(Solution) - Use potential flow to approximate -(2025 Original AI-Free Solution)

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Use potential flow to approximate the flow of air being sucked into a vacuum cleaner through a 2-D slit attachment, as in the figure. Model the flow as a line sink of strength (?m), with its axis in the zdirection at height a above the floor.
(a) Sketch the streamlines and locate any stagnation points.
(b) Find the velocity V(x) along the floor in terms of a and m.
(c) Define a velocity scale U = m/a and plot the pressure coefficient Cp = (p ? p?)/ Fig. C8.4 [(1/2) ?U2] along the floor
(d) Find where Cp is a minimum?the vacuum cleaner should be most effective here.
(e) Where did you expect the cleaner to be most effective, at x = 0 or elsewhere? (Experiment with dust later.)