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A two dimensional flow has velocities in x and y directions given by u = 2xyt and v = -y²t, where t denotes time. The equation for streamline passing through x = 1, y = 1 is

1. x²y = 1
2. xy² = 1
3. x²y² = 1
4. x/y = 1

Correct answer: xy² = 1

Solution

Streamline: dx/(2xyt)=dy/(-y^2 t) gives -dx/x = 2 dy/y, so -ln x = 2 ln y + C, i.e. x*y^2 = constant. At (1,1) the constant is 1, so the streamline is x*y^2 = 1.

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