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Sketch a streamline, pathline, and streakline

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For a given flow the velocity from time t=0 to t=5s was u=2 m/s, v=0. Then from t=5s to t=10s the velocity was u=+3 m/s, v=-4 m/s. A dye streak was started at t=0, and a path was traced from that same point at the same time. Draw to scale the streakline, pathline, and streamlines at t=10s. Please solve and explain.

I have seen the solution to this problem and am still confused at how to solve/sketch. Is there a fluids reference website that you may suggest?

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Solution Preview

Because, the differential equation of stream line is given as;
dx/u = dy/v
from 0 to 5 sec:
=>dy/dx = v/u = 0/2 = 0
=> y = constant.
Let initial point is the origin (0,0)
Because, velocity along y-direction is ...

Solution Summary

The solution is a step-by-step equation process. The attachment is an image to further understanding of the answer.