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A velocity field of a flow is given by V = (y − 1) i + (y − 2) j, where V is in m/s and x and y are in metres. What will be the equation of stream line passing through the point (5, 3)?
  • a)
    y = x + ln (y − 2) + 2
  • b)
    y = x + ln (y + 2) + 2
  • c)
    x = y + ln (y − 2) − 2
  • d)
    x = y + ln (y − 2) + 2
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A velocity field of a flow is given by V = (y − 1) i + (y − 2) j, whe...
V = (y − 1) i + (y − 2) j ...(i)
From equation (i), the velocity components are
u = y − 1, v = y − 2, w = 0
From the equation of stream line
On integrating, we get
(y – 2) + 2 In (y – 2) – In (y – 2) = x + C
Let (y – 2 = t) and solve
(y – 2) + In (y – 2) = x + C
At (5, 3) 1 + In (1) = 5 + C
C = 1 – 5 = – 4
Hence, equation of stream line becomes
y – 2 + In (y – 2) = x – 4
x = y + In (y – 2) + 2
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A velocity field of a flow is given by V = (y − 1) i + (y − 2) j, where V is in m/s and x and y are in metres. What will be the equation of stream line passing through the point (5, 3)?a)y = x + ln (y − 2) + 2b)y = x + ln (y + 2) + 2c)x = y + ln (y − 2) − 2d)x = y + ln (y − 2) + 2Correct answer is option 'D'. Can you explain this answer?
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