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Air flows at the rate of 1.5 m³/s through a horizontal pipe with a gradually reducing cross-section as shown in the figure. The two cross-sections of the pipe have diameters of 400 mm and 200 mm. Take the air density as 1.2 kg/m³ and assume inviscid incompressible flow. The change in pressure (p2 - p1) (in kPa) between sections 1 and 2 is

1. -1.28
2. 2.56
3. -2.13
4. 1.28

Correct answer: -1.28

Solution

The correct option is -1.28 kPa because, according to Bernoulli's principle, as the air flows from a wider section of the pipe to a narrower section, its velocity increases, resulting in a decrease in pressure. The calculations using the continuity equation and Bernoulli's equation confirm this pressure drop.

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