Question

Blood is pumped from the heart at a rate of 5L/min into the aorta of radius 2.0cm. Assuming that the density of blood 1x103 kg/m3 .Determine the velocity of blood through
the aorta

Answer 1

Q=vA
Q=5L/min=8.3e-5 m^3/sec
A= pi*r^2=3.14*4*10^-4=0.001256 m2
v=Q/A
v=8.3e-5/0.001256 = 0.006m/sec = 0.6cm/sec

Answer 2

for rate 4.5 L/min and radius r = 1.1 cm
Given

rate of blood pumped from the heart is = 4.5 L/min

we know that 1 L = 1000 cm^3


the flow rate in cm^3/s , by heart is = 4.5*1000/60 cm^3/s = 75 cm^3/s -------------(H)

the area of aorta is A = pi*r^2 = pi*1.1^2 = 3.80132 cm^2


now the rate of flow is A*v ----------(A)

where A is area of aorta and v is speed of blood in aorta


equating (H) to (A) ( from equation of continuity A1*V1 = A2*V2)


75 = A*v

v = 75/A

v = 75/3.80132 cm/s

v = 19.7299885303 cm/s