The human circulatory system In the human circulatory system, depicted in Figure 11....

The human circulatory system In the human circulatory system, depicted in Figure 11.14, the heart’s left ventricle pumps about 80 cm3 of blood into the aorta. The blood then moves into

a larger and larger number of smaller radius vessels (aorta, arteries, arterioles, and capillaries). After the capillaries, which deliver nutrients to the body cells and absorb waste products, the vessels begin to combine into a smaller number of larger radius vessels (venules, small veins, large veins, and finally the vena cava). The vena cava returns blood to the heart (see Table 11.5). The flow rate Q of blood through the arteries equals the flow rate through the arterioles, which equals the flow rate through the capillaries, and so forth. The average blood gauge pressure in the aorta is about 100 mm Hg. The pressure drops as blood passes through the different groups of vessels and is approximately 0 mm Hg when it returns to the heart at the vena cava. A working definition of the resistance R to flow by a group of vessels is the ratio of the gauge pressure drop ΔP across those vessels divided by the flow rate Q through the vessels:

The gauge pressure drop across the whole system is (100 mm Hg – 0), and the total resistance is

The gauge pressure drop across the whole system is the sum of the drops across each type of vessel:

Now rearrange and insert Eq. (11.13) into the above for the pressure drop across each part:

Canceling the common flow rate through each group of vessels, we have an expression for the total resistance of the circulatory system:

The measured gauge pressure drop across the arterioles is about 50 mm Hg, and the arteriole resistance is

or about 50% of the total resistance. The next most resistive group of vessels is the capillaries, at about 25% of the total resistance. These percentages vary significantly from person to person. A person with essential hypertension has arterioles and capillaries that are reduced in radius. The resistance to blood flow increases dramatically (the resistance has a 1/r4 dependence). The blood pressure has to be greater (for example, double the normal value) in order to produce reasonable flow to the body cells. Even with the increased pressure, the flow rate may still be lower than normal.

The capillaries typically produce about 25% of the resistance to blood flow. Which pressure drop below is closest to the pressure drop across the group of capillaries?

(a) 5 mm Hg (b) 15 mm Hg (c) 25 mm Hg (d) 35 mm Hg (e) 45 mm Hg