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Chapter 14: Q26P (page 408)

To suck lemonade of density 1000kg/m3up a straw to a maximum height of 4.0cm, what minimum gauge pressure (in atmospheres) must you produce in your lungs?

Short Answer

Expert verified

Gauge pressure produced in the lungs in atmospheric unit is-3.9×103atm

Step by step solution

01

The given data

Maximum height,h=4cmor0.04m

Density of lemonade, ρ=1000kg/m3

Acceleration due to gravity,g=9.8m/s2

02

Understanding the concept of pressure

To find gauge pressure in the atm, we can use the formula for pressure in terms of density, acceleration due to gravity, and height. Using the conversion factor, we can convert the pressure into atmospheric pressure.

Formula:

Pressure applied on a body,p=ρgh

03

Calculation of gauge pressure in atm

The pressure produced in the lungs in SI unit using equation (i) can be given as follows:

p=−1000kg/m3×0.04m×9.8m/s2

=-392Pa

role="math" localid="1657535402885" =−392Pa×1atm1.01×105Pa(1atm=1.01×105Pa)

=-3.9×10-3atm

So, the pressure value is-3.9×10-3atm

Negative sign indicates that the pressure inside the lung is less than the outside pressure.

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