Question

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 !"!

Answer 1

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.