UNDERSTANDING OF NAVIER-STOKES EQUATIONS VIA A MODEL FOR BLOOD FLOW

A pedagogic model for blood flow is introduced to help medicine majors understand a simplified version of Navier-Stokes equations which is known to be a good tool for interpreting the phenomena in blood flow. The pressure gradient consists of a time-independent part known as Hagen-Poiseuille's gradient and a time-dependent part known as Sexl's, and the model formula for the volume rate of blood flow is reduced to a very simple form. For demonstration, the blood rate in human aorta system is analyzed in connection with the time-dependence of pressure gradient. It is shown for Sexl's part that the flow rate lags the pressure gradient by ${\pi}/2$, which is thought to be due to the relaxation process involved.