An alternative method for examining the effects of fatty acids on blood flow would be to measure changes in blood pressure. If blood pressure were measured, one would predict that it would be lowest in which of the following?
Capillaries

The pumping of the heart is the major contributor to pressure in the blood vessels. Blood pressure:
artery > arteriole > capillaries > venule > vein

As the blood pressure in each of the blood vessels is measured, it can be predicted to be lowest in the capillaries.

Explanation:

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Once the blood leaves the heart, it is distributed in a network of arterial vessels -arteries and arterioles- that bridge the venules and veins through the capillaries. Blood pressure depends on the pumping strength of the heart and the force that blood produces on the vessel walls. There is a marked difference between arterial and venous pressure. Some conclusions can be drawn from this:  

Based on this, it can be deduced that the blood vessels with the lowest pressure are the capillaries, with very thin walls and where gas and nutrients or metabolites enter and leave the vessel.

The question gives an answer, but does not explain why.

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Hydrostatic pressure in capillaries link

answer; both surfaces of the membrane are nonpermeable