Consider the vacuum cleaner of Prob. 4–112. For the case where b = 2.0 cm, L = 35 cm, and V̇ = 0.1098 m3/s, create a velocity vector plot in the upper half of the xy-plane from x = –3 cm to 3 cm and from y = 0 cm to 2.5 cm. Draw as many vectors as you need to get a good feel of the flow field. The velocity is infinite at the point (x, y) = (0, 2.0 cm), so do not attempt to draw a velocity vector at that point.

Data from problem 4-112

We approximate the flow of air into a vacuum cleaner attachment by the following velocity components in the centerplane (the xy-plane):

where b is the distance of the attachment above the floor, L is the length of the attachment, and V̇ is the volume flow rate of air being sucked up into the hose (Fig. P4–112). Determine the location of any stagnation point(s) in this flow field.

FIGURE P4–112

Transcribed Image Text:

and U = V - Úx x² + y² + b² TL x + 2x²y² + 2x²b²+ y4 - 2y²b² + b² - Vy TL x² + 2x²y² + 2x²b² + y² = 2y²b² + b² x² + y² = 6² -