Consider the approximate velocity field given for the vacuum cleaner of Prob. 4–112. Calculate the flow speed along the floor. Dust particles on the floor are most likely to be sucked up by the vacuum cleaner at the location of maximum speed. Where is that location? Do you think the vacuum cleaner will do a good job at sucking up dust directly below the inlet (at the origin)? Why or why not?

Data from problem 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 -