Question

For blood flow through arteries, which one of the following relations approximates the pulse wave propagation speed \( C \) as a function of the inner diameter \( D \) of the artery, wall thickness \( t \), modulus of elasticity \( E \), and fluid density \( \rho \)?

• A. \( C = \sqrt{\frac{E t}{\rho D}} \)
• B. \( C = \sqrt{\frac{\rho D}{E t}} \)
• C. \( C = \sqrt{\frac{\rho D^3 t^3}{E}} \)
• D. \( C = \sqrt{\frac{E \rho}{D t}} \)

Hint:

In blood flow through arteries, the pulse wave propagation speed depends on the stiffness of the artery wall, the thickness of the wall, and the density of the blood. The smaller the artery diameter and the higher the wall thickness, the faster the pulse wave speed.

Answer 1

The Correct Option is A

The speed of the pulse wave propagation \( C \) in blood flow through arteries is influenced by several factors: the modulus of elasticity \( E \) of the arterial wall, the density of the fluid \( \rho \), the thickness of the artery wall \( t \), and the diameter of the artery \( D \). These factors interact with each other in a specific relationship to determine the propagation speed. For the pulse wave speed, the relationship can be derived using principles from the study of wave propagation in a medium with elastic properties. In this case, the wave propagation speed in the blood vessel is proportional to the modulus of elasticity and inversely proportional to the density of the fluid. Additionally, the thickness of the wall and the diameter of the artery affect the dynamics of the wave propagation. The correct formula for the pulse wave speed is: \[ C = \sqrt{\frac{E t}{\rho D}} \] Where:
- \( E \) is the modulus of elasticity of the arterial wall (indicating the stiffness of the material),
- \( t \) is the thickness of the artery wall,
- \( \rho \) is the density of the blood (fluid),
- \( D \) is the inner diameter of the artery (the dimension through which the blood flows).
This relationship suggests that as the stiffness of the arterial wall increases (higher \( E \)) or the wall thickness increases (higher \( t \)), the pulse wave speed increases. On the other hand, an increase in the diameter of the artery or the density of the blood tends to reduce the pulse wave speed.