Question

If the pressure in the oesophagus is\[{\rm{ - 2}}{\rm{.00 mm Hg}}\]while that in the stomach is\[{\rm{ + 20}}{\rm{.00 mm Hg}}\], to what height could stomach fluid rise in the oesophagus, assuming a density of\[{\rm{1}}{\rm{.10 g/mL}}\]? (This movement will not occur if the muscle closing the lower end of the oesophagus is working properly.)

Short answer

The height of the fluid is obtained as: \[{\rm{0}}{\rm{.272 m}}\].

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 density of the stomach fluid is:\[1.1 g/mL\].

The density is = \[1.1 \times 1{0^3} kg/{m^3}\].

The net pressure exerted is:

\(\begin{array}{c}{P_{net}} = 20 - \left( { - 2} \right)\\ = 22 \,mm Hg\end{array}\)

Height of the fluid

By putting all the value into the equation we get:

\[\begin{array}{l}{P_{net}} = {P_F}\\{h_m}{\rho _m}g = {h_F}{\rho _F}g\\{h_F} = \frac{{{h_m}{\rho _m}}}{{{\rho _F}}}\\{h_F} = \frac{{0.022 \times 13600}}{{1.1 \times 1{0^3}}}\\{h_F} = 0.272\,meter\end{array}\]

Hence, the height of the fluid is: \[{\rm{0}}{\rm{.272 m}}\].