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We approximate the flow of air into a vacuum cleaner

Chapter 4, Problem 107P

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QUESTION:

Problem 107P

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 107P

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 107P

Step 1 of 4:

In this question, we need to determine stagnation point on the

It is given

of the attachment above the floor

 is the length of the attachment

 is the volume flow rate of air

The velocity components given  are

Initial position

        

Final position

        

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