Question

a typical arteriole has a diameter of 0.030 mm and carries blood at the rate of 5.5×10⁻⁴ cm³/s. what is the speed of blood in an arteriole?
a. 0.78 cm/s
b. 0.11 cm/s
c. 0.32 cm/s
d. 0.79 cm/s
e. 0.54 cm/s

Explanation:

Step1: Calculate the cross - sectional area of the arteriole

The arteriole is circular. The formula for the area of a circle is $A=\pi r^{2}$, where the radius $r=\frac{d}{2}$. Given $d = 0.030\ mm=0.003\ cm$, so $r=\frac{0.003}{2}=0.0015\ cm$. Then $A = \pi\times(0.0015)^{2}\ cm^{2}\approx7.069\times 10^{-6}\ cm^{2}$.

Step2: Use the volume - flow rate formula

The volume - flow rate formula is $Q = Av$, where $Q$ is the volume - flow rate, $A$ is the cross - sectional area, and $v$ is the speed of the fluid. We know $Q = 5.5\times 10^{-4}\ cm^{3}/s$ and $A\approx7.069\times 10^{-6}\ cm^{2}$. Rearranging for $v$, we get $v=\frac{Q}{A}$. Substituting the values, $v=\frac{5.5\times 10^{-4}}{7.069\times 10^{-6}}\ cm/s\approx 78\ cm/s$.

Answer:

a. $0.78\ cm/s$