Solution Found!
Consider the approximate velocity field given for the
Chapter 4, Problem 109P(choose chapter or problem)
PROBLEM: We approximate the flow of air into a vacuum cleaner attachment by the following velocity components in the centerplane (the xy-plane):
and
where bis the distance of the attachment above the floor, L is the length of the attachment, and is the volume flow rate of air being sucked up into the hose (Fig. P11–54). Determine the location of any stagnation point(s) in this flow field.
FIGURE P11-54
Questions & Answers
QUESTION: Problem 109PConsider the approximate velocity field given for the vacuum cleaner of Prob. 11–54. 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?
PROBLEM: We approximate the flow of air into a vacuum cleaner attachment by the following velocity components in the centerplane (the xy-plane):
and
where bis the distance of the attachment above the floor, L is the length of the attachment, and is the volume flow rate of air being sucked up into the hose (Fig. P11–54). Determine the location of any stagnation point(s) in this flow field.
FIGURE P11-54
ANSWER:
Solution
Step 1 of 4
The velocity components in the center field (xy plane) are given for the flow of air into a vacuum cleaner. We need to calculate the flow speed of air along the floor due to vacuum cleaner and also need we need to find the location of the maximum speed.
Given components of velocity for the xy plane are,
………..1
And
Where b is the distance of the attachment above the floor, L is the length of attachment and is the volume rate of air sucked into the hose.
The vector field will be