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. 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.

   Answer ID
   523823

   Created
   April 1, 2011 6:11am UTC

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   https://questions.llc/answers/523823