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.