Answer:
The average speed of the blood in the capillaries is 0.047 cm/s.
Note: The question is incomplete. The complete question is as follows:
The radius of the aorta is about 1 cm and the blood flowing through it has a speed of about 30 cm/s. Calculate the average speed of the blood in the capillaries given the total cross section of all the capillaries is about 2000 cm².
Explanation:
From the given values:
radius of the aorta, r₁ = 1 cm
speed of blood, v₁ = 30 cm/s
Area of the aorta, A₁ = πr₁² where π = 3.142
Area of aorta = 3.142 × (1)² = 3.142 cm²
Area of the capillaries, A₂ = 2000 cm²
let the average speed of the blood in the capillaries = v₂
From the continuity equation of fluid flow, the product of cross-sectional area of the pipe and the fluid speed at any point along the pipe is always constant. In formula, A₁v₁ = A₂v₂
Using the continuity equation, the average the average speed of the blood in the capillaries can be calculated thus:
A₁v₁ = A₂v₂
v₂ = (A₁v₁) / (A₂)
v₂ = (3.142 x 30) / (2000)
v₂ = 0.047 cm/s
Therefore, the average speed of the blood in the capillaries is 0.047 cm/s.
