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Stream Line

If at any fixed instant of time, the velocity vector is tangential to a imaginary space curve,  in a fluid flow, the space curve so drawn is called a stream line.

The equation of a general stream line is given by

d x / u = d y / u = d z / u

In two rectangular coordinates in x and y, we have

d x / u = d y / u or  d y / d x = u / v

which states that the slope of a plane stream line equals to the ratio of their respective velocity.