Worked exercise — Blood pressure of the heart

Problem

The maximum blood pressure at the outlet of the left ventricle is about $120\;\text{mmHg}$. Express it in pascals and estimate the force exerted on the wall of an artery of internal diameter $4\;\text{mm}$ and length $5\;\text{cm}$.

Solution

Step 1 — Conversion to pascals. One millimetre of mercury is worth $133{,}3\;\text{Pa}$:

$P = 120\cdot 133{,}3 \approx 1{,}60\cdot 10^{4}\;\text{Pa}$

Step 2 — Lateral surface of the artery. The artery is a cylinder; the internal surface of the wall is $A = \pi d\,\ell$:

$A = \pi d\,\ell = \pi\cdot 0{,}004\cdot 0{,}05 \approx 6{,}3\cdot 10^{-4}\;\text{m}^2$

Step 3 — Force on the wall. From $P = F/A$:

$F = P A \approx 1{,}60\cdot 10^{4}\cdot 6{,}3\cdot 10^{-4} \approx 10\;\text{N}$

$\ev{F \approx 10\;\text{N}}$

About ten newtons pushes outward on every five centimetres of artery: not a small amount.

Linked atoms

Argomenti: Fluid statics and dynamics Concetti: Pressure Competenze: Unit conversion