Artery Blood Flow Problem: A.) What\'s the pressure drop along a 10cm segment of

Question

Artery Blood Flow Problem:

A.) What's the pressure drop along a 10cm segment of the aorta?

B.) Find the maximum & average flow speed in the blood vessel.

C.) Estimate Reynolds number for this flow.

Artery Blood Flow Problem: The left ventricle of the human heart expels blood at a typical flow rate Q=50cm^3/s into the aorta with diameter D=2cm. The viscosity of blood is three times that of water, n=3*10^-2cm^3/s. A.) What's the pressure drop along a 10cm segment of the aorta? B.) Find the maximum & average flow speed in the blood vessel. C.) Estimate Reynolds number for this flow.

Explanation / Answer

volume flow rate Q=pi*P*r^4/8*n*l

a)

pressure difference P=8*Q*n*l/Pi*r^4

=(8*50*10^-6*3*3*10^-2*10^-6*10*10^-2)/3.14*(1*10^-2)^4

=1146.48*10^-7 pascal

=1.14648*10^-4 pascal

b)

flow speed v=volume flow rate /area

=Q/pi*r^2

=50*10^-6/3.14*(1*10^-2)^2

=15.923*10^-2 m/sec

=0.1592 m/sec ............ is maximum speed

and

vavg=v/2=0.0796 m/sec .........is avg speed

c)

Reynolds number

R=rho*v*D/n

=1060*0.1592*2*10^-2/3*3*10^-2*10^-6

=37.5*10^6 .... is answer

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.