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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
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- x²y = constant
- xy² = constant
- xy = constant
- not possible to determine
Correct Option: A
Given, u = x²t and v = – 2xyt
| We know, | = v = -2xyt..........(i) | |
| δy |
| = -u = x²t..........(ii) | |
| δy |
Integrating equation (i), we get
ψ = –x²yt + f(y) ...(iii)
Differentiating equation (iii) with respect to y, we get
| = -x²t + f(y)........(v) | |
| δy |
Equating the value of δψ/δy 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
