Mechanical Properties of Fluids

Question : 26

Total: 31

(a) What is the largest average velocity of blood flow in an artery of radius 2×10–3 m if the flow must remain laminar?
(b) What is the corresponding flow rate? (Take viscosity of blood to be 2.084×10–3Pa s).
Density of blood is 1.06×103kg∕m3

Solution:

Here, ρ=2×10−3m;
D=2r=2×2×10−3
=4×10−3m
η=2.084×10−3Pa s
For flow to be laminar, NR=2000
(a) ‌ Now, vc=

NRη

ρD

2000×(2.084×10−3)

(1.06×103)×(4×10−3)

=0.98ms−1
(b) Volume flowing per second
=πr2vc
=

×(2×10−3)2×0.98
=1.23×10−5 m3 s−1.

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