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A 1 : 20 model of a spillw ay dissipated 0.25 hp. The corresponding prototype horsepower dissipated will, be
- a)0.25 hp
- b)5.00 hp
- c)447.20 hp
- d)8944.30 hp
Correct answer is option 'D'. Can you explain this answer?
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A 1 : 20 model of a spillw ay dissipated 0.25 hp. The corresponding pr...
Given:
- Model scale: 1:20
- Power dissipated by model: 0.25 hp
To find:
- Prototype horsepower dissipated
Assumptions:
- The model and prototype have similar geometries and flow characteristics.
Explanation:
1. Understanding the concept of model and prototype:
- In engineering, models are often used to study and test the behavior of a system before building the actual prototype.
- A model is a scaled-down version of the prototype, designed to represent the key features and behavior of the prototype.
- The model and prototype should have similar geometries and flow characteristics so that the results obtained from the model can be extrapolated to the prototype.
2. Applying the concept of the model and prototype:
- In this problem, we have a model of a spillway that dissipates 0.25 hp of power.
- The model is at a scale of 1:20, which means that every dimension of the model is 1/20th of the corresponding dimension of the prototype.
3. Determining the relationship between power and scale:
- The power dissipated by a hydraulic system is proportional to the cube of the flow rate.
- Since the model and prototype have similar geometries and flow characteristics, the power dissipated by the model can be related to the power dissipated by the prototype using the scale factor.
4. Applying the scale factor:
- The scale factor for linear dimensions is 1:20, which means that the volume flow rate is reduced by a factor of (1/20)^3 = 1/8000.
- Since power is proportional to the cube of the flow rate, the power dissipated by the model is also reduced by a factor of 1/8000.
5. Calculating the prototype horsepower dissipated:
- The prototype power dissipated can be calculated by multiplying the model power dissipated by the scale factor.
- Prototype horsepower dissipated = Model horsepower dissipated * (1/8000)
- Prototype horsepower dissipated = 0.25 hp * (1/8000) = 0.00003125 hp
6. Converting to the appropriate unit:
- The answer is given in horsepower, but it is more common to express power in terms of kilowatts.
- 1 horsepower (hp) is equal to 0.7457 kilowatts (kW).
- Converting the prototype power dissipated to kilowatts:
- Prototype power dissipated = 0.00003125 hp * 0.7457 kW/hp = 0.00002328 kW
7. Rounding off:
- The prototype power dissipated can be rounded off to the nearest hundredth.
- Prototype power dissipated ≈ 0.00002 kW ≈ 0.00002 hp
8. Answer:
- The corresponding prototype horsepower dissipated is approximately 0.00002 hp.
- Model scale: 1:20
- Power dissipated by model: 0.25 hp
To find:
- Prototype horsepower dissipated
Assumptions:
- The model and prototype have similar geometries and flow characteristics.
Explanation:
1. Understanding the concept of model and prototype:
- In engineering, models are often used to study and test the behavior of a system before building the actual prototype.
- A model is a scaled-down version of the prototype, designed to represent the key features and behavior of the prototype.
- The model and prototype should have similar geometries and flow characteristics so that the results obtained from the model can be extrapolated to the prototype.
2. Applying the concept of the model and prototype:
- In this problem, we have a model of a spillway that dissipates 0.25 hp of power.
- The model is at a scale of 1:20, which means that every dimension of the model is 1/20th of the corresponding dimension of the prototype.
3. Determining the relationship between power and scale:
- The power dissipated by a hydraulic system is proportional to the cube of the flow rate.
- Since the model and prototype have similar geometries and flow characteristics, the power dissipated by the model can be related to the power dissipated by the prototype using the scale factor.
4. Applying the scale factor:
- The scale factor for linear dimensions is 1:20, which means that the volume flow rate is reduced by a factor of (1/20)^3 = 1/8000.
- Since power is proportional to the cube of the flow rate, the power dissipated by the model is also reduced by a factor of 1/8000.
5. Calculating the prototype horsepower dissipated:
- The prototype power dissipated can be calculated by multiplying the model power dissipated by the scale factor.
- Prototype horsepower dissipated = Model horsepower dissipated * (1/8000)
- Prototype horsepower dissipated = 0.25 hp * (1/8000) = 0.00003125 hp
6. Converting to the appropriate unit:
- The answer is given in horsepower, but it is more common to express power in terms of kilowatts.
- 1 horsepower (hp) is equal to 0.7457 kilowatts (kW).
- Converting the prototype power dissipated to kilowatts:
- Prototype power dissipated = 0.00003125 hp * 0.7457 kW/hp = 0.00002328 kW
7. Rounding off:
- The prototype power dissipated can be rounded off to the nearest hundredth.
- Prototype power dissipated ≈ 0.00002 kW ≈ 0.00002 hp
8. Answer:
- The corresponding prototype horsepower dissipated is approximately 0.00002 hp.
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A 1 : 20 model of a spillw ay dissipated 0.25 hp. The corresponding prototype horsepower dissipated will, bea)0.25 hpb)5.00 hpc)447.20 hpd)8944.30 hpCorrect answer is option 'D'. Can you explain this answer?
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