# Fluid Dynamics (flow rate, Re,)

1. Dec 7, 2009

### lmnt

1. The problem statement, all variables and given/known data

An average person has about 5 litres of blood in
their body. The heart circulates all this blood
around the body in only about 1 minute. Find the
time averaged volumetric flow rate Q of the aorta,
which is a pipe of inner diameter 2.2 cm. Find
the time and space averaged flow velocity (i.e. the
flow velocity if it were uniform across the pipe and
steady in time). Estimate the Reynolds number of
this flow. Is it laminar or turbulent? Of course, this
completely neglects the complicated pulsing motion
of the blood!

Other useful info:
density of blood $$\approx$$ 1025kg/m3
viscosity $$\approx$$ 4Pa$$\cdot$$s

2. Relevant equations

Q=vA
Re=$$\rho$$Ud / $$\eta}$$

3. The attempt at a solution

Well, To figure out flow rate, I just divided the 5 litres by 60 seconds since it's averaged. This gave me 0.083 L/s. Then i just rearranged Q=vA $$\rightarrow$$ v=Q/A $$\rightarrow$$ v=pi(0.083)(0.011^2) but this gave me 219m/s. I was suspicious at his point, but i continued to calculate Re giving me about 1000. This looks very wrong. The flow would be horribly turbulent at 1000. This doesn't have a precise answer but I would like to understand if my method is correct given the information available. Did I incorrectly calculate the volumetric flow rate since that is where all the other answers stem from? or was it something else.