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A hydraulic model of a spillway is constructed with a scale 1:16. If the prototype discharge is 2048 cumecs, then the corresponding discharge for which the model should be tested is:
- a)1 cumecs
- b)2 cumecs
- c)4 cumecs
- d)8 cumecs
Correct answer is option 'B'. Can you explain this answer?
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A hydraulic model of a spillway is constructed with a scale 1:16. If t...
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Spillway model obeys Froude’s Law
Spillway model obeys Froude’s Law
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A hydraulic model of a spillway is constructed with a scale 1:16. If t...
Introduction:
In hydraulic modeling, it is common to construct scaled-down physical models to simulate the behavior of a larger prototype. These models help engineers understand and predict the flow characteristics of water through various hydraulic structures, such as spillways. To ensure accurate representation of the prototype, it is important to establish the correct scaling ratio.
Given:
- Prototype discharge: 2048 cumecs
- Scale of the model: 1:16
Approach:
To determine the corresponding discharge for which the model should be tested, we need to consider the relationship between the prototype and the model. Since the model is a scaled-down version of the prototype, the discharges in the prototype and model are proportional to the cube of their linear dimensions.
Formula:
Discharge ratio = (Model scale)^3 = (Prototype discharge)/(Model discharge)
Solution:
1. Calculate the discharge ratio using the given information:
- Model scale = 1:16 = 1/16
- Prototype discharge = 2048 cumecs
- Discharge ratio = (1/16)^3 = 1/4096
2. Substitute the discharge ratio and prototype discharge into the formula to find the model discharge:
Discharge ratio = (Prototype discharge)/(Model discharge)
1/4096 = 2048/(Model discharge)
3. Rearrange the equation to solve for the model discharge:
Model discharge = 2048/(1/4096)
Model discharge = 2048*4096
Model discharge = 8388608 cumecs
Conclusion:
The corresponding discharge for which the model should be tested is 8388608 cumecs. However, none of the given options match this value. Therefore, it seems there might be an error in the provided options.
In hydraulic modeling, it is common to construct scaled-down physical models to simulate the behavior of a larger prototype. These models help engineers understand and predict the flow characteristics of water through various hydraulic structures, such as spillways. To ensure accurate representation of the prototype, it is important to establish the correct scaling ratio.
Given:
- Prototype discharge: 2048 cumecs
- Scale of the model: 1:16
Approach:
To determine the corresponding discharge for which the model should be tested, we need to consider the relationship between the prototype and the model. Since the model is a scaled-down version of the prototype, the discharges in the prototype and model are proportional to the cube of their linear dimensions.
Formula:
Discharge ratio = (Model scale)^3 = (Prototype discharge)/(Model discharge)
Solution:
1. Calculate the discharge ratio using the given information:
- Model scale = 1:16 = 1/16
- Prototype discharge = 2048 cumecs
- Discharge ratio = (1/16)^3 = 1/4096
2. Substitute the discharge ratio and prototype discharge into the formula to find the model discharge:
Discharge ratio = (Prototype discharge)/(Model discharge)
1/4096 = 2048/(Model discharge)
3. Rearrange the equation to solve for the model discharge:
Model discharge = 2048/(1/4096)
Model discharge = 2048*4096
Model discharge = 8388608 cumecs
Conclusion:
The corresponding discharge for which the model should be tested is 8388608 cumecs. However, none of the given options match this value. Therefore, it seems there might be an error in the provided options.
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