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In two dimensional flow the components of velocity are given by u = ax; v = by. The stream lines will be
- a)circular
- b)parabolic
- c)hyperbolic
- d)elliptical.
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
In two dimensional flow the components of velocity are given byu=ax;v=...
Explanation:
- Streamlines are the lines that are everywhere tangent to the velocity vectors at a given instant.
- To find the streamlines, we need to solve the equation of motion for the given velocity components.
- The equation of continuity gives us the relationship between the velocity components and the stream function.
- The stream function is defined as the function whose partial derivatives with respect to x and y are equal to the velocity components.
- In this case, the continuity equation gives us ψ = C + (a/2)*(x^2) + (b/2)*(y^2), where C is a constant.
- The streamlines are given by the equation ψ = constant.
- Substituting the given values of u and v in the continuity equation, we get ψ = C + (a/2)*(x^2) + (b/2)*(y^2).
- The streamlines are given by ψ = constant, which is a family of hyperbolas.
- Therefore, the streamlines for the given velocity components are hyperbolic.
Conclusion:
- The streamlines for the given velocity components are hyperbolic.
- Streamlines are the lines that are everywhere tangent to the velocity vectors at a given instant.
- To find the streamlines, we need to solve the equation of motion for the given velocity components.
- The equation of continuity gives us the relationship between the velocity components and the stream function.
- The stream function is defined as the function whose partial derivatives with respect to x and y are equal to the velocity components.
- In this case, the continuity equation gives us ψ = C + (a/2)*(x^2) + (b/2)*(y^2), where C is a constant.
- The streamlines are given by the equation ψ = constant.
- Substituting the given values of u and v in the continuity equation, we get ψ = C + (a/2)*(x^2) + (b/2)*(y^2).
- The streamlines are given by ψ = constant, which is a family of hyperbolas.
- Therefore, the streamlines for the given velocity components are hyperbolic.
Conclusion:
- The streamlines for the given velocity components are hyperbolic.
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In two dimensional flow the components of velocity are given byu=ax;v=by. The stream lines will bea)circularb)parabolicc)hyperbolicd)elliptical.Correct answer is option 'C'. Can you explain this answer?
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