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For a stream function to exist, which of the following conditions should hold?
1. The flow should always be irrotational.
2. Equation of continuity should be satisfied.
3. The fluid should be incompressible.
4. Equation of continuity and momentum should be satisfied.Select the correct answer using the codes given below:
Codes:
1. The flow should always be irrotational.
2. Equation of continuity should be satisfied.
3. The fluid should be incompressible.
4. Equation of continuity and momentum should be satisfied.Select the correct answer using the codes given below:
Codes:
- a)1, 2, 3 and 4
- b)1, 3 and 4
- c)2 and 3
- d)2alone
Correct answer is option 'D'. Can you explain this answer?
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For a stream function to exist, which of the following conditions shou...
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Conditions for the Existence of Stream Function
The stream function is a mathematical function that describes the flow of a fluid in two dimensions. For a stream function to exist, certain conditions must be satisfied. These conditions are:
1. Equation of Continuity: The equation of continuity relates the mass flow rate and velocity of a fluid. It states that the mass flow rate of a fluid is constant along a streamline. Therefore, for a stream function to exist, the equation of continuity must be satisfied.
2. Incompressibility: Incompressibility is a condition where the density of a fluid remains constant. For a stream function to exist, the fluid must be incompressible. This is because the stream function assumes that the fluid density is constant.
3. Irrotational Flow: Irrotational flow is a condition where the fluid particles move in a way that the angular velocity of the fluid is zero. For a stream function to exist, the flow must always be irrotational.
Conclusion
From the above discussion, it can be concluded that for a stream function to exist, the equation of continuity, incompressibility, and irrotational flow conditions must be satisfied. Therefore, option 'D' which states that only conditions 2 and 3 are necessary for the existence of a stream function is the correct answer.
The stream function is a mathematical function that describes the flow of a fluid in two dimensions. For a stream function to exist, certain conditions must be satisfied. These conditions are:
1. Equation of Continuity: The equation of continuity relates the mass flow rate and velocity of a fluid. It states that the mass flow rate of a fluid is constant along a streamline. Therefore, for a stream function to exist, the equation of continuity must be satisfied.
2. Incompressibility: Incompressibility is a condition where the density of a fluid remains constant. For a stream function to exist, the fluid must be incompressible. This is because the stream function assumes that the fluid density is constant.
3. Irrotational Flow: Irrotational flow is a condition where the fluid particles move in a way that the angular velocity of the fluid is zero. For a stream function to exist, the flow must always be irrotational.
Conclusion
From the above discussion, it can be concluded that for a stream function to exist, the equation of continuity, incompressibility, and irrotational flow conditions must be satisfied. Therefore, option 'D' which states that only conditions 2 and 3 are necessary for the existence of a stream function is the correct answer.
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For a stream function to exist, which of the following conditions should hold?1. The flow should always be irrotational.2. Equation of continuity should be satisfied.3. The fluid should be incompressible.4. Equation of continuity and momentum should be satisfied.Select the correct answer using the codes given below:Codes:a)1, 2, 3 and 4b)1, 3 and 4c)2 and 3d)2aloneCorrect answer is option 'D'. Can you explain this answer?
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