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.
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
1 answer
1 answer