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problem: Consider laminar newtonian flow in a tubeof radius R (a)Show that the w

ID: 1815109 • Letter: P

Question

problem:
     Consider laminar newtonian flow in a tubeof radius R
(a)Show that the wall shear stress can be written in terms of themean velocity V by:
                                        = 4V/R.

(b)Assuming Newtonian flow with viscosity 3cP,estimate for thevessels
vessels shown in table:

     Vessel                      MeanVelocity(cm/s)           Radius(cm)
ascendingaorta                              20                                   0.75
abdorrinalartery                             15                                   0.45
femortalartery                                 10                                  0.20
arteriole                                           0.3                                 0.0025
inferior venaoava                             12                                  0.5

(c)For Blood at a normal hematocrit of 45%,the yield shear stressis approximately 0.05 dynes/cm.For each of the above vessels canthe flow of blood be approximated as newtonian ? why or whynot?

Explanation / Answer

(b) Given that viscosity =3cp =3*10^-3 N-s/m^2 Equation for shear stress is given by             = 4V/R. Shear stress for different values of radius andmean velosity for different vessels
Vessel                            MeanVelocity(m/s)                     Radius(m) Shear stress    =4V/R.
ascending                   0.20                                            0.0075 0.32 abdorrinal artery                        0.15                                               0.0045 0.4 femortalartery                            0.10                                              0.0020 0.6 arteriole                                    0.003                                            0.000025 1.44 inferior venaoava                                0.12                                                   0.005 0.288 Vessel                            MeanVelocity(m/s)                     Radius(m) Shear stress    =4V/R.
ascending                   0.20                                            0.0075 0.32 abdorrinal artery                        0.15                                               0.0045 0.4 femortalartery                            0.10                                              0.0020 0.6 arteriole                                    0.003                                            0.000025 1.44 inferior venaoava                                0.12                                                   0.005 0.288