Question

A full-term fetus typically has a mass of\[{\rm{3}}{\rm{.50 kg}}\]. (a) What pressure does the weight of such a foetus create if it rests on the mother’s bladder, supported on an area of\[{\rm{90}}{\rm{.0 c}}{{\rm{m}}^{\rm{2}}}\]? (b) Convert this pressure to millimetres of mercury and determine if it alone is great enough to trigger the micturition reflex (it will add to any pressure already existing in the bladder).

Short answer

(a) The pressure exerted on the bladder is obtained as: \[{\rm{3}}{\rm{.81 \times 1}}{{\rm{0}}^{\rm{3}}}{\rm{ Pa}}\].

(b) The above pressure is obtained as \[{\rm{28}}{\rm{.6 mm Hg}}\] which is alone is great enough to trigger the micturition reflex

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 force per unit perpendicular area across which the force is exerted is known as pressure.

Pressure is defined as follows in equation form:

\[P = \frac{F}{A}\]

The surface area is \[{\rm{90 c}}{{\rm{m}}^{\rm{2}}}\].

The surface area in meter square is \[{\rm{0}}{\rm{.0090 }}{{\rm{m}}^{\rm{2}}}\].

The mass of the baby is \[{\rm{3}}{\rm{.5 kg}}\].

The force applied on the bladder will be in mg.

Pressure exerted on the bladder

1. By putting all the value into the equation we get:

\[\begin{array}{l}P = \frac{F}{A}\\P = \frac{{mg}}{A}\\P = \frac{{\left( {3.5} \right)\left( {9.8} \right)}}{{0.009}}\\P = 3.81 \times 1{0^3}Pa\end{array}\]

Hence the pressure exerted on the bladder is: \[{\rm{3}}{\rm{.81 \times 1}}{{\rm{0}}^{\rm{3}}}{\rm{ Pa}}\].

Pressure exerted in mmHg

1. The pressure exerted into mm Hg can be calculated by below way:

\(\begin{array}{l} = 3.81 \times 1{0^3} \times \frac{{760}}{{1.013 \times 1{0^5}}}\\ = 28.6\,mmHg\end{array}\)

Therefore, above pressure \[{\rm{28}}{\rm{.6 mm Hg}}\] alone is great enough to trigger the micturition reflex.