Bernoulli's law and the continuity equation can help us understand some aspects of the circulatory system. According to Bernoulli's law,
p1 + r + rgh1 = r2 + r + rgh2,
where p refers to the pressure, v refers to the speed, and h refers to the height of the fluid. The subscripts "1" and "2" refer to the fluid at two different points in the system.
According to the continuity equation, if a piece of the "pipeline" gets thicker, gets thinner, or branches, the volume of fluid per second passing two imaginary cross-sectional "slices" must be the same. For instance, in both cases drawn in figure 1, the volume of fluid per second passing slice 1 must equal the volume of fluid per second passing slice 2.
In case 1, the pipeline doesn't branch. In such cases, for essentially incompressible fluids, the continuity equation can be written
A1v1 = A2v2,
where A denotes the cross-sectional area of the "pipe."
FIGURE 1

1. | Consider case 1. The blood at point B flows at 10 m/s. The blood at point C flows at a speed:

A. | greater than 10 m/s

B. | equal to 10 m/s

C. | less than 10 m/s

D. | Impossible to determine from the information provided

2. | Consider case 2. The blood at point P flows at speed 10 m/s. The blood at point Q flows at a speed:

A. | greater than 10 m/s.

B. | equal to 10 m/s.

C. | less than 10 m/s.

D. | Impossible to determine from the information provided

3. | Assume that points B and C are at the same height. Let pB and pC denote the pressure at points B and C, respectively. Which of the following is true?

A. | pB > pC

B. | pB = pC

C. | pB < pC

D. | We cannot determine the relationship between pB and pC.

4. | Suppose a blood vessel gets thinner, but doesn't "branch." Case 1 is an example. Which of the following graphs best shows the relationship between the cross-sectional area of the blood vessel and the speed of the blood flowing through it?

A. | A

B. | B

C. | C

D. | D

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