Question

(a) The volume flow rate in an artery supplying the brain is 2.6 x 10-6 m3/s. If the radius of the artery is 4.8 mm, determine the average blood speed.
(b) Find the average blood speed as a constriction in the artery if the constriction reduces the radius by a factor of 4. Assume that the volume flow rate is the same as that in part (a).

Answer 1

Answer:

(a) Speed will be 0.03594 m/sec

(b) Speed will be 0.0575 m/sec

Explanation:

(a) We have given volume flow rate $V=2.6\times 10^{-6}m^3/sec$

Radius of the artery r = 4.8 mm = 0.0048 m

We know that area $A=\pi r^2=3.14\times 0.0048^2=7.234\times 10^{-5}m^2$

We know that volume flow rate $V=Av$ , here v is velocity

So $2.6\times 10^{-6}=7.234\times 10^{-5}\times v$

$v=0.03594m/sec$

(b) Now radius is reduced by factor 4

So new radius = $\frac{4.8}{4}=1.2mm=0.0012m$

We know that area $A=\pi r^2=3.14\times 0.0012^2=4.5216\times 10^{-6}m^2$

We know that volume flow rate $V=Av$ , here v is velocity

So $2.6\times 10^{-6}=4.5216\times 10^{-6}\times v$

$v=0.0575m/sec$