A steady two-dimensional flow (pure straining) is given by u = kx, v = -ky, for k constant.(adsbygoogle = window.adsbygoogle || []).push({});

(i) Find the equation for a general streamline of the flow, and sketch some of them.

(ii) At t = 0,the fluid on the curve x^2 = y^2 = a^2 is marked (by an electro-chemical technique). Find the equation for this material fluid cuve for t > 0.

For part (i), I used that the partial derivative of x with respect to s is kx, and that of y with respect to s is -ky. So integrating these, and using the initial condition x = xo, y = yo at s = i, I found that

ln x = ks + ln xo, and ln y = ln yo - ks.

But I don't understand what part (ii) of the question is asking. What equation does it mean for me to find? I know I could write x^2 + y^2 as (u/k)^2 + (v/k)^2, but I'm not sure that helps atall.

Thanks in advance for any help.

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# Homework Help: Fluid Dynamics equation

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