Question

A.) The blood low out of the heart is about 83 mL/sec. Assuming that the blood flows equally through all capillaries, estimate the blood flow through each capillary.

B.) The blood pressure difference across a capillary is 20 mmHg. Assuming that a capillary is about 7um in diameter on average, and that the viscosity of blood is 0.04 poise, calculate the theoretical length of a capillary.

C.) The length of a capillary can be measure directly with a microscope and it usually ranges from 0.3 to 1.0 mm. Let us assume that the average length of a capillary is 0.65 mm. From this length and the answer to part B, as well as the pressures and diameter values cited above, calculate the effective viscosity of blood in a capillary.

D.) The value of viscosity obtained in part C is higher than the value of 0.04 poise normally quoted for blood passing through larger vessels. What is the reason for the difference?

Answer 1

(a) Capillaries have a diameters of about 5-10 micro meters. Let us assume that the capillary dia is 7 micrometer. There are about 20 million capillaries This gives the flow rate as,

$Q = Av$

v is the blood flow rate, Q is volumetric blood flow rate, and A is area of cross section.

$\Rightarrow 83 \times 10^{-3} \times 10^{-3} \, m^3/s = (\pi \times 0.25 \times (7 \times 10^{-6})^2 \times 20 \times 10^6)v$

$\Rightarrow 83 \times 10^{-6} = (7.7 \times 10^{-4})v$

$\Rightarrow v = \frac{83 \times 10^{-6}}{7.7 \times 10^{-4}} = 0.108 \, m/s$