Question

The buildup of plaque on the walls of an artery may decrease its diameter from 1.1 cm to 0.75 cm. If the speed of blood flow was 15 cm/s before reaching the region of plaque buildup, find (a) the speed of blood flow and (b) the pressure drop within the plaque region.

Answer 1

You have a part of a whole, so a fraction.
\[\frac{0.75cm}{1.1cm}\]You will get that fraction of the blood flow.\[\frac{0.75cm}{1.1cm}\times15cm/s=10cm/s\]

Answer 2

You can also think of it in ratios.\[\frac{x}{0.75cm}=\frac{15cm/s}{1.1cm}\]

Answer 3

Pressure and Volume are inversely proportional. Double the volume, half the pressure.
If you decrease the volume by 0.75/1.1, you increase the pressure by 0.75/1.1. So it is a pressure drop of -0.69.