Question

After traveling through the body, blood flows into the main (M) pulmonary artery, which splits into the right (R) and left (L) pulmonary arteries to get oxygenated in the lungs. Assume the process is continuous and steady-state. Density (rho) of blood = 1.06 g/cm^3 Diameters (D): D_M = 2.95 cm; D_R = 1.98 cm; D_L = 2.21 cm Velocities (V): V_M = 10 cm/s; V_R = 8 cm/s a. If the relationship between flow velocity (V), cross-sectional area (A) and volumetric flow (Q) is given by Q = VA, what is the velocity through the left pulmonary artery? b. What are the mass flow rates through each artery?

Answer 1

Answer a:

• Velocity of blood through main pulmonary artery = V_M = 10 cm/s (given)
• Cross-sectional area of main pulmonary artery =   $\pi$ x (D_M / 2)² = 3.142 x (2.95 / 2)² = 6.8358 cm^2.

$\therefore$ Quantity of blood collected in the main pulmonary artery (Q_M) = V_M X A_M = 10 X 6.8358 = 68.358 cc.

• Quantity of blood flowed through the right pulmonary artery (Q_R) = V_R X A_R = 8 X (3.142 X (1.98 / 2)² = 24.635 cc.

$\therefore$ Quantity of blood that flows through the left pulmonary artery (Q_L) = Q_M - Q_R = 68.358 - 24.635 = 43.723 cc.

$\therefore$ Velocity of blood that flows through the left pulmonary artery (V_L) = Q_{L $\div$} A_L = 43.723 $\div$ (3.142 X (2.21 / 2)²) = 11.39 cm/s.

Answer b:

Mass Flow Rate(kg/hr) through right pulmonary artery = ( $\rho$ × V_R × A_R) × 3600 x (1/1000) = 1.06 x 8 x (3.142 X (1.98 / 2)²) x 3600 x (1/1000) = 94.01 kg/hr

Mass Flow Rate(kg/hr) through left pulmonary artery = ( $\rho$ × V_L × A_L) × 3600 = 1.06 x 11.39 x (3.142 X (2.21 / 2)²) x 3600 x (1/1000) = 53.07 kg/hr