Blood flows in an aorta of radius 10 mm at a speed of 0.30 m/s.?

Question

a)What is the volume flow rate: give your answer in litre/minute?

b)What is the Reynolds number for the flow? Comment on the value obtained. (The viscosity of blood is 3.7 mPa s at 37°C, and blood density is 1060 kg/m3.)

Answer 1

firstly wow, i thought nobody would ask a fluid flow question, its kinda my area. (biochemical engineer) okay sorry,

flow rate (Q) = velocity (U) x Area (A)
Q=ua
0.3 x 10mm=1cm=0.01m area=pi r^2 area = 3.1416x10^-4m

Q = 9.4248X10^-5 m^3/s convert to litres per min = x1000 to get to litres as there are 1000 litres per m^3 /60 seconds to minutes

Q = 1.57X10^-3 L min^-1

okay thats the Q

Reynolds number for flow in a pipe (reynolds is dimensionless number which can determine whether something flows turbulent or laminar, im sure you already knew this.

Re(f) = (density x velocity x pipe diametre) / viscosity

so in your example 1060 x 0.3 x (20mm convert to metres 0.02) divided by vicosity which is 3.7x10^-3 (m is milli pascals)

this gives a reynolds number of 1718.91 it has no units obviously, from this you can determine that it Re<2100 so the flow is still Laminar flow. which is right!

HOORAY FOR ENGINEERS! im guessing your a medic so i would now like to do a little victory dance, for us biochemical engineers, who didnt quite manage to get into medical school. :p

Answer 2

If you had an empty tube with a radius of 10mm, and a liquid flowed into it at 0.30 m/s, in 1 second 0.3 meters of the 10mm radius tube would be full. We'll treat the tube as a cylinder, where Volume = Base area * Length = pi*(0.01)^2 * .3 = 9.425e-5 m^3 / s. Then you can convert this to liters per minute, where 1 Liter = .001 m^3.

Alas, I'm unsure what Reynold's number is. Sorry!