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A two-dimensional flow field has velocities along the x and y directions given by u = x2t and v = –2xyt respectively, where t is time. The equation of streamline is
[2006]
- a)x2y = constant
- b)xy2 = constant
- c)xy = constant
- d)not possible to determine
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A two-dimensional flow field has velocities along the x and y directio...
Given, u = x2t and v = – 2xyt
Integrating equation (i), we get
Integrating equation (i), we getψ =-x2yt + f(y) ...(iii)
Differentiating equation (iii) with respect to y, we get
∂ψ/∂y =–x2t + f(y) ...(v)
Equating the value of ∂ψ/∂y from equations (ii)
and (iv), we get
–x2t = –x2t + f'(y)
Since, f'(y) = 0, thus f(y) = C
(where 'C' is constant of integration)
ψ = -x2yt + C
C is a numerical constant so it can be taken as zero
ψ = -x2yt
For equation of stream lines,
ψ = constant
-x2yt =constant
For a particular instance,
x2y = constant
Differentiating equation (iii) with respect to y, we get
∂ψ/∂y =–x2t + f(y) ...(v)
Equating the value of ∂ψ/∂y from equations (ii)
and (iv), we get
–x2t = –x2t + f'(y)
Since, f'(y) = 0, thus f(y) = C
(where 'C' is constant of integration)
ψ = -x2yt + C
C is a numerical constant so it can be taken as zero
ψ = -x2yt
For equation of stream lines,
ψ = constant
-x2yt =constant
For a particular instance,
x2y = constant
Most Upvoted Answer
A two-dimensional flow field has velocities along the x and y directio...
Y2t, where t is the time.
To find the acceleration of a particle in this flow field, we need to find the time derivative of the velocity components.
The x-component of the velocity, u, is given by u = x^2t. Taking the time derivative of u with respect to t, we get:
du/dt = 2xt
The y-component of the velocity, v, is given by v = y^2t. Taking the time derivative of v with respect to t, we get:
dv/dt = 2yt
Therefore, the acceleration of a particle in this flow field is given by the derivatives of the velocity components:
a = (du/dt, dv/dt) = (2xt, 2yt)
To find the acceleration of a particle in this flow field, we need to find the time derivative of the velocity components.
The x-component of the velocity, u, is given by u = x^2t. Taking the time derivative of u with respect to t, we get:
du/dt = 2xt
The y-component of the velocity, v, is given by v = y^2t. Taking the time derivative of v with respect to t, we get:
dv/dt = 2yt
Therefore, the acceleration of a particle in this flow field is given by the derivatives of the velocity components:
a = (du/dt, dv/dt) = (2xt, 2yt)
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Community Answer
A two-dimensional flow field has velocities along the x and y directio...
Given, u = x2t and v = – 2xyt
Integrating equation (i), we get
Integrating equation (i), we getψ =-x2yt + f(y) ...(iii)
Differentiating equation (iii) with respect to y, we get
∂ψ/∂y =–x2t + f(y) ...(v)
Equating the value of ∂ψ/∂y from equations (ii)
and (iv), we get
–x2t = –x2t + f'(y)
Since, f'(y) = 0, thus f(y) = C
(where 'C' is constant of integration)
ψ = -x2yt + C
C is a numerical constant so it can be taken as zero
ψ = -x2yt
For equation of stream lines,
ψ = constant
-x2yt =constant
For a particular instance,
x2y = constant
Differentiating equation (iii) with respect to y, we get
∂ψ/∂y =–x2t + f(y) ...(v)
Equating the value of ∂ψ/∂y from equations (ii)
and (iv), we get
–x2t = –x2t + f'(y)
Since, f'(y) = 0, thus f(y) = C
(where 'C' is constant of integration)
ψ = -x2yt + C
C is a numerical constant so it can be taken as zero
ψ = -x2yt
For equation of stream lines,
ψ = constant
-x2yt =constant
For a particular instance,
x2y = constant
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A two-dimensional flow field has velocities along the x and y directions given by u = x2t and v = –2xyt respectively, where t is time. The equation of streamline is[2006]a)x2y = constantb)xy2 = constantc)xy = constantd)not possible to determineCorrect answer is option 'A'. Can you explain this answer?
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A two-dimensional flow field has velocities along the x and y directions given by u = x2t and v = –2xyt respectively, where t is time. The equation of streamline is[2006]a)x2y = constantb)xy2 = constantc)xy = constantd)not possible to determineCorrect answer is option 'A'. 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 A two-dimensional flow field has velocities along the x and y directions given by u = x2t and v = –2xyt respectively, where t is time. The equation of streamline is[2006]a)x2y = constantb)xy2 = constantc)xy = constantd)not possible to determineCorrect answer is option 'A'. 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 A two-dimensional flow field has velocities along the x and y directions given by u = x2t and v = –2xyt respectively, where t is time. The equation of streamline is[2006]a)x2y = constantb)xy2 = constantc)xy = constantd)not possible to determineCorrect answer is option 'A'. Can you explain this answer?.
A two-dimensional flow field has velocities along the x and y directions given by u = x2t and v = –2xyt respectively, where t is time. The equation of streamline is[2006]a)x2y = constantb)xy2 = constantc)xy = constantd)not possible to determineCorrect answer is option 'A'. 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 A two-dimensional flow field has velocities along the x and y directions given by u = x2t and v = –2xyt respectively, where t is time. The equation of streamline is[2006]a)x2y = constantb)xy2 = constantc)xy = constantd)not possible to determineCorrect answer is option 'A'. 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 A two-dimensional flow field has velocities along the x and y directions given by u = x2t and v = –2xyt respectively, where t is time. The equation of streamline is[2006]a)x2y = constantb)xy2 = constantc)xy = constantd)not possible to determineCorrect answer is option 'A'. Can you explain this answer?.
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