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

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