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Chapter 1: Q26 DQ (page 390)

In a store-window vacuum cleaner display, a table-tennis ball is suspended in mid-air in a jet of air blown from the outlet hose of a tank-type vacuum cleaner. The ball bounces around a little but always moves back toward the centre of the jet, even if the jet is tilted from the vertical. How does this behaviour illustrate Bernoulli’s equation?

Short Answer

Expert verified

The speed of the vacuum cleaner's air slows down as it strikes the bottom of the tennis ball.

Step by step solution

01

Understanding about Bernoulli’s equation

Bernoulli’s equation- Pressure, kinetic energy, and gravity potential energy per volume are all preserved along a streamline for an idle fluid in their combined form

02

Solution

After a few seconds, the vacuum cleaner's air begins to slow down. To generate a region of high pressure, an air stream moves slowly. This pressure is higher than the air pressure in the surrounding area. Pressure difference causes the ball to travel in a certain direction from the lower pressure zone to the higher pressure zone, as seen in the equation for pressure difference. As a result of this force, the ball's gravitational pull is balanced.

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Comparing Example 12.1 (Section 12.1) and Example 12.2 (Section 12.2), it seems that 700 N of air is exerting a downward force of 2.0×106Non the floor. How is this possible?
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