As blood moves through a vein or an artery its velocity v is greatest along the central axis. And decrease as the distance r from the central axis increases the formula that gives v as function of r is called law of laminar flow for an artery with radius 0.5cm the relation between v in cm/s and r in cm is given by function v(r)=18,500(0.25-r^2)
Find v(0.1) and v(0.4) in cm/s
What do you answer to part a tell you about the flow of blood in this artery
To find v(0.1), we substitute r = 0.1 into the function v(r):
v(0.1) = 18,500(0.25 - (0.1)^2)
v(0.1) = 18,500(0.25 - 0.01)
v(0.1) ≈ 18,500(0.24)
v(0.1) ≈ 4,440 cm/s
To find v(0.4), we substitute r = 0.4 into the function v(r):
v(0.4) = 18,500(0.25 - (0.4)^2)
v(0.4) = 18,500(0.25 - 0.16)
v(0.4) ≈ 18,500(0.09)
v(0.4) ≈ 1,665 cm/s
The values v(0.1) and v(0.4) represent the velocities of blood flow at distances 0.1cm and 0.4cm from the central axis, respectively.
From these values, we can observe that v(0.1) > v(0.4), indicating that the velocity of blood flow is greater closer to the central axis and decreases as the distance from the central axis increases. This is consistent with the law of laminar flow and demonstrates the concept of laminar flow in this artery.
To find v(0.1) and v(0.4), we need to substitute the respective values of r into the function v(r)=18,500(0.25-r^2).
a) To find v(0.1):
v(0.1) = 18,500(0.25-(0.1)^2)
v(0.1) = 18,500(0.25-0.01)
v(0.1) = 18,500(0.24)
v(0.1) = 4,440 cm/s
b) To find v(0.4):
v(0.4) = 18,500(0.25-(0.4)^2)
v(0.4) = 18,500(0.25-0.16)
v(0.4) = 18,500(0.09)
v(0.4) = 1,665 cm/s
Part a tells us that at a distance of 0.1 cm from the central axis, the velocity of blood flow in the artery is 4,440 cm/s. This means that blood flows faster closer to the central axis in this artery.
Part b tells us that at a distance of 0.4 cm from the central axis, the velocity of blood flow in the artery is 1,665 cm/s. This indicates that as the distance from the central axis increases, the velocity of blood flow decreases.