Define model. Write down its advantages and applications.

Model analysis is an experimental method of finding solutions of a complex flow problems.

A Model is a small scale replication of the actual machine or structure. The actual machine or structure is called prototype.

Advantages of Model Analysis:

• The performance of hydraulic structures, hydraulic machines can be predicted using model.

• Model testing can be done to detect the defects of an existing structures.

• It is the only means of determining the safety and reliability of a particular portion of a structure in which clear cut analytical and reliable method is not available.

• The model test are quite economical and convenient.

Application of Model Analysis:

• For analysis of civil engineering structures such as dams, spillways, canals, weirs etc.

• Flood control mechanism

• Turbines, pumps and compressor

• A....

Model analysis is an experimental method of finding solutions of a complex flow problems.

A Model is a small scale replication of the actual machine or structure. The actual machine or structure is called prototype.

Advantages of Model Analysis:

• The performance of hydraulic structures, hydraulic machines can be predicted using model.

• Model testing can be done to detect the defects of an existing structures.

• It is the only means of determining the safety and reliability of a particular portion of a structure in which clear cut analytical and reliable method is not available.

• The model test are quite economical and convenient.

Application of Model Analysis:

• For analysis of civil engineering structures such as dams, spillways, canals, weirs etc.

• Flood control mechanism

• Turbines, pumps and compressor

• Aeroplanes, rocket missiles

• Tall buildings

Types of Models:

The hydraulic models, in general, are classified as:

• Undistorted models

• Distorted models

Undistorted Models:

An undistorted model is the one which is geometrically similar to its prototype. The conditions of similitude are completely satisfied for such models, hence the results obtained from the model tests are easily used to predict the performance of prototype body. In such models, the design and construction of the model and the interpretation of the model results are simpler.

Distorted Models:

A distorted model is the one which is not geometrically similar to its prototype. In such a model, different scale ratios for the linear dimensions are adopted.

A distorted model may have the following distortions:

• Geometrical distortion

• Material distortion

• Distortion of hydraulic quantities

Typical examples for which distorted models are to be prepared are;

• Rivers

• Dams across very wide rivers

• Harbors etc.

Two scale ratios are adopted, horizontal scale ratio for horizontal dimensions, `L_(r_H)` and Vertical scale ratio for vertical dimensions, `L_(r_V)`.

Scale ratio for horizontal dimensions is,

`L_(r_H)=L_p/L_m=B_p/B_m`

Scale ratio for vertical dimensions is,

`L_(r_V)=D_p/D_m` 

Similarly, the scale ratio for velocity based on froude model law is,

`(F_r)_m=(F_r)_p`

`V_m/root(2)D_m=V_p/root(2)D_p`

`V_p/V_m=root(2)(D_p/D_m)=root(2)L_(r_V)`

Similarly, the scale ratio for area of flow is,

`A_p/A_m=(B_p*D_p)/(B_m*D_m)=(L_r)_H*(L_r)_V`

Similarly, the scale ratio for discharge through model and prototype is,

`Q_p/Q_m=(V_p*A_p)/(V_m*A_m)`

`=root(2)(D_p/D_m)*(b_p*D_p)/(b_m*D_m)`

`=b_p/b_m*(D_p/D_m)^(3/2)`

`=(L_r)_H*((L_r)_V)^(3/2)  `

Reasons for adopting distorted Models:

• Maintaining the accuracy in vertical dimensions.

• Maintaining turbulent flow.

• Obtaining suitable roughness conditions.

• Obtaining suitable bed material and its adequate movements.

• Accommodating the available facilities such as money, water supply, space etc.

Merits of distorted models:

• The surface tension can be reduced.

• Model size can be reduced sufficiently.

• The Reynolds number of flow can be increased that will yield better results.

• Accurate measurement can be done.

• Sufficient attractive force can be developed to move the bed material of the model.

Demerits of distorted models:

• The pressure and velocity distribution are not truly reproduced.

• A model wave may differ in type and possibly in action from that of the prototype.

• Slopes of river beds, earthcuts and dikes cannot be truly reproduced.

• It is difficult to extrapolate and interpolate the results obtained from the distorted models.

• The observer may experience an unfavourable psychological effect.