Question

What is the greatest average speed (in m/s) of blood flow at 37° C in an artery of radius 1.25 mm if the flow is to remain laminar? Take the density of blood to be 1050 kg/m3. m/s What is the corresponding flow rate (in L/s)? L/s

Answer 1

given

r = 1.25 mm

N_R = 2000

= 2.084 x 10^-3 Pa.s

= 1050 kg/m³

the equation is using for Reynolds number is

N_R = 2 V r /

then

V = N_R / 2 r

= 2.084 x 10^-3 x 2000 / 2 x 1050 x 1.25 x 10^-3

V = 1.5878 m/sec

using equation

Q = A V

= 3.14 x r² x V

= 3.14 x ( 1.25 x 10^-3 )² x 1.5878

Q = 7.79014 x 10^-6 m³/sec

or

the corresponding flow rate is Q = 7.79014 x 10^-6 L/sec