(20 Pt) Consider the blood flow through a mitral valve into the left artery, whi
ID: 1783849 • Letter: #
Question
(20 Pt) Consider the blood flow through a mitral valve into the left artery, which then subdivides into 108 capillaries each having radius of 8 m. The maximum velocity through the mitral valve is 2.1 m/s. The arterial velocity is 0.4 m/s. The cross- sectional diameter in the left atrium where the maximum velocity was recorded was 1.3 cm. (1) Calculate the pressure drop between the left atrium and the mitral valve (2) Calculate the cross-sectional diameter of the mitral valve (3) Calculate the velocity in the capillaries. State your assumptions in the above calculations.Explanation / Answer
a)
Use Bernoulli’s eqn,
P1+1/2v1^2+gh1= P2+1/2v2^2+gh2
v1=velocity in mitral,P1=Pressure in mitral, v2=velocity in artery ,P2=pressure in artery
Where =density of blood
Since h1=h2
P1+1/2v1^2= P2+1/2v2^2
P2-P1 = ½**(v1^2-v2^2)
Plug values,
P2-P1 = ½*1000*(2.1^2-0.4^2)
P2-P1= 2125 Pa
b)
Use continuity eqn,
A1v1=A2v2
r1^2*v1= r2^2*v2
r1^2*v1= r2^2*v2
(d1/2)^2*v1=(d2/2)^2*v2
Where d1=diameter of mitral, d2=diameter of artery
Plug values,
(d1/2)^2*2.1=(0.013/2)^2*0.4
d1= 0.0057m = 0.57cm
c)
Use continuity eqn,
A2v2=10^8*A3v3
r2^2*v2= 10^8*r3^2*v3
v3=velocity in capallaries
r2^2*v2= 10^8*r3^2*v3
(0.013/2)^2*v1=10^8*8*10^-6^2*v3
v3 = 0.26cm/s
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