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Q18 CQ

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Found in: Page 437

### Physics For Scientists & Engineers

Book edition 9th Edition
Author(s) Raymond A. Serway, John W. Jewett
Pages 1624 pages
ISBN 9781133947271

# In Figure CQ14.18, an airstream moves from right to left through a tube that is constricted at the middle. Three table-tennis balls are levitated in equilibrium above the vertical columns through which the air escapes. (a) Why is the ball at the right higher than the one in the middle? (b) Why is the ball at the left lower than the ball at the right even though the horizontal tube has the same dimensions at these two points?

(a) The pressure is higher that’s why the ball at the right higher than the one in the middle

(b) If the pressure at the left were not lower than at the right, the flow would stop.

See the step by step solution

## Concept

The flow rate (volume flux) through a pipe that varies in cross-sectional area is constant; that is equivalent to stating that the product of the cross-sectional area A and the speed v at any point is a constant. This result is expressed in the equation of continuity for fluids:

${A}_{1}{V}_{1}={A}_{2}{V}_{2}=\text{constant}$

## (a): Explain why is the ball at the right higher than the one in the middle

Since the velocity of the air in the right-hand section of the pipe is lower than that in the middle, the pressure is higher.

## (c): Explain why the ball at the left is lower than the ball at the right even though the horizontal tube has the same dimensions at these two points

• The equation that predicts the same pressure in the far right and left-hand sections of the tube assumes laminar flow without viscosity.
• The equation also assumes the fluid is incompressible, but air is not. Also, the left-hand tube is open to the atmosphere while the right-hand tube is not.
• Internal friction will cause some loss of mechanical energy, and turbulence will also progressively reduce the pressure. If the pressure at the left were not lower than at the right, the flow would stop.