The volume flow rate in an artery supplying the brain is 4.59E-6 m3/s. If the radius of the artery is 5.33 mm, determine the average blood speed.
4.59e-6/pi r^2 = v
Watch your units.
To determine the average blood speed in the artery, we can use the equation for volume flow rate (Q) and the equation for the cross-sectional area of a cylinder (A). The equation for volume flow rate is:
Q = A * v
where Q is the volume flow rate, A is the cross-sectional area of the artery, and v is the average blood speed.
First, we need to find the cross-sectional area (A) of the artery. The equation for the cross-sectional area of a cylinder is:
A = π * r^2
where r is the radius of the artery.
Given that the radius of the artery is 5.33 mm, we should convert it to meters:
r = 5.33 mm = 5.33 * 10^-3 m
Now, we can plug in the values into the equation to find the cross-sectional area:
A = π * (5.33 * 10^-3 m)^2
Next, we can rearrange the equation for volume flow rate to solve for the average blood speed (v):
v = Q / A
Now, we can calculate the average blood speed:
v = 4.59E-6 m^3/s / A
Remembering that A is in square meters, we calculate A first:
A = π * (5.33 * 10^-3 m)^2
Now, substitute the value of A into the equation:
v = 4.59E-6 m^3/s / [π * (5.33 * 10^-3 m)^2]
Finally, we can calculate the average blood speed by evaluating the expression on the right side of the equation.