Question

(a) The pressure inside an alveolus with a\[{\rm{2}}{\rm{.00 \times 1}}{{\rm{0}}^{{\rm{ - 4}}}}{\rm{ m}}\]radius is\[{\rm{1}}{\rm{.40 \times 1}}{{\rm{0}}^{\rm{3}}}{\rm{ Pa}}\], due to its fluid-lined walls. Assuming the alveolus acts like a spherical bubble, what is the surface tension of the fluid? (b) Identify the likely fluid. (You may need to extrapolate between values in Table\[{\rm{11}}{\rm{.3}}\].)

Short answer

(a) The surface tension of the fluid is obtained as: \[{\rm{0}}{\rm{.07 N/m}}\].

(b) The fluid is either water (\[{\rm{2}}{{\rm{0}}^{\rm{o}}}\]) or blood plasma (\[{\rm{3}}{{\rm{7}}^{\rm{o}}}\]).

Step-by-step solution

Conceptual Introduction

Fluid statics, often known as hydrostatics, is a branch of fluid mechanics that investigates the state of balance of a floating and submerged body, as well as the pressure in a fluid, or imposed by a fluid, on an immersed body.

Given data

The tensions between molecules that cause a liquid's surface to compress to the lowest feasible surface area.

The radius r of the alveolus is:\[{\rm{2}}{\rm{.0 \times 1}}{{\rm{0}}^{{\rm{ - 4}}}}{\rm{ m}}\].

The Pressure P exerted in it is: \[{\rm{1}}{\rm{.4 \times 1}}{{\rm{0}}^{\rm{3}}}{\rm{ Pa}}\].

Surface tension Calculation

The formula for surface tension is

\(\begin{array}{c}P = \frac{{4\sigma }}{r}\\\sigma = \frac{{P \times r}}{4}\\ = \frac{{2 \times {{10}^{ - 4}}\;{\rm{Pa}} \times 1.4 \times {{10}^3}\;{\rm{m}}}}{4}\\ = 0.07\,\;{\rm{N/m}}\end{array}\)

Therefore, surface tension of the fluid is \[{\rm{0}}{\rm{.07 N/m}}\], which is near to the value of surface tension of water.

Identifying the likely fluid

The surface tension of water at \[{\rm{2}}{{\rm{0}}^{\rm{o}}}\], according to table \[{\rm{11}}{\rm{.3}}\], is:

\[{\gamma _{water}} = {\rm{0}}{\rm{.0728 N}}{{\rm{m}}^{{\rm{ - 1}}}}\]

The surface tension of blood plasma at \[{\rm{3}}{{\rm{7}}^{\rm{o}}}\] is calculated from table \[{\rm{11}}{\rm{.3}}\].

\[{\gamma _{blood}} = {\rm{0}}{\rm{.073 N}}{{\rm{m}}^{{\rm{ - 1}}}}\]

As a result, the fluid is either \[{\rm{2}}{{\rm{0}}^{\rm{o}}}\] water or \[{\rm{3}}{{\rm{7}}^{\rm{o}}}\] blood plasma.