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

`n=2.9* 10^9`

`A=1.88* 10^(-8)\ m^2`

Step-by-step 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=(\pi)/(4)d^2`

`A=(\pi)/(4)* (6* 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=(0.083* 10^(-3) )/( 2.8* 10^(-14))`

`n=2.9* 10^9`

Surface area A

A= π d L

`A=\pi * 6* 10^(-6)* 10^(-3)\ m^2`

`A=1.88* 10^(-8)\ m^2`