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 vesselsVessel 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
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