Answer:
There are approximately 5 × 10¹⁰ capillaries in the human body
Step-by-step explanation:
The motion of a fluid is such that the mass of the fluid flowing remains constant. This is known as the principle of conservation of mass in liquid flow.
The mass flow rate is the mass that passes a given point per unit time. According to the principle of conservation of mass, the flow rates at any two points must be equal, as long as no fluid is being added or taken away.
The principle gives rise tonthe continuity equation which is given below:
ρ₁A₁v₁ = ρ₂A₂v₂
Where ρ is density of fluid, A is internal area of the vessel or pipe the fluid is flowing through, v is velocity of the fluid
Since the density of blood is constant, the continuity equation above reduces to:
A₁v₁ = nA₂v₂
where A₁ is the area of the aorta, v₁ is velocity of bloodmin the aorta, n is number of capillaries, A₂ area of capillary, v₂ is velocity of blood in the capillary.
n = A₁v₁/A₂v₂
n = πr₁² × v₁ / πr₂² × v₂ where r₁ is radius of aorta and r₂ is radius of capillaries
n = (22/7 × 1.2² × 42) / (22/7 × 0.0005² × 0.005)
n = 4.8384 × 10¹⁰capillaries
Therefore, there are approximately 5 × 10¹⁰ capillaries in the human body