Pulsatile Flow in Rigid Tubes — Lesson 4

This lesson covers the concept of pulsatile flow in rigid tubes, focusing on the Womersley solution and the relationship between velocity and pressure gradient. It explains how any periodic function can be decomposed into an infinite number of sinusoidal functions using Fourier transform. The lesson also discusses the importance of the Womersley number, which is the ratio of transient inertial force to viscous force. It further elaborates on the calculation of flow rate and wall shear stress, and the concept of viscous impedance. The lesson concludes with a discussion on the turbulence in pulsatile flows and the significance of the transient Reynolds number.

Video Highlights

02:19 - Explanation of the Womersley solution and Bessel function
11:15 - Calculation of flow rate
23:50 - Calculation of wall shear stress
28:39 - Discussion on viscous impedance
30:24 - Explanation of Womersley number
43:03 - Discussion on turbulence in pulsatile flows

Key Takeaways

- The Womersley solution provides a relationship between velocity and pressure gradient in pulsatile flow in rigid tubes.
- The Womersley number, representing the ratio of transient inertial force to viscous force, is a critical parameter in pulsatile flow.
- The flow rate and wall shear stress can be calculated using the velocity profile and pressure gradient.
- Viscous impedance, the ratio of pressure gradient to flow rate, is a significant concept in understanding pulsatile flow.
- Turbulence in pulsatile flows is defined by random fluctuations in flow velocity, and the transient Reynolds number is a key factor in determining turbulence.