Question

What is the pressure gradient (the drop of pressure per length unit) in a blood vessel with a volume flow rate of ÄV/Ät = 35 cm3/s and an inner diameter of 15 mm. Hint: the viscosity coefficient of blood in the specific case we study is çblood= 2.7 x 10-3 Ns/m2

Answer 1

From the volume flow rate (Q = 35 cm^3/s)and the vessel cross sectional area (A = 1.767 cm^2), get the average flow velocity:

V = Q/A = 19.8 cm/s

In cgs units, the viscosity is 0.027 g/cm*s

The Reynolds number is
Re = (rho*D*V/(viscosity)
= (1.00 g/cm^3*1.5 cm*19.8 cm/s)/0.027 g/cm*s)
= 1100 (dimensionless)

There will be laminar flow at this Reynolds number.

Pressure drop per unit length at this Reynolds number is
dP/dL = f*(1/2)*(rho)*V^2/D
where f = 64/Re = 0.058

Now you can go ahead and calculate the pressure drop per unit length

This is standard pipe flow engineering; you should have been exposed to it by now. Sometimes it is called Hagen-Poiseuille flow.

http://www.fas.harvard.edu/~scdiroff/lds/NewtonianMechanics/PoiseuillesLaw/PoiseuillesLaw.html flow.

It is important to calculate the Reynolds number first to make sure that the flow is laminar and not turbulent.