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

Short Answer

Expert verified

Answer :

Gauge pressure produced in the lungs in atmospheric unit is -3.9×10-3atm

Step by step solution

01

The given data 

Maximum height,h=4cmor0.04m

Density of lemonade, p=1000kg/m3

Acceleration due to gravity,g=9.8m/s2

02

Understanding the concept of pressure 

To find gauge pressure in theatm, 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 atmosphericpressure.

Formula:

Pressure applied on a body, p=pgh (i)

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=-392pa×1atm1.01×105pa(atm=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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