Practice Problem 13.6 In this example we’ll explore the effects of gravity on yo

Question

Practice Problem 13.6 In this example we’ll explore the effects of gravity on your blood pressure. Suppose you have a healthy systolic (maximum) blood pressure of 1.30×104Pa (about 100 mmHg), measured at the level of your heart. (a) If the density of blood is 1.06×103kg/m3, find the blood pressure at a point in your head, 35.0 cm above your heart. (b) Find the difference in blood pressure between your head and your feet when you are sitting down, a distance of 1.10 m. (Ignore the fact that the blood is in motion and is not in equilibrium.) SOLUTION SET UP (Figure 1) shows our sketch, in which we have identified the relevant distances. SOLVE We use p2=p1+gh, for the variation in pressure with height. Part (a): Let p1 be the pressure at the level of the head; p2=1.30×104Pa is the pressure at the level of the heart, and the depth h1 is 35.0cm=0.350m. Rearranging, we obtain p1===p2gh1.30×104Pa(1.06×103kg/m3)(9.80m/s2)(0.350m)9.4×103Pa As expected, we get a blood pressure for the head that is lower than the pressure at heart level. (If our result had been higher than the blood pressure at heart level, we would know we had made a mistake.) Part (b): This time, p2 is the pressure at the level of the foot, and the depth is h2=1.10m. Then p2=p1+gh We can rearrange this equation to get the pressure difference, p2p1==(1.06×103kg/m3)(9.80m/s2)(1.10m)+1.14×104Pa As expected, the blood pressure at foot level is higher than the pressure at heart level. REFLECT Notice that we didn't need to know anything about the shape or volume of the blood vessels—just the relative heights of the head, heart, and feet. If you lie down, then your head and feet are at the same level as your heart, and the differences we calculated disappear. Also, our results are somewhat simplistic because Pascal's law is valid only for fluids in equilibrium. As we will see later in the chapter, internal frictional forces in the circulating blood have effects on its local pressure, in addition to the pressure differences due to relative height.

Part A - Practice Problem: When a person 1.81 m tall stands up, what is the difference in blood pressure between head and feet? Express your answer in pascals to two significant figures.

Explanation / Answer

You can use Pascal's principle: P=pg(h).

So, with the information given:

p = So, with the information given:

p = 1.06×103kg/m3
g = 9.8 m/s^2
h = (1.10 m - 0.35 m) = 0.75 m

Plugging all your values in:

P = pgh
=(1.06*103 kg/m^3)(9.8 m/s^2)(0.75 m)
= 7,791Pa or 7.8 x 10^3 Pa

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