Question

Problem 7. (The speed of blood) The aorta (the main blood vessel coming out of the heart) has a radius of about 1.0 cm and the total cross section of the major arteries is about 20 cm². The density of blood is 1.05 g/cm3. A. Given that the velocity of blood pumping through the aorta is about 48 cm/s, what is the total current of the blood passing through the aorta (in grams of blood per second)?

Answer 1

Density of blood = $\rho$ = 1.05 g/cm³

Radius of the aorta = R = 1 cm

Cross-sectional area of the aorta = A₁

A₁ = $\pi$R²

A₁ = $\pi$(1)²

A₁ = 3.1416 cm²

Velocity of the blood through the aorta = V₁ = 48 cm/s

Mass flow rate of the blood = Q

Q = $\rho$A₁V₁

Q = (1.05)(3.1416)(48)

Q = 158.33 g/sec

Total cross-sectional area of the major arteries = A₂ = 20 cm²

Velocity of blood through the major arteries = V₂

By continuity equation,

A₁V₁ = A₂V₂

(3.1416)(48) = (20)V₂

V₂ = 7.54 cm/s

Velocity of blood in the capillaries = V₃ = 0.03 cm/s

Cross-sectional area of the capillary system = A₃

By continuity equation,

A₁V₁ = A₃V₃

(3.1416)(48) = A₃(0.03)

A₃ = 5026.5 cm²

A) Total current of blood passing through the aorta = 158.33 g/sec

B) Velocity of the blood in the major arteries = 7.54 cm/s

C) Cross-sectional area of the capillary system = 5026.5 cm²