Question

(II) A physician judges the health of a heart by measuring the pressure with which it pumps blood. If the physician mistakenly attaches the pressurized cuff around a standing patient’s calf (about 1 m below the heart) instead of the arm (Fig. 10–42), what error (in Pa) would be introduced in the heart’s blood pressure measurement?

Short answer

The error in the heart’s blood pressure measurement is \(10300.5\;{\rm{Pa}}\).

Step-by-step solution

Concept

When a physician mistakenly attaches the pressurized cuff around a standing patient’s calf instead of the arm, there is a change in the value of the heart’s blood pressure measurement. This change in blood pressure can be determined by applying the hydrostatic pressure principle.

Given data

The change in the height of the pressurized cuff is, \(\Delta h = 1\;{\rm{m}}\).

Calculation

Using the material property table, the density of blood at normal body temperature is given by,

\(\rho = 1050\;{\rm{kg/}}{{\rm{m}}^3}\)

The expression for the error in the blood pressure measurement due to the change in the height of the pressurized cuff is given by,

\(\Delta P = \rho g\Delta h\)

Substituting the values in the above equation,

\(\begin{array}{l}\Delta P = 1050\;{\rm{kg/}}{{\rm{m}}^3} \times 9.81\;{\rm{m/}}{{\rm{s}}^2} \times 1\;{\rm{m}} \times \frac{{1\;{\rm{Pa}}}}{{1\;{\rm{kg/m}} \cdot {{\rm{s}}^2}}}\\\Delta P = 10300.5\;{\rm{Pa}}\end{array}\)

Therefore, the error in the heart’s blood pressure measurement is \(10300.5\;{\rm{Pa}}\).