A typical aorta, the main artery from the heart, is 1.80 cm in diameter and carr

Question

A typical aorta, the main artery from the heart, is 1.80 cm in diameter and carries blood at a speed of 35 cm/s.

A particular aorta vessel had a clot that reduced the area to 70% of its normal value.

(i) What would be the speed of the blood in the aorta?

A typical pressure in an unobstructed aortal would be about 16 kPa.

(ii) What would be the blood pressure in the obstructed aorta?

(iii)What is the flow rate (in m3/s) though a typical aorta?

(d) What is the density of a fluid whose pressure increases by 70.6 kPa for every 6.0 m increase in depth?

Explanation / Answer

let,

blood speed v1=35 cm/sec

area A1=pi*(1.8*10^-2/2)^2=2

pressure P1=16 kPa

area reduced A2=70% of A1

A2=(70/100)*A1

A2=0.7*A1

density of the blood rho=1060 kg/m^3

a)

by using continuity equation ,

A1*v1=A2*v2

(35)=(A2/A1)*v2

(35)=(0.7)*v2

====> v2=50 cm/sec^2

speed of the blood v2=50 cm/sec^2 -----is answer

b)

by using Bernoulli's equation,

P1+1/2*rho*v1^2=P2+1/2*rho*v2^2

P2=P1+1/2*rho*(v1^2-v2^2)

P2=(16*10^3)+1/2*1060*(35^2-50^2)*10^-4

P2=15.932*10^3 pa

P2=15.932 kpa -----is answer

c)

diameter d1=1.8cm

flow rate =A1*V1

=pi*(d1/2)^2*V1

=pi*(1.8*10^-2/2)^2*(35*10^-2)

=8.91*10^-5 m^3/sec -----is answer

d)

let

h=6m

(p1-p2)=70.6 kpA

now,

(P1-P2)=rho*g*h

70*10^3=rho*9.8*6

===> rho=1190.48 kg/m^3

density, rho=1190.48 kg/m^3 -----is answer

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