Question

The volume flow rate of blood leaving the heart to circulate throughout the body is about 5 L/min for a person at rest. All this blood eventually must pass through the smallest of blood vessels, the capillaries. A typical capillary is 6 μm (micrometer) in diameter, 1 mm long, and the blood flows through it at an average speed of 1 mm/s.a. Estimate the total number of capillaries in the body. b. Estimate the total surface area of all the capillaries. (hint: the surface area of one capillary is A = circumference x length).

Answer 1

Answer:

$n=2.9\times 10^9$

$A=1.88\times 10^{-8}\ m^2$

Explanation:

Given that

Q= 5 L/min

1 L = 10⁻³ m³/s

1 min = 60 s

Q=0.083 x 10⁻³ m³/s

d= 6 μm

v= 1 mm/s

So the discharge flow through one tube

q = A v

$A=\dfrac{\pi}{4}d^2$

$A=\dfrac{\pi}{4}\times (6\times 10^{-6})^2\ m^2$

A=2.8 x 10⁻¹¹ m²

v= 1 x 10⁻³  m/s

q= 2.8 x 10⁻¹⁴  m³/s

Lets take total number of tube is n

Q= n q

n=Q/q

$n=\dfrac{0.083\times 10^{-3} }{ 2.8\times 10^{-14}}$

$n=2.9\times 10^9$

Surface  area A

A= π d L

$A=\pi \times 6\times 10^{-6}\times 10^{-3}\ m^2$

$A=1.88\times 10^{-8}\ m^2$