The pulmonary artery, which pumps blood from the heart to the lungs, has an inner radius of 1.34 mm and is 5.0 cm long. If the pressure drop between the heart and lungs is 420.0 Pa, what is the volume flow rate of blood in the pulmonary artery? Give your answer in cm3/s. The viscosity of blood at 37°C is 2.1 x 10-3 Pa s.

To calculate the volume flow rate of blood in the pulmonary artery, we can use Poiseuille's law, which relates flow rate to pressure drop, vessel length, vessel radius, and viscosity.

Poiseuille's law can be written as:

Q = ((π * ΔP * r^4) / (8 * η * L))

Where:
Q is the volume flow rate
ΔP is the pressure drop
r is the radius of the vessel
η is the viscosity of the fluid
L is the length of the vessel

Given values:
ΔP = 420.0 Pa
r = 1.34 mm = 0.134 cm
L = 5.0 cm
η = 2.1 x 10^-3 Pa s

Substituting these values into the equation:

Q = ((π * 420.0 * (0.134)^4) / (8 * 2.1 x 10^-3 * 5.0))

Calculating further:

Q = ((π * 420.0 * (0.00179)^4) / (8 * 2.1 x 10^-3 * 5.0))
Q = (3.14 * 420.0 * 1.26 x 10^-12) / (8 * 2.1 x 10^-3 * 5.0)
Q = (1.6572 x 10^-9) / (0.021)
Q = 7.8928 x 10^-8 cm^3/s

Therefore, the volume flow rate of blood in the pulmonary artery is approximately 7.8928 x 10^-8 cm^3/s.

To find the volume flow rate of blood in the pulmonary artery, we can use Poiseuille's Law, which relates the volume flow rate to the pressure drop, length, and radius of a cylindrical tube. The formula is as follows:

Flow rate (Q) = (π * ΔP * r^4) / (8 * μ * L)

Where:
Q is the volume flow rate,
ΔP is the pressure drop,
r is the radius of the tube,
μ is the viscosity of the fluid,
L is the length of the tube.

Given:
ΔP = 420.0 Pa
r = 1.34 mm = 0.134 cm
L = 5.0 cm
μ = 2.1 x 10^-3 Pa s

Now, plug these values into the formula to find the volume flow rate:

Q = (π * ΔP * r^4) / (8 * μ * L)

Q = (π * 420.0 * (0.134)^4) / (8 * 2.1 x 10^-3 * 5.0)

Q ≈ 0.283 cm^3/s

Therefore, the volume flow rate of blood in the pulmonary artery is approximately 0.283 cm^3/s.