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.

Question

doc.brown · Answer

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

doc.brown · Answer

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

doc.brown · Answer

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.