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Chapter 1: Q18E (page 391)

The lower end of a long plastic straw is immersed below the surface of the water in a plastic cup. An average person sucking on the upper end of the straw can pull water into the straw to a vertical height of 1.1 m above the surface of the water in the cup. (a) What is the lowest gauge pressure that the average person can achieve inside his lungs? (b) Explain why your answer in part (a) is negative.

Short Answer

Expert verified

(a) The lowest gauge pressure is -10780N/m2and (b) The pressure is negative because the pressure in the lungs should be lower than the atmospheric pressure

Step by step solution

01

Given Data

The vertical height ish=1.1m

02

Understanding the gauge pressure

In this problem, the formula of gauge pressure will be applied to find the lowest pressure any average person can achieve in his lungs.

03

Determining the gauge pressure in the lungs

The relation of gauge pressure can be written as:

Pg=-蚁gh

Here, 蚁is the density of water and g is the gravitational acceleration.

Substitute1.1mforh,1000kg/m3for蚁,and9.80m/s2forgintheaboverelation.Pg=-1000kg/m39.80m/s21.1mPg=-10780N/m2

Thus, the required gauge pressure is -10780 N/m2 .

04

Determining the significance of negative gauge pressure

The obtained value of gauge pressure in the lungs is -10780N/m2, which is negative because the pressure in the lungs should be lower than the atmospheric pressure for raising the level of liquid in the straw.

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