Question

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?

Short answer

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

Step-by-step solution

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,$g=9.8\mathrm{m}/{\mathrm{s}}^2$

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,$\mathrm{p}=\mathrm{\rho gh}$

Calculation of gauge pressure in atm

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

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

$=-392\mathrm{Pa}$

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

$=-3.9\times {10}^{-3}\mathrm{atm}$

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

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