Question

Why is the following situation impossible? The figure shows Superman attempting to drink cold water through a straw of length $l=12.0\,m$. The walls of the tabular straw are very strong and do not collapse. With his great strength, he achieves maximum possible suction and enjoys drinking cold water.

Answer 1

Hint: Here in this question the concept of Bernoulli’s principle is used. The theorem states that for a steady flow of an incompressible and non-viscous liquid the sum of the pressure, kinetic energy per unit volume, and potential energy per unit volume remains constant through the flow.

Complete step by step answer:
When the superman raises the water from one end of the straw by the process of suction, there should be a pressure difference between the two ends of the straw. When the air is removed a vacuum will be formed at one of the ends, where there is no atmospheric pressure.

Bernoulli's principle states that for a steady flow of an incompressible and non-viscous liquid the sum of the pressure, kinetic energy per unit volume, and potential energy per unit volume remains constant through the flow. Therefore, as there is no flow of water in a horizontal way the pressure difference between the two points is given by the conservation of energy.
${P_1} + \rho g{h_1} = {P_2} + \rho g{h_2}$
$ \Rightarrow {p_2} - {p_1} = \rho g\left( {{h_1} - {h_2}} \right)$
Here, ${p_2} - {p_1} = {p_{atm}}$ i.e., atmospheric pressure
$\rho = {\text{density of water = 1000}}\dfrac{{kg}}{{{m^3}}}$
${h_1} - {h_2}{\text{ is }}h\left( {heigth/length} \right)$

$g$ is acceleration due to gravity $ = 9.8{\text{ m/}}{{\text{s}}^2}$
$ \Rightarrow {p_{atm}} = \rho g\left( h \right)$
$ \Rightarrow h = \dfrac{{{p_{atm}}}}{{\rho g}}$
Substituting the given values,
$ \Rightarrow h = \dfrac{{1.013 \times {{10}^5}}}{{1000 \times 9.8}}$
$ \therefore h \approx 10.3{\text{ m}}$
So, from this, we came to know that Superman can only raise water up to nearly $10.3{\text{ m}}$ but the length of the straw is 12 m.Therefore, this situation makes Superman impossible to do.

Note: In this question, students have the knowledge of the terms surface tension, pressure, atmospheric pressure, gravity, pascal’s law, and mainly Bernoulli’s theorem to solve this question correctly and accurately.