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Found in: Page 408

### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

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# To suck lemonade of density ${\mathbf{1000}}{\mathbf{kg}}{\mathbf{/}}{{\mathbf{m}}}^{{\mathbf{3}}}$ up a straw to a maximum height of ${\mathbf{4}}{\mathbf{.}}{\mathbf{0}}{\mathbf{}}{\mathbf{cm}}$, what minimum gauge pressure (in atmospheres) must you produce in your lungs?

Gauge pressure produced in the lungs in atmospheric unit is $-3.9×{10}^{3}\mathrm{atm}$

See the step by step solution

## Step 1: The given data

Maximum height, $\mathrm{h}=4\mathrm{cm}\text{or}0.04\mathrm{m}$

Density of lemonade, $\rho =1000\mathrm{kg}/{\mathrm{m}}^{3}$

Acceleration due to gravity, $g=9.8\mathrm{m}/{\mathrm{s}}^{2}$

## Step 2: 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, $\mathrm{p}=\mathrm{\rho gh}$

## Step 3: Calculation of gauge pressure in atm

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

$p=-1000\mathrm{kg}/{\mathrm{m}}^{3}×0.04\mathrm{m}×9.8\mathrm{m}/{\mathrm{s}}^{2}$

$=-392\mathrm{Pa}$

role="math" localid="1657535402885" $=-392\mathrm{Pa}×\frac{1\mathrm{atm}}{1.01×{10}^{5}\mathrm{Pa}}\left(1\mathrm{atm}=1.01×{10}^{5}\mathrm{Pa}\right)$

$=-3.9×{10}^{-3}\mathrm{atm}$

So, the pressure value is $-3.9×{10}^{-3}\mathrm{atm}$

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

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