The radius of the aorta is about 1.2cm , and the blood passing through it has a speed of about 50cm/s . Coefficient of viscosity for the whole blood (37∘) is n = 4×10^−3 Pa⋅s.
Calculate the pressure drop per cm along the aorta.
To calculate the pressure drop per cm along the aorta, we can use the Hagen-Poiseuille equation, which relates pressure drop to flow rate, radius, viscosity, and length of the vessel. The Hagen-Poiseuille equation is given by:
△P = (8 * n * L * Q) / (π * r^4)
where △P is the pressure drop, n is the coefficient of viscosity, L is the length of the vessel, Q is the flow rate, and r is the radius.
Given:
Radius of the aorta, r = 1.2 cm = 0.012 m
Viscosity, n = 4 × 10^−3 Pa⋅s
Flow rate, Q = 50 cm/s = 0.5 m/s
We are looking to calculate the pressure drop per cm, so we need to know the length of the vessel, L.
Once we know the length of the aorta, we can substitute all the given values into the Hagen-Poiseuille equation to find the pressure drop per cm along the aorta.