# Finding Vel. and Pressure of blood flow in vessel

1. Dec 7, 2011

helping a relative with their final studying but its been a few years since i've taken intro phys

Suppose a blood vessel is horizontal and it has wide and narrow cross sections as shown in Fig 1. In the real life the edges are not sharp and we assume their effects are negligible. Suppose the diameter of the wider portion is d = 6.5 mm and the diameter of the narrower part is 4/5 of the wider part. The viscosity of blood is n = 2.1 x 10"3 Pa.s and L = 4 cm. At cross-section A the average velocity is 0.2 m/s and the pressure is 100 mmHg. The direction of the blood flow is from A to B.
a)Find the average velocity at cross section
b)Find the pressure at cross section B.

when worked it out i came to P=99.72mmHg and V=.3125m/s

thanks for the help

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2. Dec 8, 2011

### Spinnor

I will ignore viscosity and use Bernoulli's equation,

p1 - p2 = rho(v2^2 - v1^2)/2

Using your numbers, and the density of blood of 1060 kg/m^3 (see http://hypertextbook.com/facts/2004/MichaelShmukler.shtml0 [Broken]

p2 = p1 - rho(v2^2 - v1^2)/2 = 100 - 1060(.3125^2 - .2^2)/2 = 69.4mmHg

I don't have a clue how we work viscosity into this problem but including it makes p1 even smaller? Your number seems too high?

Last edited by a moderator: May 5, 2017