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DISTORTED MODEL ANALYSIS Distorted Model: The model does not have complete geometrical similarity with its prototype is called Distorted Model. For example rivers, harbors, reservoirs etc have very large horizontal dimension compared to vertical dimension. If model of such prototype have complete geometric similarity then vertical depth of water in the model will be too small and can not be measured accurately.To overcome this difficulty the model of such prototype or structures are made with different horizontal and vertical scales (i.e. greater vertical scales than the horizontal ones).A model having complete geometrical similarity with the prototype but working under different head of water also behaves as a distorted model.The prediction of a distorted model is relatively difficult and the result of the models being distorted can not be easily transferred to the prototype, as the basic condition of geometric similarity is not satisfied.

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DISTORTED MODEL ANALYSIS Advantages and Disadvantages of Distorted Model: A distorted model has the following advantages and disadvantages:

Advantages:1) The model size can be sufficiently reduced by its distortion as a

result the cost of the model is considerably reduced and its operation is simplified.

2) The vertical exaggeration results in steeper slope of water surface, which can be easily and accurately measured.

3) The Reynold’s number of a model is considerably increased and surface resistance is decreased due to exaggerated water slopes. This helps in simulation of the flow conditions in the model and prototype.

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DISTORTED MODEL ANALYSIS Advantages and Disadvantages of Distorted Model: Disadvantages:1) There is an unfavorable psychological effect on the observer.2) The behavior of flow of a model differs in action from that of the

prototype.3) The magnitude and direction of the pressure is not correctly

reproduced.4) The velocities are not correctly reproduced, as the vertical

exaggeration causes distortion of lateral velocity and kinetic energy.

(Note: despite of disadvantages of distorted model, it is sometimes preferred to use a distorted model. By exercising an utmost care, the results of the model may be transferred to the prototype.)

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DISTORTED MODEL ANALYSIS Prediction of Various Parameters of a Prototype from its Distorted Model:

1) Velocity of water in the prototype for the given velocity at the corresponding point of model.

2) Discharge of the prototype for the given discharge of the model.3) Speed of the prototype for the given speed of the model4) Power developed by the prototype for the given power of the

model.5) Time of emptying a prototype for the given time of emptying a

model.

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DISTORTED MODEL ANALYSIS Velocity of Water in the Prototype for the Given Velocity of Water of a Distorted Model:Consider a distorted model of prototype like a weir, dam or spillway etc.

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DISTORTED MODEL ANALYSIS Discharge of the Prototype for the Given Discharge of a Distorted Model:Consider a distorted model of a prototype like a weir, notch, spillway etc.

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DISTORTED MODEL ANALYSIS Speed of the Prototype for the Given Speed of a Distorted Model:Consider a distorted model of a prototype like a centrifugal pump or turbine.

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DISTORTED MODEL ANALYSIS Power Developed by the Prototype for the Given Power Developed by a Distorted Model:Consider a distorted model of a prototype like a turbine.

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DISTORTED MODEL ANALYSIS Time of Emptying a Prototype for the Given Time of Emptying a Distorted Model:Consider a distorted model of a prototype like a tank or reservoir.

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DISTORTED MODEL ANALYSIS Summery:

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DISTORTED MODEL ANALYSIS Problem-1:A diversion weir 240 m long has discharging capacity of 250 m3/s under a head of 1.2 m. A model of this weir has to be constructed in a laboratory where the available channel is 3.0 m long and 500 m deep. Design the suitable model for the weir if the water available in the laboratory is 25 liters/s.

SEE HAND ANALYSIS

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DISTORTED MODEL ANALYSIS Problem-2:A turbine model of 1:8 is tested under a head of 6.0 m of water. The full scale turbine is required to work under head of 30 m of water and run at 428 rpm. At what speed the model must be run?If the model develops 5 kw and uses 110 liters of water per second, at this speed what power will be obtained from the full scale turbine, assuming that its efficiency is 3% better than that of the model?