Poiseuille’s equation does not hold if the flow velocity

Chapter 4, Problem 57P

(choose chapter or problem)

(II) Poiseuille's equation does not hold if the flow velocity is high enough that turbulence sets in. The onset of turbulence occurs when the Reynolds number, , exceeds approximately  Re is defined as

                                  \(R e=\frac{2 v^{-} r \rho}{\eta}\)

where \(v^{-}\) is the average speed of the fluid, \(\rho\) is its density, \(\eta\) is its viscosity, and  is the radius of the tube in which the fluid is flowing.

() Determine if blood flow through the aorta is laminar or turbulent when the average speed of blood in the aorta \((r=1.2 \mathrm{~cm})\) during the resting part of the heart's cycle is about

\(40 \mathrm{~cm} / \mathrm{s}\)

 During exercise, the blood-flow speed approximately doubles. Calculate the Reynolds number in this case, and determine if the flow is laminar or turbulent.

Equation Transcription:

     

   

     

   

Text Transcription:

R e=\frac{2 v^- r \rho \eta

v^-

\rho

\eta

(r=1.2 cm)

40 cm/s