Calculate Average Blood Speed with Volume Flow Rate | Physics Problem Help

[diamond_dust]

Volume Flow Rate, Help?

1. The problem statement, all variable and given/known data

The volume flow rate in an artery supplying the brain is 3.5E-6 m^3/s.

(a.) If the radius of the artery is 5.4E-3 m, determine the average blood speed.
(b.) Find the average blood speed at a constriction in the artery if the constriction reduces the radius by a factor of 7. Assume that the volume flow rate is the same as in part (a.)

Homework Equations

Q = Volume flow rate = AV

The Attempt at a Solution

I got (a.) but I need help with (b.). I think my radius for part (b.) is wrong, but I don't know how else to get it.

For part (a.) I got 0.0382 m/s by using

Q = Volume flow rate = AV = pi x r^2 x v = 3.5E-6 m^3/s

and using the given radius in part (a.) I solved for v.

For part (b.) I divided the given radius by 7, and subtracted that from the original radius to get a radius of 4.63E-3, and I put it into the equation the same way as part (a.) and I got 0.0520 m/s, but it's wrong. Help?

 

[Redbelly98]

They mean that the constricted radius is 1/7 of the original radius, not 6/7 of it.

 

[thomate1]

2.

To solve part (b.), we can use the equation Q = AV, where Q is the volume flow rate, A is the cross-sectional area of the artery, and V is the average blood speed. Since the volume flow rate is the same in both parts (a.) and (b.), we can set the equations equal to each other and solve for the average blood speed in part (b.).

Q = AV

3.5E-6 m^3/s = (pi)(r^2)(v)

We know that the radius in part (b.) is reduced by a factor of 7, so the new radius would be 5.4E-3 m / 7 = 0.771E-3 m.

Substituting this into the equation, we get:

3.5E-6 m^3/s = (pi)(0.771E-3 m)^2(v)

Solving for v, we get an average blood speed of 0.75 m/s.

Therefore, the average blood speed at the constriction in the artery is 0.75 m/s. It is important to note that this is an approximation, as the actual blood flow in the body is much more complex and may not follow a simple equation. However, this calculation can provide a rough estimate for the average blood speed at a constriction in an artery.