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Consider the following
The components of velocity u and v along X and Y directions in a 2D flow problem of an incompressible fluid are
1. u = x2 cos y; v = – 2x sin y
2. u = x + 2; v = 1 – y
3. u = xyt; v = x3 – y2t/2
4. u = ln x + y; v = xy – y/x
Which of these will satisfy the continuity equation?
  • a)
    1, 2 and 3 only
  • b)
    1, 2 and 4 only
  • c)
    2, 3 and 4 only
  • d)
    1, 2, 3 and 4
Correct answer is option 'A'. Can you explain this answer?
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Consider the followingThe components of velocity u and v along X and Y...







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Consider the followingThe components of velocity u and v along X and Y...
-2xy sin y

To find the components of velocity u and v along the X and Y directions, we can differentiate the given functions with respect to x and y.

Differentiating u = x^2 cos y with respect to x, we get:

du/dx = 2x cos y

Differentiating u = x^2 cos y with respect to y, we get:

du/dy = -x^2 sin y

Therefore, the component of velocity u along the X direction is du/dx = 2x cos y, and the component of velocity u along the Y direction is du/dy = -x^2 sin y.

Similarly, differentiating v = -2xy sin y with respect to x and y, we get:

dv/dx = -2y sin y
dv/dy = -2xy cos y

Therefore, the component of velocity v along the X direction is dv/dx = -2y sin y, and the component of velocity v along the Y direction is dv/dy = -2xy cos y.

So, the components of velocity u and v along the X and Y directions in the given 2D flow problem of an incompressible fluid are:

u = 2x cos y along the X direction and -x^2 sin y along the Y direction
v = -2y sin y along the X direction and -2xy cos y along the Y direction
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Consider the followingThe components of velocity u and v along X and Y directions in a 2D flow problem of an incompressible fluid are1. u = x2 cos y; v = – 2x sin y2. u = x + 2; v = 1 – y3. u = xyt; v = x3 – y2t/24. u = ln x + y; v = xy – y/xWhich of these will satisfy the continuity equation?a)1, 2 and 3 onlyb)1, 2 and 4 onlyc)2, 3 and 4 onlyd)1, 2, 3 and 4Correct answer is option 'A'. Can you explain this answer?
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Consider the followingThe components of velocity u and v along X and Y directions in a 2D flow problem of an incompressible fluid are1. u = x2 cos y; v = – 2x sin y2. u = x + 2; v = 1 – y3. u = xyt; v = x3 – y2t/24. u = ln x + y; v = xy – y/xWhich of these will satisfy the continuity equation?a)1, 2 and 3 onlyb)1, 2 and 4 onlyc)2, 3 and 4 onlyd)1, 2, 3 and 4Correct answer is option 'A'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Consider the followingThe components of velocity u and v along X and Y directions in a 2D flow problem of an incompressible fluid are1. u = x2 cos y; v = – 2x sin y2. u = x + 2; v = 1 – y3. u = xyt; v = x3 – y2t/24. u = ln x + y; v = xy – y/xWhich of these will satisfy the continuity equation?a)1, 2 and 3 onlyb)1, 2 and 4 onlyc)2, 3 and 4 onlyd)1, 2, 3 and 4Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the followingThe components of velocity u and v along X and Y directions in a 2D flow problem of an incompressible fluid are1. u = x2 cos y; v = – 2x sin y2. u = x + 2; v = 1 – y3. u = xyt; v = x3 – y2t/24. u = ln x + y; v = xy – y/xWhich of these will satisfy the continuity equation?a)1, 2 and 3 onlyb)1, 2 and 4 onlyc)2, 3 and 4 onlyd)1, 2, 3 and 4Correct answer is option 'A'. Can you explain this answer?.
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