Question

ΔP = 1.88 x 10^4 Pa. Use this answer to estimate the volume flow rate of blood from the head to the feet of a six-foot-tall person assuming an effective radius of 23cm

Answer 1

Answer: $3765.66 \frac{m^{3}}{s}$

Explanation:

We can solve this problem using the Poiseuille equation:

$Q=\frac{\pi r^{4}\Delta P}{8\eta L}$

Where:

$Q$  is the Volume flow rate

$r=23 cm \frac{1 m}{100 cm}=0.23 m$  is the effective radius

$L=6 ft \frac{0.3048 m}{1 ft}=1.8288 m$  is the length

$\Delta P=1.88(10)^{4} Pa$  is the difference in pressure

$\eta=3(10)^{-3} Pa.s$ is the viscosity of blood

Solving:

$Q=\frac{\pi (0.23 m)^{4}(1.88(10)^{4} Pa)}{8(3(10)^{-3} Pa.s)(1.8288 m)}$

$Q=3765.66 \frac{m^{3}}{s}$