Question

The segment on the left has diameter 1.6 mm, and each of the segments on the right has diameter 0.4 mm. Assume the blood can be treated as an ideal fluid. If blood enters the segment on the left with speed v, at what speed does the blood leave the segments on the right?

Answer 1

To determine the speed at which blood leaves the segments on the right, you can use the flow rate equation and calculate the cross-sectional areas for each segment.

The blood flow rate in each section can be determined using the equation:

Flow rate = velocity x cross-sectional area

For the segment on the left with diameter 1.6 mm, the cross-sectional area can be calculated using the formula for the area of a circle:

Area = π x (radius)²

Since the diameter is given, we can calculate the radius by dividing the diameter by 2. Then, we can calculate the cross-sectional area of the segment on the left. Using the flow rate equation, we can solve for the velocity at which blood enters the segment on the left.

For the segments on the right with diameter 0.4 mm, we can repeat the same steps to calculate the cross-sectional areas and use the flow rate equation to solve for the velocities at which blood leaves each segment on the right.

Answer 2

Step-by-step explanation:

The flow entering the first segment will be the same as the flow exiting the second segment, and in both cases it will be equal to the velocity multiplied by the area of the segment. If
`Flow_(a) = Flow_(b)` and Flow = VxA, then you have:

`V_(a) x A_(a) = V_(b) x A_(b)` (1)

You can also calculate the transversal area of each segment, because blood vessels are cylinders and you know each segment's diameter. The formula to calculate this is:

`A = \pi /4 x d^(2)`

Replacing d for each segment you have:

`Area_(a) = 2.01 mm</p><p>Area_(b) = 0.13 mm`

Now, replacing these values on (1), you have:

`V_(a) x 2.01 mm = V_(b) x 0.13 mm`

`(V_(a) x 2.01 mm)/0.13 mm = V_(b)`

`15.4 x V_(a) = V_(b)`

This means that velocity in the second segment is 15.4 times the velocity in which blood entered the first segment.