flow include pipe flow and flow through valves, fittings, and metering devices.

Geometric and Reynolds number similarity is usually required for models involving flow through closed conduits.

General formulation for such cases

Geometric similarity Reynolds number similarity


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ch-7-similitude,dimensional analysis & modeling

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modeling laws

model design conditions

pi terms

similitudean engineering

scale experimental system

desired prediction equation

thatabove equation

desired respect