Air pressure is 1.0 ´ 10⁵ N/m²,air density is 1.3 kg/m³,and the density of soft drinks is 1.0 ´ 10³ kg/m³.If one blows carefully across the top of a straw sticking up 0.100 m from the liquid in a soft drink can,it is possible to make the soft drink rise half way up the straw and stay there.How fast must the air be blown across the top of the straw?

Question

Quizplus · Accepted Answer

The pressure difference between the top of the straw and the liquid in the can needs to be equal to or greater than the weight of the column of liquid that is being lifted, which is:

$\Delta P = ho_{soft\,drink}\cdot g \cdot h$

where $ho_{soft\,drink}$ is the density of the soft drink, $g$ is the acceleration due to gravity, and $h$ is the height of the lifted column of liquid.

The velocity of the air blown across the top of the straw can be calculated using Bernoulli's equation, which relates the pressure, density, and velocity of a fluid:

$P + \frac{1}{2}ho v^2 = 	ext{constant}$

We can assume that the pressure on either side of the straw is approximately atmospheric pressure, so we can set $P$ equal to atmospheric pressure. The velocity of the air needed to lift the liquid half way up the straw can be found by solving for $v$:

$v = \sqrt{\frac{2\cdot \Delta P}{ho_{air}}} = \sqrt{\frac{2\cdot ho_{soft\,drink} \cdot g \cdot h}{ho_{air}}}$

Plugging in the given values, we get:

$v = \sqrt{\frac{2\cdot 1.0	imes10^{3}\,kg/m^3 \cdot 9.81\,m/s^2 \cdot 0.100\,m}{1.3\,kg/m^3}} \approx 26.8\,m/s$

Therefore, the best choice is B) 27 m/s.

Air Pressure Is 1