The radius of the aorta is about 1 cm and the blood flowing through it has a speed of about 30 !" ! . Calculate the average speed of the blood in the capillaries given the total cross section of all the capillaries is about 2000 !"!

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.