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The concept of continuum in fluid flow assumes that the characteristics length of the flow is
- a)smaller than the mean free path of the molecules.
- b)larger than the mean free path of the molecule
- c)larger than the dimensions of the suspended particles
- d)larger than the wavelength of sound in the medium.
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The concept of continuum in fluid flow assumesthat the characteristics...
- The concept of the continuum is a kind of idealization of the continuous description of matter where the properties of the matter are considered as continuous functions of space variables.
- In this approach, the matter is continuously distributed with no void present continuum concept be applied if the mean free path is much less than the system dimensions.
- Although any matter is composed of several molecules, the concept of continuum assumes a continuous distribution of mass within the matter or system with no empty space, instead of the actual conglomeration of separate molecules.
- Describing a fluid flow quantitatively makes it necessary to assume that flow variables (pressure, velocity etc.) and fluid properties vary continuously from one point to another.
- One of the factors considered important in determining the validity of the continuum model is molecular density. It is the distance between the molecules which is characterized by a mean free path ( λ ). It is calculated by finding statistical average distance the molecules travel between two successive collisions.
- If the mean free path is very small as compared with some characteristic length in the flow domain (i.e., the molecular density is very high) then the gas can be treated as a continuous medium.
- If the mean free path is large in comparison to some characteristic length, the gas cannot be considered continuous and it should be analysed by the molecular theory.
- A dimensionless parameter is known as Knudsen number, Kn = λ/L, where λ is the mean free path and L is the characteristic length. It describes the degree of departure from the continuum.
- Usually when Kn > 0.01, the concept of the continuum does not hold good and when Kn < 0.01, the concept of the continuum does hold good.
- In the continuum approach, fluid properties such as density, viscosity, thermal conductivity, temperature, etc. can be expressed as continuous functions of space and time.
Most Upvoted Answer
The concept of continuum in fluid flow assumesthat the characteristics...
Explanation:
The concept of continuum in fluid flow suggests that the fluid is considered as a continuous medium, even though it is composed of individual molecules. The characteristics length of the flow plays a crucial role in determining whether a fluid can be treated as a continuum or not. The correct option is B because the characteristics length of the flow is larger than the mean free path of the molecule.
Mean free path:
Mean free path is the average distance a molecule travels between two successive collisions with other molecules. For example, if we consider air at room temperature, the mean free path is around 0.066 μm.
Characteristics length:
Characteristics length is a length scale that characterizes the flow. It can be defined as the length scale over which the flow properties change significantly. Some examples of characteristics length are the diameter of a pipe, the length of a nozzle, the chord length of an airfoil, etc.
Continuum hypothesis:
The continuum hypothesis states that a fluid can be considered as a continuous medium if the mean free path of the molecule is much smaller than the characteristics length of the flow. In other words, the fluid can be treated as a continuum if the molecules are close enough together that their individual behavior can be ignored.
Option B:
If the characteristics length of the flow is larger than the mean free path of the molecule, then the fluid can be treated as a continuum. This is because the molecules are close enough together that their individual behavior can be ignored.
Conclusion:
In summary, the concept of continuum in fluid flow assumes that the fluid is a continuous medium, even though it is composed of individual molecules. The fluid can be treated as a continuum if the characteristics length of the flow is larger than the mean free path of the molecule.
The concept of continuum in fluid flow suggests that the fluid is considered as a continuous medium, even though it is composed of individual molecules. The characteristics length of the flow plays a crucial role in determining whether a fluid can be treated as a continuum or not. The correct option is B because the characteristics length of the flow is larger than the mean free path of the molecule.
Mean free path:
Mean free path is the average distance a molecule travels between two successive collisions with other molecules. For example, if we consider air at room temperature, the mean free path is around 0.066 μm.
Characteristics length:
Characteristics length is a length scale that characterizes the flow. It can be defined as the length scale over which the flow properties change significantly. Some examples of characteristics length are the diameter of a pipe, the length of a nozzle, the chord length of an airfoil, etc.
Continuum hypothesis:
The continuum hypothesis states that a fluid can be considered as a continuous medium if the mean free path of the molecule is much smaller than the characteristics length of the flow. In other words, the fluid can be treated as a continuum if the molecules are close enough together that their individual behavior can be ignored.
Option B:
If the characteristics length of the flow is larger than the mean free path of the molecule, then the fluid can be treated as a continuum. This is because the molecules are close enough together that their individual behavior can be ignored.
Conclusion:
In summary, the concept of continuum in fluid flow assumes that the fluid is a continuous medium, even though it is composed of individual molecules. The fluid can be treated as a continuum if the characteristics length of the flow is larger than the mean free path of the molecule.
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The concept of continuum in fluid flow assumesthat the characteristics...
Concept of Continuum
The concept of the continuum is a kind of idealization of the continuous description of matter where the properties of the matter are considered as continuous functions of space variables.
In this approach, the matter is continuously distributed with no void present continuum concept be applied if the mean free path is much less than the system dimensions.
Although any matter is composed of several molecules, the concept of continuum assumes a continuous distribution of mass within the matter or system with no empty space, instead of the actual conglomeration of separate molecules.
Describing a fluid flow quantitatively makes it necessary to assume that flow variables (pressure, velocity etc.) and fluid properties vary continuously from one point to another.
One of the factors considered important in determining the validity of the continuum model is molecular density. It is the distance between the molecules which is characterized by a mean free path ( λ ). It is calculated by finding statistical average distance the molecules travel between two successive collisions.
If the mean free path is very small as compared with some characteristic length in the flow domain (i.e., the molecular density is very high) then the gas can be treated as a continuous medium.
If the mean free path is large in comparison to some characteristic length, the gas cannot be considered continuousand it should be analysed by the molecular theory.
A dimensionless parameter is known as Knudsen number, Kn = λ/L, where λ is the mean free path and L is the characteristic length. It describes the degree of departure from the continuum.
Usually when Kn > 0.01, the concept of the continuum does not hold good and when Kn < 0.01,="" the="" concept="" of="" the="" continuum="" does hold="" />
In the continuum approach, fluid properties such as density, viscosity, thermal conductivity, temperature, etc. can be expressed as continuous functions of space and time
The concept of the continuum is a kind of idealization of the continuous description of matter where the properties of the matter are considered as continuous functions of space variables.
In this approach, the matter is continuously distributed with no void present continuum concept be applied if the mean free path is much less than the system dimensions.
Although any matter is composed of several molecules, the concept of continuum assumes a continuous distribution of mass within the matter or system with no empty space, instead of the actual conglomeration of separate molecules.
Describing a fluid flow quantitatively makes it necessary to assume that flow variables (pressure, velocity etc.) and fluid properties vary continuously from one point to another.
One of the factors considered important in determining the validity of the continuum model is molecular density. It is the distance between the molecules which is characterized by a mean free path ( λ ). It is calculated by finding statistical average distance the molecules travel between two successive collisions.
If the mean free path is very small as compared with some characteristic length in the flow domain (i.e., the molecular density is very high) then the gas can be treated as a continuous medium.
If the mean free path is large in comparison to some characteristic length, the gas cannot be considered continuousand it should be analysed by the molecular theory.
A dimensionless parameter is known as Knudsen number, Kn = λ/L, where λ is the mean free path and L is the characteristic length. It describes the degree of departure from the continuum.
Usually when Kn > 0.01, the concept of the continuum does not hold good and when Kn < 0.01,="" the="" concept="" of="" the="" continuum="" does hold="" />
In the continuum approach, fluid properties such as density, viscosity, thermal conductivity, temperature, etc. can be expressed as continuous functions of space and time
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The concept of continuum in fluid flow assumesthat the characteristics length of the flow isa)smaller than the mean free path of the molecules.b)larger than the mean free path of the moleculec)larger than the dimensions of the suspended particlesd)larger than the wavelength of sound in the medium.Correct answer is option 'B'. Can you explain this answer?
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The concept of continuum in fluid flow assumesthat the characteristics length of the flow isa)smaller than the mean free path of the molecules.b)larger than the mean free path of the moleculec)larger than the dimensions of the suspended particlesd)larger than the wavelength of sound in the medium.Correct answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The concept of continuum in fluid flow assumesthat the characteristics length of the flow isa)smaller than the mean free path of the molecules.b)larger than the mean free path of the moleculec)larger than the dimensions of the suspended particlesd)larger than the wavelength of sound in the medium.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The concept of continuum in fluid flow assumesthat the characteristics length of the flow isa)smaller than the mean free path of the molecules.b)larger than the mean free path of the moleculec)larger than the dimensions of the suspended particlesd)larger than the wavelength of sound in the medium.Correct answer is option 'B'. Can you explain this answer?.
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